The effect of density fluctuations on electron cyclotron beam broadening and implications for ITER

NASA Astrophysics Data System (ADS)

Snicker, A.; Poli, E.; Maj, O.; Guidi, L.; Köhn, A.; Weber, H.; Conway, G.; Henderson, M.; Saibene, G.

2018-01-01

We present state-of-the-art computations of propagation and absorption of electron cyclotron waves, retaining the effects of scattering due to electron density fluctuations. In ITER, injected microwaves are foreseen to suppress neoclassical tearing modes (NTMs) by driving current at the q=2 and q=3/2 resonant surfaces. Scattering of the beam can spoil the good localization of the absorption and thus impair NTM control capabilities. A novel tool, the WKBeam code, has been employed here in order to investigate this issue. The code is a Monte Carlo solver for the wave kinetic equation and retains diffraction, full axisymmetric tokamak geometry, determination of the absorption profile and an integral form of the scattering operator which describes the effects of turbulent density fluctuations within the limits of the Born scattering approximation. The approach has been benchmarked against the paraxial WKB code TORBEAM and the full-wave code IPF-FDMC. In particular, the Born approximation is found to be valid for ITER parameters. In this paper, we show that the radiative transport of EC beams due to wave scattering in ITER is diffusive unlike in present experiments, thus causing up to a factor of 2-4 broadening in the absorption profile. However, the broadening depends strongly on the turbulence model assumed for the density fluctuations, which still has large uncertainties.

Higher-Order Extended Lagrangian Born-Oppenheimer Molecular Dynamics for Classical Polarizable Models.

PubMed

Albaugh, Alex; Head-Gordon, Teresa; Niklasson, Anders M N

2018-02-13

Generalized extended Lagrangian Born-Oppenheimer molecular dynamics (XLBOMD) methods provide a framework for fast iteration-free simulations of models that normally require expensive electronic ground state optimizations prior to the force evaluations at every time step. XLBOMD uses dynamically driven auxiliary degrees of freedom that fluctuate about a variationally optimized ground state of an approximate "shadow" potential which approximates the true reference potential. While the requirements for such shadow potentials are well understood, constructing such potentials in practice has previously been ad hoc, and in this work, we present a systematic development of XLBOMD shadow potentials that match the reference potential to any order. We also introduce a framework for combining friction-like dissipation for the auxiliary degrees of freedom with general-order integration, a combination that was not previously possible. These developments are demonstrated with a simple fluctuating charge model and point induced dipole polarization models.

Migration and HIV risk: Life histories of Mexican-born men living with HIV in North Carolina

PubMed Central

Mann, Lilli; Valera, Erik; Hightow-Weidman, Lisa B.; Barrington, Clare

2015-01-01

Latino men in the Southeastern USA are disproportionately affected by HIV, but little is known about how the migration process influences HIV-related risk. In North Carolina (NC), a relatively new immigrant destination, Latino men are predominantly young and from Mexico. We conducted 31 iterative life history interviews with 15 Mexican-born men living with HIV. We used holistic content narrative analysis methods to examine HIV vulnerability in the context of migration and to identify important turning points. Major themes included the prominence of traumatic early life experiences, migration as an ongoing process rather than a finite event, and HIV diagnosis as a final turning point in migration trajectories. Findings provide a nuanced understanding of HIV vulnerability throughout the migration process and have implications including the need for bi-national HIV prevention approaches, improved outreach around early testing and linkage to care, and attention to mental health. PMID:24866206

An adaptive segment method for smoothing lidar signal based on noise estimation

NASA Astrophysics Data System (ADS)

Wang, Yuzhao; Luo, Pingping

2014-10-01

An adaptive segmentation smoothing method (ASSM) is introduced in the paper to smooth the signal and suppress the noise. In the ASSM, the noise is defined as the 3σ of the background signal. An integer number N is defined for finding the changing positions in the signal curve. If the difference of adjacent two points is greater than 3Nσ, the position is recorded as an end point of the smoothing segment. All the end points detected as above are recorded and the curves between them will be smoothed separately. In the traditional method, the end points of the smoothing windows in the signals are fixed. The ASSM creates changing end points in different signals and the smoothing windows could be set adaptively. The windows are always set as the half of the segmentations and then the average smoothing method will be applied in the segmentations. The Iterative process is required for reducing the end-point aberration effect in the average smoothing method and two or three times are enough. In ASSM, the signals are smoothed in the spacial area nor frequent area, that means the frequent disturbance will be avoided. A lidar echo was simulated in the experimental work. The echo was supposed to be created by a space-born lidar (e.g. CALIOP). And white Gaussian noise was added to the echo to act as the random noise resulted from environment and the detector. The novel method, ASSM, was applied to the noisy echo to filter the noise. In the test, N was set to 3 and the Iteration time is two. The results show that, the signal could be smoothed adaptively by the ASSM, but the N and the Iteration time might be optimized when the ASSM is applied in a different lidar.

Mitigating nonlinearity in full waveform inversion using scaled-Sobolev pre-conditioning

NASA Astrophysics Data System (ADS)

Zuberi, M. AH; Pratt, R. G.

2018-04-01

The Born approximation successfully linearizes seismic full waveform inversion if the background velocity is sufficiently accurate. When the background velocity is not known it can be estimated by using model scale separation methods. A frequently used technique is to separate the spatial scales of the model according to the scattering angles present in the data, by using either first- or second-order terms in the Born series. For example, the well-known `banana-donut' and the `rabbit ear' shaped kernels are, respectively, the first- and second-order Born terms in which at least one of the scattering events is associated with a large angle. Whichever term of the Born series is used, all such methods suffer from errors in the starting velocity model because all terms in the Born series assume that the background Green's function is known. An alternative approach to Born-based scale separation is to work in the model domain, for example, by Gaussian smoothing of the update vectors, or some other approach for separation by model wavenumbers. However such model domain methods are usually based on a strict separation in which only the low-wavenumber updates are retained. This implies that the scattered information in the data is not taken into account. This can lead to the inversion being trapped in a false (local) minimum when sharp features are updated incorrectly. In this study we propose a scaled-Sobolev pre-conditioning (SSP) of the updates to achieve a constrained scale separation in the model domain. The SSP is obtained by introducing a scaled Sobolev inner product (SSIP) into the measure of the gradient of the objective function with respect to the model parameters. This modified measure seeks reductions in the L2 norm of the spatial derivatives of the gradient without changing the objective function. The SSP does not rely on the Born prediction of scale based on scattering angles, and requires negligible extra computational cost per iteration. Synthetic examples from the Marmousi model show that the constrained scale separation using SSP is able to keep the background updates in the zone of attraction of the global minimum, in spite of using a poor starting model in which conventional methods fail.

Least-squares reverse time migration in elastic media

NASA Astrophysics Data System (ADS)

Ren, Zhiming; Liu, Yang; Sen, Mrinal K.

2017-02-01

Elastic reverse time migration (RTM) can yield accurate subsurface information (e.g. PP and PS reflectivity) by imaging the multicomponent seismic data. However, the existing RTM methods are still insufficient to provide satisfactory results because of the finite recording aperture, limited bandwidth and imperfect illumination. Besides, the P- and S-wave separation and the polarity reversal correction are indispensable in conventional elastic RTM. Here, we propose an iterative elastic least-squares RTM (LSRTM) method, in which the imaging accuracy is improved gradually with iteration. We first use the Born approximation to formulate the elastic de-migration operator, and employ the Lagrange multiplier method to derive the adjoint equations and gradients with respect to reflectivity. Then, an efficient inversion workflow (only four forward computations needed in each iteration) is introduced to update the reflectivity. Synthetic and field data examples reveal that the proposed LSRTM method can obtain higher-quality images than the conventional elastic RTM. We also analyse the influence of model parametrizations and misfit functions in elastic LSRTM. We observe that Lamé parameters, velocity and impedance parametrizations have similar and plausible migration results when the structures of different models are correlated. For an uncorrelated subsurface model, velocity and impedance parametrizations produce fewer artefacts caused by parameter crosstalk than the Lamé coefficient parametrization. Correlation- and convolution-type misfit functions are effective when amplitude errors are involved and the source wavelet is unknown, respectively. Finally, we discuss the dependence of elastic LSRTM on migration velocities and its antinoise ability. Imaging results determine that the new elastic LSRTM method performs well as long as the low-frequency components of migration velocities are correct. The quality of images of elastic LSRTM degrades with increasing noise.

Extended Lagrangian Excited State Molecular Dynamics.

PubMed

Bjorgaard, J A; Sheppard, D; Tretiak, S; Niklasson, A M N

2018-02-13

An extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).

Applying Evidence-Based Medicine in Telehealth: An Interactive Pattern Recognition Approximation

PubMed Central

Fernández-Llatas, Carlos; Meneu, Teresa; Traver, Vicente; Benedi, José-Miguel

2013-01-01

Born in the early nineteen nineties, evidence-based medicine (EBM) is a paradigm intended to promote the integration of biomedical evidence into the physicians daily practice. This paradigm requires the continuous study of diseases to provide the best scientific knowledge for supporting physicians in their diagnosis and treatments in a close way. Within this paradigm, usually, health experts create and publish clinical guidelines, which provide holistic guidance for the care for a certain disease. The creation of these clinical guidelines requires hard iterative processes in which each iteration supposes scientific progress in the knowledge of the disease. To perform this guidance through telehealth, the use of formal clinical guidelines will allow the building of care processes that can be interpreted and executed directly by computers. In addition, the formalization of clinical guidelines allows for the possibility to build automatic methods, using pattern recognition techniques, to estimate the proper models, as well as the mathematical models for optimizing the iterative cycle for the continuous improvement of the guidelines. However, to ensure the efficiency of the system, it is necessary to build a probabilistic model of the problem. In this paper, an interactive pattern recognition approach to support professionals in evidence-based medicine is formalized. PMID:24185841

A differential equation for the Generalized Born radii.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

The Generalized Born (GB) model offers a convenient way of representing electrostatics in complex macromolecules like proteins or nucleic acids. The computation of atomic GB radii is currently performed by different non-local approaches involving volume or surface integrals. Here we obtain a non-linear second-order partial differential equation for the Generalized Born radius, which may be solved using local iterative algorithms. The equation is derived under the assumption that the usual GB approximation to the reaction field obeys Laplace's equation. The equation admits as particular solutions the correct GB radii for the sphere and the plane. The tests performed on a set of 55 different proteins show an overall agreement with other reference GB models and "perfect" Poisson-Boltzmann based values.

Remote sensing of earth terrain

NASA Technical Reports Server (NTRS)

Yueh, Herng-Aung; Kong, Jin AU

1991-01-01

In remote sensing, the encountered geophysical media such as agricultural canopy, forest, snow, or ice are inhomogeneous and contain scatters in a random manner. Furthermore, weather conditions such as fog, mist, or snow cover can intervene the electromagnetic observation of the remotely sensed media. In the modelling of such media accounting for the weather effects, a multi-layer random medium model has been developed. The scattering effects of the random media are described by three-dimensional correlation functions with variances and correlation lengths corresponding to the fluctuation strengths and the physical geometry of the inhomogeneities, respectively. With proper consideration of the dyadic Green's function and its singularities, the strong fluctuation theory is used to calculate the effective permittivities which account for the modification of the wave speed and attenuation in the presence of the scatters. The distorted Born approximation is then applied to obtain the correlations of the scattered fields. From the correlation of the scattered field, calculated is the complete set of scattering coefficients for polarimetric radar observation or brightness temperature in passive radiometer applications. In the remote sensing of terrestrial ecosystems, the development of microwave remote sensing technology and the potential of SAR to measure vegetation structure and biomass have increased effort to conduct experimental and theoretical researches on the interactions between microwave and vegetation canopies. The overall objective is to develop inversion algorithms to retrieve biophysical parameters from radar data. In this perspective, theoretical models and experimental data are methodically interconnected in the following manner: Due to the complexity of the interactions involved, all theoretical models have limited domains of validity; the proposed solution is to use theoretical models, which is validated by experiments, to establish the region in which the radar response is most sensitive to the parameters of interest; theoretically simulated data will be used to generate simple invertible models over the region. For applications to the remote sensing of sea ice, the developed theoretical models need to be tested with experimental measurements. With measured ground truth such as ice thickness, temperature, salinity, and structure, input parameters to the theoretical models can be obtained to calculate the polarimetric scattering coefficients for radars or brightness temperature for radiometers and then compare theoretical results with experimental data. Validated models will play an important role in the interpretation and classification of ice in monitoring global ice cover from space borne remote sensors in the future. We present an inversion algorithm based on a recently developed inversion method referred to as the Renormalized Source-Type Integral Equation approach. The objective of this method is to overcome some of the limitations and difficulties of the iterative Born technique. It recasts the inversion, which is nonlinear in nature, in terms of the solution of a set of linear equations; however, the final inversion equation is still nonlinear. The derived inversion equation is an exact equation which sums up the iterative Neuman (or Born) series in a closed form and, thus, is a valid representation even in the case when the Born series diverges; hence, the name Renormalized Source-Type Integral Equation Approach.

Beyond Born-Mayer: Improved models for short-range repulsion in ab initio force fields

DOE PAGES

Van Vleet, Mary J.; Misquitta, Alston J.; Stone, Anthony J.; ...

2016-06-23

Short-range repulsion within inter-molecular force fields is conventionally described by either Lennard-Jones or Born-Mayer forms. Despite their widespread use, these simple functional forms are often unable to describe the interaction energy accurately over a broad range of inter-molecular distances, thus creating challenges in the development of ab initio force fields and potentially leading to decreased accuracy and transferability. Herein, we derive a novel short-range functional form based on a simple Slater-like model of overlapping atomic densities and an iterated stockholder atom (ISA) partitioning of the molecular electron density. We demonstrate that this Slater-ISA methodology yields a more accurate, transferable, andmore » robust description of the short-range interactions at minimal additional computational cost compared to standard Lennard-Jones or Born-Mayer approaches. Lastly, we show how this methodology can be adapted to yield the standard Born-Mayer functional form while still retaining many of the advantages of the Slater-ISA approach.« less

Imaging Internal Structure of Long Bones Using Wave Scattering Theory.

PubMed

Zheng, Rui; Le, Lawrence H; Sacchi, Mauricio D; Lou, Edmond

2015-11-01

An ultrasonic wavefield imaging method is developed to reconstruct the internal geometric properties of long bones using zero-offset data acquired axially on the bone surface. The imaging algorithm based on Born scattering theory is implemented with the conjugate gradient iterative method to reconstruct an optimal image. In the case of a multilayered velocity model, ray tracing through a smooth medium is used to calculate the traveled distance and traveling time. The method has been applied to simulated and real data. The results indicate that the interfaces of the top cortex are accurately imaged and correspond favorably to the original model. The reconstructed bottom cortex below the marrow is less accurate mainly because of the low signal-to-noise ratio. The current imaging method has successfully recovered the top cortical layer, providing a potential tool to investigate the internal structures of long bone cortex for osteoporosis assessment. Copyright © 2015 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Vleet, Mary J.; Misquitta, Alston J.; Stone, Anthony J.

Short-range repulsion within inter-molecular force fields is conventionally described by either Lennard-Jones or Born-Mayer forms. Despite their widespread use, these simple functional forms are often unable to describe the interaction energy accurately over a broad range of inter-molecular distances, thus creating challenges in the development of ab initio force fields and potentially leading to decreased accuracy and transferability. Herein, we derive a novel short-range functional form based on a simple Slater-like model of overlapping atomic densities and an iterated stockholder atom (ISA) partitioning of the molecular electron density. We demonstrate that this Slater-ISA methodology yields a more accurate, transferable, andmore » robust description of the short-range interactions at minimal additional computational cost compared to standard Lennard-Jones or Born-Mayer approaches. Lastly, we show how this methodology can be adapted to yield the standard Born-Mayer functional form while still retaining many of the advantages of the Slater-ISA approach.« less

Gaussian closure technique applied to the hysteretic Bouc model with non-zero mean white noise excitation

NASA Astrophysics Data System (ADS)

Waubke, Holger; Kasess, Christian H.

2016-11-01

Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

Computational helioseismology in the frequency domain: acoustic waves in axisymmetric solar models with flows

NASA Astrophysics Data System (ADS)

Gizon, Laurent; Barucq, Hélène; Duruflé, Marc; Hanson, Chris S.; Leguèbe, Michael; Birch, Aaron C.; Chabassier, Juliette; Fournier, Damien; Hohage, Thorsten; Papini, Emanuele

2017-04-01

Context. Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Aims: Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is the cross-covariance of the seismic wavefield. Methods: We choose sources of wave excitation that enable us to relate the cross-covariance of the oscillations to the Green's function in a straightforward manner. We illustrate the method by considering the 3D acoustic wave equation in an axisymmetric reference solar model, ignoring the effects of gravity on the waves. The symmetry of the background model around the rotation axis implies that the Green's function can be written as a sum of longitudinal Fourier modes, leading to a set of independent 2D problems. We use a high-order finite-element method to solve the 2D wave equation in frequency space. The computation is embarrassingly parallel, with each frequency and each azimuthal order solved independently on a computer cluster. Results: We compute travel-time sensitivity kernels in spherical geometry for flows, sound speed, and density perturbations under the first Born approximation. Convergence tests show that travel times can be computed with a numerical precision better than one millisecond, as required by the most precise travel-time measurements. Conclusions: The method presented here is computationally efficient and will be used to interpret travel-time measurements in order to infer, e.g., the large-scale meridional flow in the solar convection zone. It allows the implementation of (full-waveform) iterative inversions, whereby the axisymmetric background model is updated at each iteration.

Comprehensive evaluation of the linear stability of Alfvén eigenmodes driven by alpha particles in an ITER baseline scenario

NASA Astrophysics Data System (ADS)

Figueiredo, A. C. A.; Rodrigues, P.; Borba, D.; Coelho, R.; Fazendeiro, L.; Ferreira, J.; Loureiro, N. F.; Nabais, F.; Pinches, S. D.; Polevoi, A. R.; Sharapov, S. E.

2016-07-01

The linear stability of Alfvén eigenmodes in the presence of fusion-born alpha particles is thoroughly assessed for two variants of an ITER baseline scenario, which differ significantly in their core and pedestal temperatures. A systematic approach based on CASTOR-K (Borba and Kerner 1999 J. Comput. Phys. 153 101; Nabais et al 2015 Plasma Sci. Technol. 17 89) is used that considers all possible eigenmodes for a given magnetic equilibrium and determines their growth rates due to alpha-particle drive and Landau damping on fuel ions, helium ashes and electrons. It is found that the fastest growing instabilities in the aforementioned ITER scenario are core-localized, low-shear toroidal Alfvén eigenmodes. The largest growth-rates occur in the scenario variant with higher core temperatures, which has the highest alpha-particle density and density gradient, for eigenmodes with toroidal mode numbers n≈ 30 . Although these eigenmodes suffer significant radiative damping, which is also evaluated, their growth rates remain larger than those of the most unstable eigenmodes found in the variant of the ITER baseline scenario with lower core temperatures, which have n≈ 15 and are not affected by radiative damping.

Compressed sensing for ultrasound computed tomography.

PubMed

van Sloun, Ruud; Pandharipande, Ashish; Mischi, Massimo; Demi, Libertario

2015-06-01

Ultrasound computed tomography (UCT) allows the reconstruction of quantitative tissue characteristics, such as speed of sound, mass density, and attenuation. Lowering its acquisition time would be beneficial; however, this is fundamentally limited by the physical time of flight and the number of transmission events. In this letter, we propose a compressed sensing solution for UCT. The adopted measurement scheme is based on compressed acquisitions, with concurrent randomised transmissions in a circular array configuration. Reconstruction of the image is then obtained by combining the born iterative method and total variation minimization, thereby exploiting variation sparsity in the image domain. Evaluation using simulated UCT scattering measurements shows that the proposed transmission scheme performs better than uniform undersampling, and is able to reduce acquisition time by almost one order of magnitude, while maintaining high spatial resolution.

The Born approximation, multiple scattering, and the butterfly algorithm

NASA Astrophysics Data System (ADS)

Martinez, Alejandro F.

Radar works by focusing a beam of light and seeing how long it takes to reflect. To see a large region the beam is pointed in different directions. The focus of the beam depends on the size of the antenna (called an aperture). Synthetic aperture radar (SAR) works by moving the antenna through some region of space. A fundamental assumption in SAR is that waves only bounce once. Several imaging algorithms have been designed using that assumption. The scattering process can be described by iterations of a badly behaving integral. Recently a method for efficiently evaluating these types of integrals has been developed. We will give a detailed implementation of this algorithm and apply it to study the multiple scattering effects in SAR using target estimates from single scattering algorithms.

Next generation extended Lagrangian first principles molecular dynamics

NASA Astrophysics Data System (ADS)

Niklasson, Anders M. N.

2017-08-01

Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.

Next generation extended Lagrangian first principles molecular dynamics.

PubMed

Niklasson, Anders M N

2017-08-07

Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.

Comparison between iteration schemes for three-dimensional coordinate-transformed saturated-unsaturated flow model

NASA Astrophysics Data System (ADS)

An, Hyunuk; Ichikawa, Yutaka; Tachikawa, Yasuto; Shiiba, Michiharu

2012-11-01

SummaryThree different iteration methods for a three-dimensional coordinate-transformed saturated-unsaturated flow model are compared in this study. The Picard and Newton iteration methods are the common approaches for solving Richards' equation. The Picard method is simple to implement and cost-efficient (on an individual iteration basis). However it converges slower than the Newton method. On the other hand, although the Newton method converges faster, it is more complex to implement and consumes more CPU resources per iteration than the Picard method. The comparison of the two methods in finite-element model (FEM) for saturated-unsaturated flow has been well evaluated in previous studies. However, two iteration methods might exhibit different behavior in the coordinate-transformed finite-difference model (FDM). In addition, the Newton-Krylov method could be a suitable alternative for the coordinate-transformed FDM because it requires the evaluation of a 19-point stencil matrix. The formation of a 19-point stencil is quite a complex and laborious procedure. Instead, the Newton-Krylov method calculates the matrix-vector product, which can be easily approximated by calculating the differences of the original nonlinear function. In this respect, the Newton-Krylov method might be the most appropriate iteration method for coordinate-transformed FDM. However, this method involves the additional cost of taking an approximation at each Krylov iteration in the Newton-Krylov method. In this paper, we evaluated the efficiency and robustness of three iteration methods—the Picard, Newton, and Newton-Krylov methods—for simulating saturated-unsaturated flow through porous media using a three-dimensional coordinate-transformed FDM.

Numerical Computation of Subsonic Conical Diffuser Flows with Nonuniform Turbulent Inlet Conditions

DTIC Science & Technology

1977-09-01

Gauss - Seidel Point Iteration Method . . . . . . . . . . . . . . . 7.0 FACTORS AFFECTING THE RATE OF CONVERGENCE OF THE POINT...can be solved in several ways. For simplicity, a standard Gauss - Seidel iteration method is used to obtain the solution . The method updates the...FACTORS AFFECTING THE RATE OF CONVERGENCE OF THE POINT ITERATION ,ŘETHOD The advantage of using the Gauss - Seidel point iteration method to

Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

NASA Astrophysics Data System (ADS)

Wang, Yi-Hong; Wu, Guo-Cheng; Baleanu, Dumitru

2013-10-01

The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method's new role.

A novel iterative scheme and its application to differential equations.

PubMed

Khan, Yasir; Naeem, F; Šmarda, Zdeněk

2014-01-01

The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method.

Iterative Methods for the Non-LTE Transfer of Polarized Radiation: Resonance Line Polarization in One-dimensional Atmospheres

NASA Astrophysics Data System (ADS)

Trujillo Bueno, Javier; Manso Sainz, Rafael

1999-05-01

This paper shows how to generalize to non-LTE polarization transfer some operator splitting methods that were originally developed for solving unpolarized transfer problems. These are the Jacobi-based accelerated Λ-iteration (ALI) method of Olson, Auer, & Buchler and the iterative schemes based on Gauss-Seidel and successive overrelaxation (SOR) iteration of Trujillo Bueno and Fabiani Bendicho. The theoretical framework chosen for the formulation of polarization transfer problems is the quantum electrodynamics (QED) theory of Landi Degl'Innocenti, which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. This first paper establishes the grounds of our numerical approach to non-LTE polarization transfer by concentrating on the standard case of scattering line polarization in a gas of two-level atoms, including the Hanle effect due to a weak microturbulent and isotropic magnetic field. We begin demonstrating that the well-known Λ-iteration method leads to the self-consistent solution of this type of problem if one initializes using the ``exact'' solution corresponding to the unpolarized case. We show then how the above-mentioned splitting methods can be easily derived from this simple Λ-iteration scheme. We show that our SOR method is 10 times faster than the Jacobi-based ALI method, while our implementation of the Gauss-Seidel method is 4 times faster. These iterative schemes lead to the self-consistent solution independently of the chosen initialization. The convergence rate of these iterative methods is very high; they do not require either the construction or the inversion of any matrix, and the computing time per iteration is similar to that of the Λ-iteration method.

Optimised Iteration in Coupled Monte Carlo - Thermal-Hydraulics Calculations

NASA Astrophysics Data System (ADS)

Hoogenboom, J. Eduard; Dufek, Jan

2014-06-01

This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration method are also tested and it is concluded that the presented iteration method is near optimal.

An iterative method for near-field Fresnel region polychromatic phase contrast imaging

NASA Astrophysics Data System (ADS)

Carroll, Aidan J.; van Riessen, Grant A.; Balaur, Eugeniu; Dolbnya, Igor P.; Tran, Giang N.; Peele, Andrew G.

2017-07-01

We present an iterative method for polychromatic phase contrast imaging that is suitable for broadband illumination and which allows for the quantitative determination of the thickness of an object given the refractive index of the sample material. Experimental and simulation results suggest the iterative method provides comparable image quality and quantitative object thickness determination when compared to the analytical polychromatic transport of intensity and contrast transfer function methods. The ability of the iterative method to work over a wider range of experimental conditions means the iterative method is a suitable candidate for use with polychromatic illumination and may deliver more utility for laboratory-based x-ray sources, which typically have a broad spectrum.

New methods of testing nonlinear hypothesis using iterative NLLS estimator

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

Solution of Cubic Equations by Iteration Methods on a Pocket Calculator

ERIC Educational Resources Information Center

Bamdad, Farzad

2004-01-01

A method to provide students a vision of how they can write iteration programs on an inexpensive programmable pocket calculator, without requiring a PC or a graphing calculator is developed. Two iteration methods are used, successive-approximations and bisection methods.

Direct determination of one-dimensional interphase structures using normalized crystal truncation rod analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kawaguchi, Tomoya; Liu, Yihua; Reiter, Anthony

Here, a one-dimensional non-iterative direct method was employed for normalized crystal truncation rod analysis. The non-iterative approach, utilizing the Kramers–Kronig relation, avoids the ambiguities due to an improper initial model or incomplete convergence in the conventional iterative methods. The validity and limitations of the present method are demonstrated through both numerical simulations and experiments with Pt(111) in a 0.1 M CsF aqueous solution. The present method is compared with conventional iterative phase-retrieval methods.

Direct determination of one-dimensional interphase structures using normalized crystal truncation rod analysis

DOE PAGES

Kawaguchi, Tomoya; Liu, Yihua; Reiter, Anthony; ...

2018-04-20

Here, a one-dimensional non-iterative direct method was employed for normalized crystal truncation rod analysis. The non-iterative approach, utilizing the Kramers–Kronig relation, avoids the ambiguities due to an improper initial model or incomplete convergence in the conventional iterative methods. The validity and limitations of the present method are demonstrated through both numerical simulations and experiments with Pt(111) in a 0.1 M CsF aqueous solution. The present method is compared with conventional iterative phase-retrieval methods.

Fourth-order numerical solutions of diffusion equation by using SOR method with Crank-Nicolson approach

NASA Astrophysics Data System (ADS)

Muhiddin, F. A.; Sulaiman, J.

2017-09-01

The aim of this paper is to investigate the effectiveness of the Successive Over-Relaxation (SOR) iterative method by using the fourth-order Crank-Nicolson (CN) discretization scheme to derive a five-point Crank-Nicolson approximation equation in order to solve diffusion equation. From this approximation equation, clearly, it can be shown that corresponding system of five-point approximation equations can be generated and then solved iteratively. In order to access the performance results of the proposed iterative method with the fourth-order CN scheme, another point iterative method which is Gauss-Seidel (GS), also presented as a reference method. Finally the numerical results obtained from the use of the fourth-order CN discretization scheme, it can be pointed out that the SOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.

Iterative methods for mixed finite element equations

NASA Technical Reports Server (NTRS)

Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.

1985-01-01

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

Leapfrog variants of iterative methods for linear algebra equations

NASA Technical Reports Server (NTRS)

Saylor, Paul E.

1988-01-01

Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial approximation, a variant of the iteration called the grand-leap method. In the case of the grand-leap variant, a set of parameters is required. An algorithm is presented to compute these parameters that is related to algorithms to compute the weights and abscissas for Gaussian quadrature. General algorithms to implement the leapfrog and grand-leap methods are presented. Algorithms for the important special case of the Chebyshev method are also given.

Deterministic compressive sampling for high-quality image reconstruction of ultrasound tomography.

PubMed

Huy, Tran Quang; Tue, Huynh Huu; Long, Ton That; Duc-Tan, Tran

2017-05-25

A well-known diagnostic imaging modality, termed ultrasound tomography, was quickly developed for the detection of very small tumors whose sizes are smaller than the wavelength of the incident pressure wave without ionizing radiation, compared to the current gold-standard X-ray mammography. Based on inverse scattering technique, ultrasound tomography uses some material properties such as sound contrast or attenuation to detect small targets. The Distorted Born Iterative Method (DBIM) based on first-order Born approximation is an efficient diffraction tomography approach. One of the challenges for a high quality reconstruction is to obtain many measurements from the number of transmitters and receivers. Given the fact that biomedical images are often sparse, the compressed sensing (CS) technique could be therefore effectively applied to ultrasound tomography by reducing the number of transmitters and receivers, while maintaining a high quality of image reconstruction. There are currently several work on CS that dispose randomly distributed locations for the measurement system. However, this random configuration is relatively difficult to implement in practice. Instead of it, we should adopt a methodology that helps determine the locations of measurement devices in a deterministic way. For this, we develop the novel DCS-DBIM algorithm that is highly applicable in practice. Inspired of the exploitation of the deterministic compressed sensing technique (DCS) introduced by the authors few years ago with the image reconstruction process implemented using l 1 regularization. Simulation results of the proposed approach have demonstrated its high performance, with the normalized error approximately 90% reduced, compared to the conventional approach, this new approach can save half of number of measurements and only uses two iterations. Universal image quality index is also evaluated in order to prove the efficiency of the proposed approach. Numerical simulation results indicate that CS and DCS techniques offer equivalent image reconstruction quality with simpler practical implementation. It would be a very promising approach in practical applications of modern biomedical imaging technology.

High resolution x-ray CMT: Reconstruction methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, J.K.

This paper qualitatively discusses the primary characteristics of methods for reconstructing tomographic images from a set of projections. These reconstruction methods can be categorized as either {open_quotes}analytic{close_quotes} or {open_quotes}iterative{close_quotes} techniques. Analytic algorithms are derived from the formal inversion of equations describing the imaging process, while iterative algorithms incorporate a model of the imaging process and provide a mechanism to iteratively improve image estimates. Analytic reconstruction algorithms are typically computationally more efficient than iterative methods; however, analytic algorithms are available for a relatively limited set of imaging geometries and situations. Thus, the framework of iterative reconstruction methods is better suited formore » high accuracy, tomographic reconstruction codes.« less

Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems

NASA Astrophysics Data System (ADS)

Wang, Xue-Zhong; Huang, Ting-Zhu; Fu, Ying-Ding

2007-09-01

In this paper, we present some comparison theorems on preconditioned iterative method for solving Z-matrices linear systems, Comparison results show that the rate of convergence of the Gauss-Seidel-type method is faster than the rate of convergence of the SOR-type iterative method.

A Least-Squares Commutator in the Iterative Subspace Method for Accelerating Self-Consistent Field Convergence.

PubMed

Li, Haichen; Yaron, David J

2016-11-08

A least-squares commutator in the iterative subspace (LCIIS) approach is explored for accelerating self-consistent field (SCF) calculations. LCIIS is similar to direct inversion of the iterative subspace (DIIS) methods in that the next iterate of the density matrix is obtained as a linear combination of past iterates. However, whereas DIIS methods find the linear combination by minimizing a sum of error vectors, LCIIS minimizes the Frobenius norm of the commutator between the density matrix and the Fock matrix. This minimization leads to a quartic problem that can be solved iteratively through a constrained Newton's method. The relationship between LCIIS and DIIS is discussed. Numerical experiments suggest that LCIIS leads to faster convergence than other SCF convergence accelerating methods in a statistically significant sense, and in a number of cases LCIIS leads to stable SCF solutions that are not found by other methods. The computational cost involved in solving the quartic minimization problem is small compared to the typical cost of SCF iterations and the approach is easily integrated into existing codes. LCIIS can therefore serve as a powerful addition to SCF convergence accelerating methods in computational quantum chemistry packages.

Annual Copper Mountain Conferences on Multigrid and Iterative Methods, Copper Mountain, Colorado

DOE Office of Scientific and Technical Information (OSTI.GOV)

McCormick, Stephen F.

This project supported the Copper Mountain Conference on Multigrid and Iterative Methods, held from 2007 to 2015, at Copper Mountain, Colorado. The subject of the Copper Mountain Conference Series alternated between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. This report describes the Copper Mountain Conference on Multigrid and Iterative Methods, 2007-2015. Information on the conference series is available at http://grandmaster.colorado.edu/~copper/.

Lattice dynamics and thermal conductivity of lithium fluoride via first-principles calculations

NASA Astrophysics Data System (ADS)

Liang, Ting; Chen, Wen-Qi; Hu, Cui-E.; Chen, Xiang-Rong; Chen, Qi-Feng

2018-04-01

The lattice thermal conductivity of lithium fluoride (LiF) is accurately computed from a first-principles approach based on an iterative solution of the Boltzmann transport equation. Real-space finite-difference supercell approach is employed to generate the second- and third-order interatomic force constants. The related physical quantities of LiF are calculated by the second- and third- order potential interactions at 30 K-1000 K. The calculated lattice thermal conductivity 13.89 W/(m K) for LiF at room temperature agrees well with the experimental value, demonstrating that the parameter-free approach can furnish precise descriptions of the lattice thermal conductivity for this material. Besides, the Born effective charges, dielectric constants and phonon spectrum of LiF accord well with the existing data. The lattice thermal conductivities for the iterative solution of BTE are also presented.

DECONVOLUTION OF IMAGES FROM BLAST 2005: INSIGHT INTO THE K3-50 AND IC 5146 STAR-FORMING REGIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roy, Arabindo; Netterfield, Calvin B.; Ade, Peter A. R.

2011-04-01

We present an implementation of the iterative flux-conserving Lucy-Richardson (L-R) deconvolution method of image restoration for maps produced by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST). Compared to the direct Fourier transform method of deconvolution, the L-R operation restores images with better-controlled background noise and increases source detectability. Intermediate iterated images are useful for studying extended diffuse structures, while the later iterations truly enhance point sources to near the designed diffraction limit of the telescope. The L-R method of deconvolution is efficient in resolving compact sources in crowded regions while simultaneously conserving their respective flux densities. We have analyzed itsmore » performance and convergence extensively through simulations and cross-correlations of the deconvolved images with available high-resolution maps. We present new science results from two BLAST surveys, in the Galactic regions K3-50 and IC 5146, further demonstrating the benefits of performing this deconvolution. We have resolved three clumps within a radius of 4.'5 inside the star-forming molecular cloud containing K3-50. Combining the well-resolved dust emission map with available multi-wavelength data, we have constrained the spectral energy distributions (SEDs) of five clumps to obtain masses (M), bolometric luminosities (L), and dust temperatures (T). The L-M diagram has been used as a diagnostic tool to estimate the evolutionary stages of the clumps. There are close relationships between dust continuum emission and both 21 cm radio continuum and {sup 12}CO molecular line emission. The restored extended large-scale structures in the Northern Streamer of IC 5146 have a strong spatial correlation with both SCUBA and high-resolution extinction images. A dust temperature of 12 K has been obtained for the central filament. We report physical properties of ten compact sources, including six associated protostars, by fitting SEDs to multi-wavelength data. All of these compact sources are still quite cold (typical temperature below {approx} 16 K) and are above the critical Bonner-Ebert mass. They have associated low-power young stellar objects. Further evidence for starless clumps has also been found in the IC 5146 region.« less

Deconvolution of Images from BLAST 2005: Insight into the K3-50 and IC 5146 Star-forming Regions

NASA Astrophysics Data System (ADS)

Roy, Arabindo; Ade, Peter A. R.; Bock, James J.; Brunt, Christopher M.; Chapin, Edward L.; Devlin, Mark J.; Dicker, Simon R.; France, Kevin; Gibb, Andrew G.; Griffin, Matthew; Gundersen, Joshua O.; Halpern, Mark; Hargrave, Peter C.; Hughes, David H.; Klein, Jeff; Marsden, Gaelen; Martin, Peter G.; Mauskopf, Philip; Netterfield, Calvin B.; Olmi, Luca; Patanchon, Guillaume; Rex, Marie; Scott, Douglas; Semisch, Christopher; Truch, Matthew D. P.; Tucker, Carole; Tucker, Gregory S.; Viero, Marco P.; Wiebe, Donald V.

2011-04-01

We present an implementation of the iterative flux-conserving Lucy-Richardson (L-R) deconvolution method of image restoration for maps produced by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST). Compared to the direct Fourier transform method of deconvolution, the L-R operation restores images with better-controlled background noise and increases source detectability. Intermediate iterated images are useful for studying extended diffuse structures, while the later iterations truly enhance point sources to near the designed diffraction limit of the telescope. The L-R method of deconvolution is efficient in resolving compact sources in crowded regions while simultaneously conserving their respective flux densities. We have analyzed its performance and convergence extensively through simulations and cross-correlations of the deconvolved images with available high-resolution maps. We present new science results from two BLAST surveys, in the Galactic regions K3-50 and IC 5146, further demonstrating the benefits of performing this deconvolution. We have resolved three clumps within a radius of 4farcm5 inside the star-forming molecular cloud containing K3-50. Combining the well-resolved dust emission map with available multi-wavelength data, we have constrained the spectral energy distributions (SEDs) of five clumps to obtain masses (M), bolometric luminosities (L), and dust temperatures (T). The L-M diagram has been used as a diagnostic tool to estimate the evolutionary stages of the clumps. There are close relationships between dust continuum emission and both 21 cm radio continuum and 12CO molecular line emission. The restored extended large-scale structures in the Northern Streamer of IC 5146 have a strong spatial correlation with both SCUBA and high-resolution extinction images. A dust temperature of 12 K has been obtained for the central filament. We report physical properties of ten compact sources, including six associated protostars, by fitting SEDs to multi-wavelength data. All of these compact sources are still quite cold (typical temperature below ~ 16 K) and are above the critical Bonner-Ebert mass. They have associated low-power young stellar objects. Further evidence for starless clumps has also been found in the IC 5146 region.

Krylov subspace iterative methods for boundary element method based near-field acoustic holography.

PubMed

Valdivia, Nicolas; Williams, Earl G

2005-02-01

The reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods. The solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements. These methods will not require the calculation of the singular value decomposition, which can be expensive when the matrix system is considerably large. Krylov subspace methods are iterative methods that have the phenomena known as "semi-convergence," i.e., the optimal regularization solution is obtained after a few iterations. If the iteration is not stopped, the method converges to a solution that generally is totally corrupted by errors on the measurements. For these methods the number of iterations play the role of the regularization parameter. We will focus our attention to the study of the regularizing properties from the Krylov subspace methods like conjugate gradients, least squares QR and the recently proposed Hybrid method. A discussion and comparison of the available stopping rules will be included. A vibrating plate is considered as an example to validate our results.

On the existence of the optimal order for wavefunction extrapolation in Born-Oppenheimer molecular dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fang, Jun; Wang, Han, E-mail: wang-han@iapcm.ac.cn; CAEP Software Center for High Performance Numerical Simulation, Beijing

2016-06-28

Wavefunction extrapolation greatly reduces the number of self-consistent field (SCF) iterations and thus the overall computational cost of Born-Oppenheimer molecular dynamics (BOMD) that is based on the Kohn–Sham density functional theory. Going against the intuition that the higher order of extrapolation possesses a better accuracy, we demonstrate, from both theoretical and numerical perspectives, that the extrapolation accuracy firstly increases and then decreases with respect to the order, and an optimal extrapolation order in terms of minimal number of SCF iterations always exists. We also prove that the optimal order tends to be larger when using larger MD time steps ormore » more strict SCF convergence criteria. By example BOMD simulations of a solid copper system, we show that the optimal extrapolation order covers a broad range when varying the MD time step or the SCF convergence criterion. Therefore, we suggest the necessity for BOMD simulation packages to open the user interface and to provide more choices on the extrapolation order. Another factor that may influence the extrapolation accuracy is the alignment scheme that eliminates the discontinuity in the wavefunctions with respect to the atomic or cell variables. We prove the equivalence between the two existing schemes, thus the implementation of either of them does not lead to essential difference in the extrapolation accuracy.« less

Nested Conjugate Gradient Algorithm with Nested Preconditioning for Non-linear Image Restoration.

PubMed

Skariah, Deepak G; Arigovindan, Muthuvel

2017-06-19

We develop a novel optimization algorithm, which we call Nested Non-Linear Conjugate Gradient algorithm (NNCG), for image restoration based on quadratic data fitting and smooth non-quadratic regularization. The algorithm is constructed as a nesting of two conjugate gradient (CG) iterations. The outer iteration is constructed as a preconditioned non-linear CG algorithm; the preconditioning is performed by the inner CG iteration that is linear. The inner CG iteration, which performs preconditioning for outer CG iteration, itself is accelerated by an another FFT based non-iterative preconditioner. We prove that the method converges to a stationary point for both convex and non-convex regularization functionals. We demonstrate experimentally that proposed method outperforms the well-known majorization-minimization method used for convex regularization, and a non-convex inertial-proximal method for non-convex regularization functional.

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

NASA Technical Reports Server (NTRS)

Williams, S. D.; Curry, D. M.

1977-01-01

For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

Comparing direct and iterative equation solvers in a large structural analysis software system

NASA Technical Reports Server (NTRS)

Poole, E. L.

1991-01-01

Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.

Upwind relaxation methods for the Navier-Stokes equations using inner iterations

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Ng, Wing-Fai; Walters, Robert W.

1992-01-01

A subsonic and a supersonic problem are respectively treated by an upwind line-relaxation algorithm for the Navier-Stokes equations using inner iterations to accelerate steady-state solution convergence and thereby minimize CPU time. While the ability of the inner iterative procedure to mimic the quadratic convergence of the direct solver method is attested to in both test problems, some of the nonquadratic inner iterative results are noted to have been more efficient than the quadratic. In the more successful, supersonic test case, inner iteration required only about 65 percent of the line-relaxation method-entailed CPU time.

AIR-MRF: Accelerated iterative reconstruction for magnetic resonance fingerprinting.

PubMed

Cline, Christopher C; Chen, Xiao; Mailhe, Boris; Wang, Qiu; Pfeuffer, Josef; Nittka, Mathias; Griswold, Mark A; Speier, Peter; Nadar, Mariappan S

2017-09-01

Existing approaches for reconstruction of multiparametric maps with magnetic resonance fingerprinting (MRF) are currently limited by their estimation accuracy and reconstruction time. We aimed to address these issues with a novel combination of iterative reconstruction, fingerprint compression, additional regularization, and accelerated dictionary search methods. The pipeline described here, accelerated iterative reconstruction for magnetic resonance fingerprinting (AIR-MRF), was evaluated with simulations as well as phantom and in vivo scans. We found that the AIR-MRF pipeline provided reduced parameter estimation errors compared to non-iterative and other iterative methods, particularly at shorter sequence lengths. Accelerated dictionary search methods incorporated into the iterative pipeline reduced the reconstruction time at little cost of quality. Copyright © 2017 Elsevier Inc. All rights reserved.

A Two-Dimensional Helmholtz Equation Solution for the Multiple Cavity Scattering Problem

DTIC Science & Technology

2013-02-01

obtained by using the block Gauss – Seidel iterative meth- od. To show the convergence of the iterative method, we define the error between two...models to the general multiple cavity setting. Numerical examples indicate that the convergence of the Gauss – Seidel iterative method depends on the...variational approach. A block Gauss – Seidel iterative method is introduced to solve the cou- pled system of the multiple cavity scattering problem, where

A RecET-assisted CRISPR-Cas9 genome editing in Corynebacterium glutamicum.

PubMed

Wang, Bo; Hu, Qitiao; Zhang, Yu; Shi, Ruilin; Chai, Xin; Liu, Zhe; Shang, Xiuling; Zhang, Yun; Wen, Tingyi

2018-04-23

Extensive modification of genome is an efficient manner to regulate the metabolic network for producing target metabolites or non-native products using Corynebacterium glutamicum as a cell factory. Genome editing approaches by means of homologous recombination and counter-selection markers are laborious and time consuming due to multiple round manipulations and low editing efficiencies. The current two-plasmid-based CRISPR-Cas9 editing methods generate false positives due to the potential instability of Cas9 on the plasmid, and require a high transformation efficiency for co-occurrence of two plasmids transformation. Here, we developed a RecET-assisted CRISPR-Cas9 genome editing method using a chromosome-borne Cas9-RecET and a single plasmid harboring sgRNA and repair templates. The inducible expression of chromosomal RecET promoted the frequencies of homologous recombination, and increased the efficiency for gene deletion. Due to the high transformation efficiency of a single plasmid, this method enabled 10- and 20-kb region deletion, 2.5-, 5.7- and 7.5-kb expression cassette insertion and precise site-specific mutation, suggesting a versatility of this method. Deletion of argR and farR regulators as well as site-directed mutation of argB and pgi genes generated the mutant capable of accumulating L-arginine, indicating the stability of chromosome-borne Cas9 for iterative genome editing. Using this method, the model-predicted target genes were modified to redirect metabolic flux towards 1,2-propanediol biosynthetic pathway. The final engineered strain produced 6.75 ± 0.46 g/L of 1,2-propanediol that is the highest titer reported in C. glutamicum. Furthermore, this method is available for Corynebacterium pekinense 1.563, suggesting its universal applicability in other Corynebacterium species. The RecET-assisted CRISPR-Cas9 genome editing method will facilitate engineering of metabolic networks for the synthesis of interested bio-based products from renewable biomass using Corynebacterium species as cell factories.

Robust iterative method for nonlinear Helmholtz equation

NASA Astrophysics Data System (ADS)

Yuan, Lijun; Lu, Ya Yan

2017-08-01

A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

Multiscale solvers and systematic upscaling in computational physics

NASA Astrophysics Data System (ADS)

Brandt, A.

2005-07-01

Multiscale algorithms can overcome the scale-born bottlenecks that plague most computations in physics. These algorithms employ separate processing at each scale of the physical space, combined with interscale iterative interactions, in ways which use finer scales very sparingly. Having been developed first and well known as multigrid solvers for partial differential equations, highly efficient multiscale techniques have more recently been developed for many other types of computational tasks, including: inverse PDE problems; highly indefinite (e.g., standing wave) equations; Dirac equations in disordered gauge fields; fast computation and updating of large determinants (as needed in QCD); fast integral transforms; integral equations; astrophysics; molecular dynamics of macromolecules and fluids; many-atom electronic structures; global and discrete-state optimization; practical graph problems; image segmentation and recognition; tomography (medical imaging); fast Monte-Carlo sampling in statistical physics; and general, systematic methods of upscaling (accurate numerical derivation of large-scale equations from microscopic laws).

Twostep-by-twostep PIRK-type PC methods with continuous output formulas

NASA Astrophysics Data System (ADS)

Cong, Nguyen Huu; Xuan, Le Ngoc

2008-11-01

This paper deals with parallel predictor-corrector (PC) iteration methods based on collocation Runge-Kutta (RK) corrector methods with continuous output formulas for solving nonstiff initial-value problems (IVPs) for systems of first-order differential equations. At nth step, the continuous output formulas are used not only for predicting the stage values in the PC iteration methods but also for calculating the step values at (n+2)th step. In this case, the integration processes can be proceeded twostep-by-twostep. The resulting twostep-by-twostep (TBT) parallel-iterated RK-type (PIRK-type) methods with continuous output formulas (twostep-by-twostep PIRKC methods or TBTPIRKC methods) give us a faster integration process. Fixed stepsize applications of these TBTPIRKC methods to a few widely-used test problems reveal that the new PC methods are much more efficient when compared with the well-known parallel-iterated RK methods (PIRK methods), parallel-iterated RK-type PC methods with continuous output formulas (PIRKC methods) and sequential explicit RK codes DOPRI5 and DOP853 available from the literature.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1992-01-01

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step.

Nested Krylov methods and preserving the orthogonality

NASA Technical Reports Server (NTRS)

Desturler, Eric; Fokkema, Diederik R.

1993-01-01

Recently the GMRESR inner-outer iteraction scheme for the solution of linear systems of equations was proposed by Van der Vorst and Vuik. Similar methods have been proposed by Axelsson and Vassilevski and Saad (FGMRES). The outer iteration is GCR, which minimizes the residual over a given set of direction vectors. The inner iteration is GMRES, which at each step computes a new direction vector by approximately solving the residual equation. However, the optimality of the approximation over the space of outer search directions is ignored in the inner GMRES iteration. This leads to suboptimal corrections to the solution in the outer iteration, as components of the outer iteration directions may reenter in the inner iteration process. Therefore we propose to preserve the orthogonality relations of GCR in the inner GMRES iteration. This gives optimal corrections; however, it involves working with a singular, non-symmetric operator. We will discuss some important properties, and we will show by experiments that, in terms of matrix vector products, this modification (almost) always leads to better convergence. However, because we do more orthogonalizations, it does not always give an improved performance in CPU-time. Furthermore, we will discuss efficient implementations as well as the truncation possibilities of the outer GCR process. The experimental results indicate that for such methods it is advantageous to preserve the orthogonality in the inner iteration. Of course we can also use iteration schemes other than GMRES as the inner method; methods with short recurrences like GICGSTAB are of interest.

Transport synthetic acceleration with opposing reflecting boundary conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zika, M.R.; Adams, M.L.

2000-02-01

The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iteratingmore » on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.« less

Reducing the latency of the Fractal Iterative Method to half an iteration

NASA Astrophysics Data System (ADS)

Béchet, Clémentine; Tallon, Michel

2013-12-01

The fractal iterative method for atmospheric tomography (FRiM-3D) has been introduced to solve the wavefront reconstruction at the dimensions of an ELT with a low-computational cost. Previous studies reported the requirement of only 3 iterations of the algorithm in order to provide the best adaptive optics (AO) performance. Nevertheless, any iterative method in adaptive optics suffer from the intrinsic latency induced by the fact that one iteration can start only once the previous one is completed. Iterations hardly match the low-latency requirement of the AO real-time computer. We present here a new approach to avoid iterations in the computation of the commands with FRiM-3D, thus allowing low-latency AO response even at the scale of the European ELT (E-ELT). The method highlights the importance of "warm-start" strategy in adaptive optics. To our knowledge, this particular way to use the "warm-start" has not been reported before. Futhermore, removing the requirement of iterating to compute the commands, the computational cost of the reconstruction with FRiM-3D can be simplified and at least reduced to half the computational cost of a classical iteration. Thanks to simulations of both single-conjugate and multi-conjugate AO for the E-ELT,with FRiM-3D on Octopus ESO simulator, we demonstrate the benefit of this approach. We finally enhance the robustness of this new implementation with respect to increasing measurement noise, wind speed and even modeling errors.

Iterative deep convolutional encoder-decoder network for medical image segmentation.

PubMed

Jung Uk Kim; Hak Gu Kim; Yong Man Ro

2017-07-01

In this paper, we propose a novel medical image segmentation using iterative deep learning framework. We have combined an iterative learning approach and an encoder-decoder network to improve segmentation results, which enables to precisely localize the regions of interest (ROIs) including complex shapes or detailed textures of medical images in an iterative manner. The proposed iterative deep convolutional encoder-decoder network consists of two main paths: convolutional encoder path and convolutional decoder path with iterative learning. Experimental results show that the proposed iterative deep learning framework is able to yield excellent medical image segmentation performances for various medical images. The effectiveness of the proposed method has been proved by comparing with other state-of-the-art medical image segmentation methods.

Genetic analysis of litter size, parturition length, and birth assistance requirements in primiparous sows using a joint linear-threshold animal model.

PubMed

Holm, B; Bakken, M; Vangen, O; Rekaya, R

2004-09-01

The aim of this study was to investigate whether selection for number of live born piglets has led to prolonged parturition and increased requirement for birth assistance, resulting in increased numbers of stillborn piglets. Data were collected from 6,718 primiparous Norwegian Landrace sows farrowing between 2001 and 2003. The need for birth assistance was recorded as a binary response. Physical intervention in the birth of piglets and/or hormonal treatment by the farmer was recorded as birth assistance. The duration of the parturition was analyzed as a binary trait (<4 h and >4 h). The statistical model used for analysis included contemporary groups of herd-year, litter breed, season of farrowing, parity in which the sow was born, a regression on the age of sow at farrowing, an additive genetic effect, and a service sire effect. A full Bayesian approach via Gibbs sampling was adopted to estimate the genetic relationships between these four traits. A total chain length of 100,000 iterations was run. The first 10,000 samples were discarded as burn-in, and the remaining 90,000 iterations were retained without thinning for post-Gibbs analysis. The highest direct heritability was estimated for the number of live-born piglets (h2 = 0.07), followed by the duration of farrowing (h2 = 0.05), the need for birth assistance (h2 = 0.05), and the number of stillborn piglets (h2 = 0.04). The genetic correlations revealed that the number of live and stillborn piglets was uncorrelated; however, the number of live piglets born had a moderate genetic correlation to the need for birth assistance (rg = 0.24 +/- 0.01) and duration of farrowing (rg = -0.20 +/- 0.01), whereas the number of stillborn piglets was highly correlated to the need for birth assistance (rg = 0.74 +/- 0.01) and the duration of parturition (rg = 0.66 +/- 0.01). The duration of farrowing and the need for birth assistance were genetically highly correlated (rg = 0.89 +/- 0.00). For all traits, the service sire variance was approximately one quarter in magnitude compared with its respective genetic variance. The results showed that selection for the number of live born piglets is not expected to influence the number of stillborn piglets. Increasing the number of live piglets born through selection should have a slight negative effect on farrowing duration and a minor increase in the need for birth assistance. Sows with a high genetic potential for birth assistance and prolonged parturition were more likely to give birth to greater numbers of stillborn piglets.

Modelling of minority ion cyclotron current drive during the activated phase of ITER

NASA Astrophysics Data System (ADS)

Laxåback, M.; Hellsten, T.

2005-12-01

Neoclassical tearing modes, triggered by the long-period sawteeth expected in tokamaks with large non-thermal α-particle populations, may impose a severe β limit on experiments with large fusion yields and on reactors. Sawtooth destabilization by localized current drive could relax the β limit and improve plasma performance. 3He minority ion cyclotron current drive around the sawtooth inversion radius has been planned for ITER. Several ion species, including beam injected D ions and fusion born α particles, are however also resonant in the plasma and may represent a parasitic absorption of RF power. Modelling of minority ion cyclotron current drive in an ITER-FEAT-like plasma is presented, including the effects of ion trapping, finite ion drift orbit widths, wave-induced radial transport and the coupled evolution of wave fields and resonant ion distributions. The parasitic absorption of RF power by the other resonant species is concluded to be relatively small, but the 3He minority current drive is nevertheless negligible due to the strong collisionality of the 3He ions and the drag current by toroidally counter-rotating background ions and co-rotating electrons. H minority current drive is found to be a significantly more effective alternative.

A fast and robust iterative algorithm for prediction of RNA pseudoknotted secondary structures

PubMed Central

2014-01-01

Background Improving accuracy and efficiency of computational methods that predict pseudoknotted RNA secondary structures is an ongoing challenge. Existing methods based on free energy minimization tend to be very slow and are limited in the types of pseudoknots that they can predict. Incorporating known structural information can improve prediction accuracy; however, there are not many methods for prediction of pseudoknotted structures that can incorporate structural information as input. There is even less understanding of the relative robustness of these methods with respect to partial information. Results We present a new method, Iterative HFold, for pseudoknotted RNA secondary structure prediction. Iterative HFold takes as input a pseudoknot-free structure, and produces a possibly pseudoknotted structure whose energy is at least as low as that of any (density-2) pseudoknotted structure containing the input structure. Iterative HFold leverages strengths of earlier methods, namely the fast running time of HFold, a method that is based on the hierarchical folding hypothesis, and the energy parameters of HotKnots V2.0. Our experimental evaluation on a large data set shows that Iterative HFold is robust with respect to partial information, with average accuracy on pseudoknotted structures steadily increasing from roughly 54% to 79% as the user provides up to 40% of the input structure. Iterative HFold is much faster than HotKnots V2.0, while having comparable accuracy. Iterative HFold also has significantly better accuracy than IPknot on our HK-PK and IP-pk168 data sets. Conclusions Iterative HFold is a robust method for prediction of pseudoknotted RNA secondary structures, whose accuracy with more than 5% information about true pseudoknot-free structures is better than that of IPknot, and with about 35% information about true pseudoknot-free structures compares well with that of HotKnots V2.0 while being significantly faster. Iterative HFold and all data used in this work are freely available at http://www.cs.ubc.ca/~hjabbari/software.php. PMID:24884954

Iterative Strain-Gage Balance Calibration Data Analysis for Extended Independent Variable Sets

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred

2011-01-01

A new method was developed that makes it possible to use an extended set of independent calibration variables for an iterative analysis of wind tunnel strain gage balance calibration data. The new method permits the application of the iterative analysis method whenever the total number of balance loads and other independent calibration variables is greater than the total number of measured strain gage outputs. Iteration equations used by the iterative analysis method have the limitation that the number of independent and dependent variables must match. The new method circumvents this limitation. It simply adds a missing dependent variable to the original data set by using an additional independent variable also as an additional dependent variable. Then, the desired solution of the regression analysis problem can be obtained that fits each gage output as a function of both the original and additional independent calibration variables. The final regression coefficients can be converted to data reduction matrix coefficients because the missing dependent variables were added to the data set without changing the regression analysis result for each gage output. Therefore, the new method still supports the application of the two load iteration equation choices that the iterative method traditionally uses for the prediction of balance loads during a wind tunnel test. An example is discussed in the paper that illustrates the application of the new method to a realistic simulation of temperature dependent calibration data set of a six component balance.

A comparison theorem for the SOR iterative method

NASA Astrophysics Data System (ADS)

Sun, Li-Ying

2005-09-01

In 1997, Kohno et al. have reported numerically that the improving modified Gauss-Seidel method, which was referred to as the IMGS method, is superior to the SOR iterative method. In this paper, we prove that the spectral radius of the IMGS method is smaller than that of the SOR method and Gauss-Seidel method, if the relaxation parameter [omega][set membership, variant](0,1]. As a result, we prove theoretically that this method is succeeded in improving the convergence of some classical iterative methods. Some recent results are improved.

Iterative approach as alternative to S-matrix in modal methods

NASA Astrophysics Data System (ADS)

Semenikhin, Igor; Zanuccoli, Mauro

2014-12-01

The continuously increasing complexity of opto-electronic devices and the rising demands of simulation accuracy lead to the need of solving very large systems of linear equations making iterative methods promising and attractive from the computational point of view with respect to direct methods. In particular, iterative approach potentially enables the reduction of required computational time to solve Maxwell's equations by Eigenmode Expansion algorithms. Regardless of the particular eigenmodes finding method used, the expansion coefficients are computed as a rule by scattering matrix (S-matrix) approach or similar techniques requiring order of M3 operations. In this work we consider alternatives to the S-matrix technique which are based on pure iterative or mixed direct-iterative approaches. The possibility to diminish the impact of M3 -order calculations to overall time and in some cases even to reduce the number of arithmetic operations to M2 by applying iterative techniques are discussed. Numerical results are illustrated to discuss validity and potentiality of the proposed approaches.

Parallel iterative methods for sparse linear and nonlinear equations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Efficient solution of the simplified P N equations

DOE PAGES

Hamilton, Steven P.; Evans, Thomas M.

2014-12-23

We show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy a robust set of solution strategies may be applied. Moreover, power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi's method, and a generalized Davidson method, each using algebraic and physics-based multigrid preconditioners, have been compared on C5G7 MOX test problem as well as an operational PWR model. These results show that the most ecient approach is the generalized Davidson method, that is 30-40 times faster than traditional power iteration and 6-10 times faster than Arnoldi's method.

An Improved Newton's Method.

ERIC Educational Resources Information Center

Mathews, John H.

1989-01-01

Describes Newton's method to locate roots of an equation using the Newton-Raphson iteration formula. Develops an adaptive method overcoming limitations of the iteration method. Provides the algorithm and computer program of the adaptive Newton-Raphson method. (YP)

An accelerated subspace iteration for eigenvector derivatives

NASA Technical Reports Server (NTRS)

Ting, Tienko

1991-01-01

An accelerated subspace iteration method for calculating eigenvector derivatives has been developed. Factors affecting the effectiveness and the reliability of the subspace iteration are identified, and effective strategies concerning these factors are presented. The method has been implemented, and the results of a demonstration problem are presented.

Iterative CT reconstruction using coordinate descent with ordered subsets of data

NASA Astrophysics Data System (ADS)

Noo, F.; Hahn, K.; Schöndube, H.; Stierstorfer, K.

2016-04-01

Image reconstruction based on iterative minimization of a penalized weighted least-square criteria has become an important topic of research in X-ray computed tomography. This topic is motivated by increasing evidence that such a formalism may enable a significant reduction in dose imparted to the patient while maintaining or improving image quality. One important issue associated with this iterative image reconstruction concept is slow convergence and the associated computational effort. For this reason, there is interest in finding methods that produce approximate versions of the targeted image with a small number of iterations and an acceptable level of discrepancy. We introduce here a novel method to produce such approximations: ordered subsets in combination with iterative coordinate descent. Preliminary results demonstrate that this method can produce, within 10 iterations and using only a constant image as initial condition, satisfactory reconstructions that retain the noise properties of the targeted image.

Parallelized implicit propagators for the finite-difference Schrödinger equation

NASA Astrophysics Data System (ADS)

Parker, Jonathan; Taylor, K. T.

1995-08-01

We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

NASA Technical Reports Server (NTRS)

Moghaddam, M.; Chew, W. C.

1993-01-01

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

SU-D-206-03: Segmentation Assisted Fast Iterative Reconstruction Method for Cone-Beam CT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, P; Mao, T; Gong, S

2016-06-15

Purpose: Total Variation (TV) based iterative reconstruction (IR) methods enable accurate CT image reconstruction from low-dose measurements with sparse projection acquisition, due to the sparsifiable feature of most CT images using gradient operator. However, conventional solutions require large amount of iterations to generate a decent reconstructed image. One major reason is that the expected piecewise constant property is not taken into consideration at the optimization starting point. In this work, we propose an iterative reconstruction method for cone-beam CT (CBCT) using image segmentation to guide the optimization path more efficiently on the regularization term at the beginning of the optimizationmore » trajectory. Methods: Our method applies general knowledge that one tissue component in the CT image contains relatively uniform distribution of CT number. This general knowledge is incorporated into the proposed reconstruction using image segmentation technique to generate the piecewise constant template on the first-pass low-quality CT image reconstructed using analytical algorithm. The template image is applied as an initial value into the optimization process. Results: The proposed method is evaluated on the Shepp-Logan phantom of low and high noise levels, and a head patient. The number of iterations is reduced by overall 40%. Moreover, our proposed method tends to generate a smoother reconstructed image with the same TV value. Conclusion: We propose a computationally efficient iterative reconstruction method for CBCT imaging. Our method achieves a better optimization trajectory and a faster convergence behavior. It does not rely on prior information and can be readily incorporated into existing iterative reconstruction framework. Our method is thus practical and attractive as a general solution to CBCT iterative reconstruction. This work is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16F010001), National High-tech R&D Program for Young Scientists by the Ministry of Science and Technology of China (Grant No. 2015AA020917).« less

GUEST EDITORS' INTRODUCTION: Testing inversion algorithms against experimental data: inhomogeneous targets

NASA Astrophysics Data System (ADS)

Belkebir, Kamal; Saillard, Marc

2005-12-01

This special section deals with the reconstruction of scattering objects from experimental data. A few years ago, inspired by the Ipswich database [1 4], we started to build an experimental database in order to validate and test inversion algorithms against experimental data. In the special section entitled 'Testing inversion algorithms against experimental data' [5], preliminary results were reported through 11 contributions from several research teams. (The experimental data are free for scientific use and can be downloaded from the web site.) The success of this previous section has encouraged us to go further and to design new challenges for the inverse scattering community. Taking into account the remarks formulated by several colleagues, the new data sets deal with inhomogeneous cylindrical targets and transverse electric (TE) polarized incident fields have also been used. Among the four inhomogeneous targets, three are purely dielectric, while the last one is a `hybrid' target mixing dielectric and metallic cylinders. Data have been collected in the anechoic chamber of the Centre Commun de Ressources Micro-ondes in Marseille. The experimental setup as well as the layout of the files containing the measurements are presented in the contribution by J-M Geffrin, P Sabouroux and C Eyraud. The antennas did not change from the ones used previously [5], namely wide-band horn antennas. However, improvements have been achieved by refining the mechanical positioning devices. In order to enlarge the scope of applications, both TE and transverse magnetic (TM) polarizations have been carried out for all targets. Special care has been taken not to move the target under test when switching from TE to TM measurements, ensuring that TE and TM data are available for the same configuration. All data correspond to electric field measurements. In TE polarization the measured component is orthogonal to the axis of invariance. Contributions A Abubakar, P M van den Berg and T M Habashy, Application of the multiplicative regularized contrast source inversion method TM- and TE-polarized experimental Fresnel data, present results of profile inversions obtained using the contrast source inversion (CSI) method, in which a multiplicative regularization is plugged in. The authors successfully inverted both TM- and TE-polarized fields. Note that this paper is one of only two contributions which address the inversion of TE-polarized data. A Baussard, Inversion of multi-frequency experimental data using an adaptive multiscale approach, reports results of reconstructions using the modified gradient method (MGM). It suggests that a coarse-to-fine iterative strategy based on spline pyramids. In this iterative technique, the number of degrees of freedom is reduced, which improves robustness. The introduction, during the iterative process, of finer scales inside areas of interest leads to an accurate representation of the object under test. The efficiency of this technique is shown via comparisons between the results obtained with the standard MGM and those from an adaptive approach. L Crocco, M D'Urso and T Isernia, Testing the contrast source extended Born inversion method against real data: the case of TM data, assume that the main contribution in the domain integral formulation comes from the singularity of Green's function, even though the media involved are lossless. A Fourier Bessel analysis of the incident and scattered measured fields is used to derive a model of the incident field and an estimate of the location and size of the target. The iterative procedure lies on a conjugate gradient method associated with Tikhonov regularization, and the multi-frequency data are dealt with using a frequency-hopping approach. In many cases, it is difficult to reconstruct accurately both real and imaginary parts of the permittivity if no prior information is included. M Donelli, D Franceschini, A Massa, M Pastorino and A Zanetti, Multi-resolution iterative inversion of real inhomogeneous targets, adopt a multi-resolution strategy, which, at each step, adaptive discretization of the integral equation is performed over an irregular mesh, with a coarser grid outside the regions of interest and tighter sampling where better resolution is required. Here, this procedure is achieved while keeping the number of unknowns constant. The way such a strategy could be combined with multi-frequency data, edge preserving regularization, or any technique also devoted to improve resolution, remains to be studied. As done by some other contributors, the model of incident field is chosen to fit the Fourier Bessel expansion of the measured one. A Dubois, K Belkebir and M Saillard, Retrieval of inhomogeneous targets from experimental frequency diversity data, present results of the reconstruction of targets using three different non-regularized techniques. It is suggested to minimize a frequency weighted cost function rather than a standard one. The different approaches are compared and discussed. C Estatico, G Bozza, A Massa, M Pastorino and A Randazzo, A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data, use a two nested iterative methods scheme, based on the second-order Born approximation, which is nonlinear in terms of contrast but does not involve the total field. At each step of the outer iteration, the problem is linearized and solved iteratively using the Landweber method. Better reconstructions than with the Born approximation are obtained at low numerical cost. O Feron, B Duchêne and A Mohammad-Djafari, Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data, adopt a Bayesian framework based on a hidden Markov model, built to take into account, as prior knowledge, that the target is composed of a finite number of homogeneous regions. It has been applied to diffraction tomography and to a rigorous formulation of the inverse problem. The latter can be viewed as a Bayesian adaptation of the contrast source method such that prior information about the contrast can be introduced in the prior law distribution, and it results in estimating the posterior mean instead of minimizing a cost functional. The accuracy of the result is thus closely linked to the prior knowledge of the contrast, making this approach well suited for non-destructive testing. J-M Geffrin, P Sabouroux and C Eyraud, Free space experimental scattering database continuation: experimental set-up and measurement precision, describe the experimental set-up used to carry out the data for the inversions. They report the modifications of the experimental system used previously in order to improve the precision of the measurements. Reliability of data is demonstrated through comparisons between measurements and computed scattered field with both fundamental polarizations. In addition, the reader interested in using the database will find the relevant information needed to perform inversions as well as the description of the targets under test. A Litman, Reconstruction by level sets of n-ary scattering obstacles, presents the reconstruction of targets using a level sets representation. It is assumed that the constitutive materials of the obstacles under test are known and the shape is retrieved. Two approaches are reported. In the first one the obstacles of different constitutive materials are represented in a single level set, while in the second approach several level sets are combined. The approaches are applied to the experimental data and compared. U Shahid, M Testorf and M A Fiddy, Minimum-phase-based inverse scattering algorithm applied to Institut Fresnel data, suggest a way of extending the use of minimum phase functions to 2D problems. In the kind of inverse problems we are concerned with, it consists of separating the contributions from the field and from the contrast in the so-called contrast source term, through homomorphic filtering. Images of the targets are obtained by combination with diffraction tomography. Both pre-processing and imaging are thus based on the use of Fourier transforms, making the algorithm very fast compared to classical iterative approaches. It is also pointed out that the design of appropriate filters remains an open topic. C Yu, L-P Song and Q H Liu, Inversion of multi-frequency experimental data for imaging complex objects by a DTA CSI method, use the contrast source inversion (CSI) method for the reconstruction of the targets, in which the initial guess is a solution deduced from another iterative technique based on the diagonal tensor approximation (DTA). In so doing, the authors combine the fast convergence of the DTA method for generating an accurate initial estimate for the CSI method. Note that this paper is one of only two contributions which address the inversion of TE-polarized data. Conclusion In this special section various inverse scattering techniques were used to successfully reconstruct inhomogeneous targets from multi-frequency multi-static measurements. This shows that the database is reliable and can be useful for researchers wanting to test and validate inversion algorithms. From the database, it is also possible to extract subsets to study particular inverse problems, for instance from phaseless data or from `aspect-limited' configurations. Our future efforts will be directed towards extending the database in order to explore inversions from transient fields and the full three-dimensional problem. Acknowledgments The authors would like to thank the Inverse Problems board for opening the journal to us, and offer profound thanks to Elaine Longden-Chapman and Kate Hooper for their help in organizing this special section.

Iteration, Not Induction

ERIC Educational Resources Information Center

Dobbs, David E.

2009-01-01

The main purpose of this note is to present and justify proof via iteration as an intuitive, creative and empowering method that is often available and preferable as an alternative to proofs via either mathematical induction or the well-ordering principle. The method of iteration depends only on the fact that any strictly decreasing sequence of…

Changes in Access to Health Services of the Immigrant and Native-Born Population in Spain in the Context of Economic Crisis †

PubMed Central

Garcia-Subirats, Irene; Vargas, Ingrid; Sanz-Barbero, Belén; Malmusi, Davide; Ronda, Elena; Ballesta, Mónica; Vázquez, María Luisa

2014-01-01

Aim: To analyze changes in access to health care and its determinants in the immigrant and native-born populations in Spain, before and during the economic crisis. Methods: Comparative analysis of two iterations of the Spanish National Health Survey (2006 and 2012). Outcome variables were: unmet need and use of different healthcare levels; explanatory variables: need, predisposing and enabling factors. Multivariate models were performed (1) to compare outcome variables in each group between years, (2) to compare outcome variables between both groups within each year, and (3) to determine the factors associated with health service use for each group and year. Results: unmet healthcare needs decreased in 2012 compared to 2006; the use of health services remained constant, with some changes worth highlighting, such as the decline in general practitioner visits among autochthons and a narrowed gap in specialist visits between the two populations. The factors associated with health service use in 2006 remained constant in 2012. Conclusion: Access to healthcare did not worsen, possibly due to the fact that, until 2012, the national health system may have cushioned the deterioration of social determinants as a consequence of the financial crisis. Further studies are necessary to evaluate the effects of health policy responses to the crisis after 2012. PMID:25272078

A new iterative triclass thresholding technique in image segmentation.

PubMed

Cai, Hongmin; Yang, Zhong; Cao, Xinhua; Xia, Weiming; Xu, Xiaoyin

2014-03-01

We present a new method in image segmentation that is based on Otsu's method but iteratively searches for subregions of the image for segmentation, instead of treating the full image as a whole region for processing. The iterative method starts with Otsu's threshold and computes the mean values of the two classes as separated by the threshold. Based on the Otsu's threshold and the two mean values, the method separates the image into three classes instead of two as the standard Otsu's method does. The first two classes are determined as the foreground and background and they will not be processed further. The third class is denoted as a to-be-determined (TBD) region that is processed at next iteration. At the succeeding iteration, Otsu's method is applied on the TBD region to calculate a new threshold and two class means and the TBD region is again separated into three classes, namely, foreground, background, and a new TBD region, which by definition is smaller than the previous TBD regions. Then, the new TBD region is processed in the similar manner. The process stops when the Otsu's thresholds calculated between two iterations is less than a preset threshold. Then, all the intermediate foreground and background regions are, respectively, combined to create the final segmentation result. Tests on synthetic and real images showed that the new iterative method can achieve better performance than the standard Otsu's method in many challenging cases, such as identifying weak objects and revealing fine structures of complex objects while the added computational cost is minimal.

Stroke localization and classification using microwave tomography with k-means clustering and support vector machine.

PubMed

Guo, Lei; Abbosh, Amin

2018-05-01

For any chance for stroke patients to survive, the stroke type should be classified to enable giving medication within a few hours of the onset of symptoms. In this paper, a microwave-based stroke localization and classification framework is proposed. It is based on microwave tomography, k-means clustering, and a support vector machine (SVM) method. The dielectric profile of the brain is first calculated using the Born iterative method, whereas the amplitude of the dielectric profile is then taken as the input to k-means clustering. The cluster is selected as the feature vector for constructing and testing the SVM. A database of MRI-derived realistic head phantoms at different signal-to-noise ratios is used in the classification procedure. The performance of the proposed framework is evaluated using the receiver operating characteristic (ROC) curve. The results based on a two-dimensional framework show that 88% classification accuracy, with a sensitivity of 91% and a specificity of 87%, can be achieved. Bioelectromagnetics. 39:312-324, 2018. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations

DOE PAGES

Banerjee, Amartya S.; Suryanarayana, Phanish; Pask, John E.

2016-01-21

Pulay's Direct Inversion in the Iterative Subspace (DIIS) method is one of the most widely used mixing schemes for accelerating the self-consistent solution of electronic structure problems. In this work, we propose a simple generalization of DIIS in which Pulay extrapolation is performed at periodic intervals rather than on every self-consistent field iteration, and linear mixing is performed on all other iterations. Lastly, we demonstrate through numerical tests on a wide variety of materials systems in the framework of density functional theory that the proposed generalization of Pulay's method significantly improves its robustness and efficiency.

Asymptotic (h tending to infinity) absolute stability for BDFs applied to stiff differential equations. [Backward Differentiation Formulas

NASA Technical Reports Server (NTRS)

Krogh, F. T.; Stewart, K.

1984-01-01

Methods based on backward differentiation formulas (BDFs) for solving stiff differential equations require iterating to approximate the solution of the corrector equation on each step. One hope for reducing the cost of this is to make do with iteration matrices that are known to have errors and to do no more iterations than are necessary to maintain the stability of the method. This paper, following work by Klopfenstein, examines the effect of errors in the iteration matrix on the stability of the method. Application of the results to an algorithm is discussed briefly.

Conceptual design of the radial gamma ray spectrometers system for α particle and runaway electron measurements at ITER

NASA Astrophysics Data System (ADS)

Nocente, M.; Tardocchi, M.; Barnsley, R.; Bertalot, L.; Brichard, B.; Croci, G.; Brolatti, G.; Di Pace, L.; Fernandes, A.; Giacomelli, L.; Lengar, I.; Moszynski, M.; Krasilnikov, V.; Muraro, A.; Pereira, R. C.; Perelli Cippo, E.; Rigamonti, D.; Rebai, M.; Rzadkiewicz, J.; Salewski, M.; Santosh, P.; Sousa, J.; Zychor, I.; Gorini, G.

2017-07-01

We here present the principles and main physics capabilities behind the design of the radial gamma ray spectrometers (RGRS) system for alpha particle and runaway electron measurements at ITER. The diagnostic benefits from recent advances in gamma-ray spectrometry for tokamak plasmas and combines space and high energy resolution in a single device. The RGRS system as designed can provide information on α ~ particles on a time scale of 1/10 of the slowing down time for the ITER 500 MW full power DT scenario. Spectral observations of the 3.21 and 4.44 MeV peaks from the 9\\text{Be}≤ft(α,nγ \\right){{}12}\\text{C} reaction make the measurements sensitive to α ~ particles at characteristic resonant energies and to possible anisotropies of their slowing down distribution function. An independent assessment of the neutron rate by gamma-ray emission is also feasible. In case of runaway electrons born in disruptions with a typical duration of 100 ms, a time resolution of at least 10 ms for runaway electron studies can be achieved depending on the scenario and down to a current of 40 kA by use of external gas injection. We find that the bremsstrahlung spectrum in the MeV range from confined runaways is sensitive to the electron velocity space up to E≈ 30 -40 MeV, which allows for measurements of the energy distribution of the runaway electrons at ITER.

A Build-Up Interior Method for Linear Programming: Affine Scaling Form

DTIC Science & Technology

1990-02-01

initiating a major iteration imply convergence in a finite number of iterations. Each iteration t of the Dikin algorithm starts with an interior dual...this variant with the affine scaling method of Dikin [5] (in dual form). We have also looked into the analogous variant for the related Karmarkar’s...4] G. B. Dantzig, Linear Programming and Extensions (Princeton University Press, Princeton, NJ, 1963). [5] I. I. Dikin , "Iterative solution of

Iterative metal artifact reduction for x-ray computed tomography using unmatched projector/backprojector pairs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hanming; Wang, Linyuan; Li, Lei

2016-06-15

Purpose: Metal artifact reduction (MAR) is a major problem and a challenging issue in x-ray computed tomography (CT) examinations. Iterative reconstruction from sinograms unaffected by metals shows promising potential in detail recovery. This reconstruction has been the subject of much research in recent years. However, conventional iterative reconstruction methods easily introduce new artifacts around metal implants because of incomplete data reconstruction and inconsistencies in practical data acquisition. Hence, this work aims at developing a method to suppress newly introduced artifacts and improve the image quality around metal implants for the iterative MAR scheme. Methods: The proposed method consists of twomore » steps based on the general iterative MAR framework. An uncorrected image is initially reconstructed, and the corresponding metal trace is obtained. The iterative reconstruction method is then used to reconstruct images from the unaffected sinogram. In the reconstruction step of this work, an iterative strategy utilizing unmatched projector/backprojector pairs is used. A ramp filter is introduced into the back-projection procedure to restrain the inconsistency components in low frequencies and generate more reliable images of the regions around metals. Furthermore, a constrained total variation (TV) minimization model is also incorporated to enhance efficiency. The proposed strategy is implemented based on an iterative FBP and an alternating direction minimization (ADM) scheme, respectively. The developed algorithms are referred to as “iFBP-TV” and “TV-FADM,” respectively. Two projection-completion-based MAR methods and three iterative MAR methods are performed simultaneously for comparison. Results: The proposed method performs reasonably on both simulation and real CT-scanned datasets. This approach could reduce streak metal artifacts effectively and avoid the mentioned effects in the vicinity of the metals. The improvements are evaluated by inspecting regions of interest and by comparing the root-mean-square errors, normalized mean absolute distance, and universal quality index metrics of the images. Both iFBP-TV and TV-FADM methods outperform other counterparts in all cases. Unlike the conventional iterative methods, the proposed strategy utilizing unmatched projector/backprojector pairs shows excellent performance in detail preservation and prevention of the introduction of new artifacts. Conclusions: Qualitative and quantitative evaluations of experimental results indicate that the developed method outperforms classical MAR algorithms in suppressing streak artifacts and preserving the edge structural information of the object. In particular, structures lying close to metals can be gradually recovered because of the reduction of artifacts caused by inconsistency effects.« less

A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Chen, Hao; Lv, Wen; Zhang, Tongtong

2018-05-01

We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

Electromagnetic scattering of large structures in layered earths using integral equations

NASA Astrophysics Data System (ADS)

Xiong, Zonghou; Tripp, Alan C.

1995-07-01

An electromagnetic scattering algorithm for large conductivity structures in stratified media has been developed and is based on the method of system iteration and spatial symmetry reduction using volume electric integral equations. The method of system iteration divides a structure into many substructures and solves the resulting matrix equation using a block iterative method. The block submatrices usually need to be stored on disk in order to save computer core memory. However, this requires a large disk for large structures. If the body is discretized into equal-size cells it is possible to use the spatial symmetry relations of the Green's functions to regenerate the scattering impedance matrix in each iteration, thus avoiding expensive disk storage. Numerical tests show that the system iteration converges much faster than the conventional point-wise Gauss-Seidel iterative method. The numbers of cells do not significantly affect the rate of convergency. Thus the algorithm effectively reduces the solution of the scattering problem to an order of O(N2), instead of O(N3) as with direct solvers.

Iteration with Spreadsheets.

ERIC Educational Resources Information Center

Smith, Michael

1990-01-01

Presents several examples of the iteration method using computer spreadsheets. Examples included are simple iterative sequences and the solution of equations using the Newton-Raphson formula, linear interpolation, and interval bisection. (YP)

Iterative methods for tomography problems: implementation to a cross-well tomography problem

NASA Astrophysics Data System (ADS)

Karadeniz, M. F.; Weber, G. W.

2018-01-01

The velocity distribution between two boreholes is reconstructed by cross-well tomography, which is commonly used in geology. In this paper, iterative methods, Kaczmarz’s algorithm, algebraic reconstruction technique (ART), and simultaneous iterative reconstruction technique (SIRT), are implemented to a specific cross-well tomography problem. Convergence to the solution of these methods and their CPU time for the cross-well tomography problem are compared. Furthermore, these three methods for this problem are compared for different tolerance values.

Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi

PubMed Central

Li, Chuan; Li, Lin; Zhang, Jie; Alexov, Emil

2012-01-01

The Gauss-Seidel method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the Gauss-Seidel method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of CPUs. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson-Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. PMID:22674480

Pseudo-time methods for constrained optimization problems governed by PDE

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1995-01-01

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

A New Newton-Like Iterative Method for Roots of Analytic Functions

ERIC Educational Resources Information Center

Otolorin, Olayiwola

2005-01-01

A new Newton-like iterative formula for the solution of non-linear equations is proposed. To derive the formula, the convergence criteria of the one-parameter iteration formula, and also the quasilinearization in the derivation of Newton's formula are reviewed. The result is a new formula which eliminates the limitations of other methods. There is…

Iterative Nonlocal Total Variation Regularization Method for Image Restoration

PubMed Central

Xu, Huanyu; Sun, Quansen; Luo, Nan; Cao, Guo; Xia, Deshen

2013-01-01

In this paper, a Bregman iteration based total variation image restoration algorithm is proposed. Based on the Bregman iteration, the algorithm splits the original total variation problem into sub-problems that are easy to solve. Moreover, non-local regularization is introduced into the proposed algorithm, and a method to choose the non-local filter parameter locally and adaptively is proposed. Experiment results show that the proposed algorithms outperform some other regularization methods. PMID:23776560

Iterative integral parameter identification of a respiratory mechanics model.

PubMed

Schranz, Christoph; Docherty, Paul D; Chiew, Yeong Shiong; Möller, Knut; Chase, J Geoffrey

2012-07-18

Patient-specific respiratory mechanics models can support the evaluation of optimal lung protective ventilator settings during ventilation therapy. Clinical application requires that the individual's model parameter values must be identified with information available at the bedside. Multiple linear regression or gradient-based parameter identification methods are highly sensitive to noise and initial parameter estimates. Thus, they are difficult to apply at the bedside to support therapeutic decisions. An iterative integral parameter identification method is applied to a second order respiratory mechanics model. The method is compared to the commonly used regression methods and error-mapping approaches using simulated and clinical data. The clinical potential of the method was evaluated on data from 13 Acute Respiratory Distress Syndrome (ARDS) patients. The iterative integral method converged to error minima 350 times faster than the Simplex Search Method using simulation data sets and 50 times faster using clinical data sets. Established regression methods reported erroneous results due to sensitivity to noise. In contrast, the iterative integral method was effective independent of initial parameter estimations, and converged successfully in each case tested. These investigations reveal that the iterative integral method is beneficial with respect to computing time, operator independence and robustness, and thus applicable at the bedside for this clinical application.

A Universal Tare Load Prediction Algorithm for Strain-Gage Balance Calibration Data Analysis

NASA Technical Reports Server (NTRS)

Ulbrich, N.

2011-01-01

An algorithm is discussed that may be used to estimate tare loads of wind tunnel strain-gage balance calibration data. The algorithm was originally developed by R. Galway of IAR/NRC Canada and has been described in the literature for the iterative analysis technique. Basic ideas of Galway's algorithm, however, are universally applicable and work for both the iterative and the non-iterative analysis technique. A recent modification of Galway's algorithm is presented that improves the convergence behavior of the tare load prediction process if it is used in combination with the non-iterative analysis technique. The modified algorithm allows an analyst to use an alternate method for the calculation of intermediate non-linear tare load estimates whenever Galway's original approach does not lead to a convergence of the tare load iterations. It is also shown in detail how Galway's algorithm may be applied to the non-iterative analysis technique. Hand load data from the calibration of a six-component force balance is used to illustrate the application of the original and modified tare load prediction method. During the analysis of the data both the iterative and the non-iterative analysis technique were applied. Overall, predicted tare loads for combinations of the two tare load prediction methods and the two balance data analysis techniques showed excellent agreement as long as the tare load iterations converged. The modified algorithm, however, appears to have an advantage over the original algorithm when absolute voltage measurements of gage outputs are processed using the non-iterative analysis technique. In these situations only the modified algorithm converged because it uses an exact solution of the intermediate non-linear tare load estimate for the tare load iteration.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1991-01-01

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

Global Asymptotic Behavior of Iterative Implicit Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1994-01-01

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

Implementation of an improved adaptive-implicit method in a thermal compositional simulator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, T.B.

1988-11-01

A multicomponent thermal simulator with an adaptive-implicit-method (AIM) formulation/inexact-adaptive-Newton (IAN) method is presented. The final coefficient matrix retains the original banded structure so that conventional iterative methods can be used. Various methods for selection of the eliminated unknowns are tested. AIM/IAN method has a lower work count per Newtonian iteration than fully implicit methods, but a wrong choice of unknowns will result in excessive Newtonian iterations. For the problems tested, the residual-error method described in the paper for selecting implicit unknowns, together with the IAN method, had an improvement of up to 28% of the CPU time over the fullymore » implicit method.« less

Calibration and compensation method of three-axis geomagnetic sensor based on pre-processing total least square iteration

NASA Astrophysics Data System (ADS)

Zhou, Y.; Zhang, X.; Xiao, W.

2018-04-01

As the geomagnetic sensor is susceptible to interference, a pre-processing total least square iteration method is proposed for calibration compensation. Firstly, the error model of the geomagnetic sensor is analyzed and the correction model is proposed, then the characteristics of the model are analyzed and converted into nine parameters. The geomagnetic data is processed by Hilbert transform (HHT) to improve the signal-to-noise ratio, and the nine parameters are calculated by using the combination of Newton iteration method and the least squares estimation method. The sifter algorithm is used to filter the initial value of the iteration to ensure that the initial error is as small as possible. The experimental results show that this method does not need additional equipment and devices, can continuously update the calibration parameters, and better than the two-step estimation method, it can compensate geomagnetic sensor error well.

Perturbation-iteration theory for analyzing microwave striplines

NASA Technical Reports Server (NTRS)

Kretch, B. E.

1985-01-01

A perturbation-iteration technique is presented for determining the propagation constant and characteristic impedance of an unshielded microstrip transmission line. The method converges to the correct solution with a few iterations at each frequency and is equivalent to a full wave analysis. The perturbation-iteration method gives a direct solution for the propagation constant without having to find the roots of a transcendental dispersion equation. The theory is presented in detail along with numerical results for the effective dielectric constant and characteristic impedance for a wide range of substrate dielectric constants, stripline dimensions, and frequencies.

Steady state numerical solutions for determining the location of MEMS on projectile

NASA Astrophysics Data System (ADS)

Abiprayu, K.; Abdigusna, M. F. F.; Gunawan, P. H.

2018-03-01

This paper is devoted to compare the numerical solutions for the steady and unsteady state heat distribution model on projectile. Here, the best location for installing of the MEMS on the projectile based on the surface temperature is investigated. Numerical iteration methods, Jacobi and Gauss-Seidel have been elaborated to solve the steady state heat distribution model on projectile. The results using Jacobi and Gauss-Seidel are shown identical but the discrepancy iteration cost for each methods is gained. Using Jacobi’s method, the iteration cost is 350 iterations. Meanwhile, using Gauss-Seidel 188 iterations are obtained, faster than the Jacobi’s method. The comparison of the simulation by steady state model and the unsteady state model by a reference is shown satisfying. Moreover, the best candidate for installing MEMS on projectile is observed at pointT(10, 0) which has the lowest temperature for the other points. The temperature using Jacobi and Gauss-Seidel for scenario 1 and 2 atT(10, 0) are 307 and 309 Kelvin respectively.

Material nonlinear analysis via mixed-iterative finite element method

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1992-01-01

The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.

On the solution of evolution equations based on multigrid and explicit iterative methods

NASA Astrophysics Data System (ADS)

Zhukov, V. T.; Novikova, N. D.; Feodoritova, O. B.

2015-08-01

Two schemes for solving initial-boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.

Differential Characteristics Based Iterative Multiuser Detection for Wireless Sensor Networks

PubMed Central

Chen, Xiaoguang; Jiang, Xu; Wu, Zhilu; Zhuang, Shufeng

2017-01-01

High throughput, low latency and reliable communication has always been a hot topic for wireless sensor networks (WSNs) in various applications. Multiuser detection is widely used to suppress the bad effect of multiple access interference in WSNs. In this paper, a novel multiuser detection method based on differential characteristics is proposed to suppress multiple access interference. The proposed iterative receive method consists of three stages. Firstly, a differential characteristics function is presented based on the optimal multiuser detection decision function; then on the basis of differential characteristics, a preliminary threshold detection is utilized to find the potential wrongly received bits; after that an error bit corrector is employed to correct the wrong bits. In order to further lower the bit error ratio (BER), the differential characteristics calculation, threshold detection and error bit correction process described above are iteratively executed. Simulation results show that after only a few iterations the proposed multiuser detection method can achieve satisfactory BER performance. Besides, BER and near far resistance performance are much better than traditional suboptimal multiuser detection methods. Furthermore, the proposed iterative multiuser detection method also has a large system capacity. PMID:28212328

The application of contraction theory to an iterative formulation of electromagnetic scattering

NASA Technical Reports Server (NTRS)

Brand, J. C.; Kauffman, J. F.

1985-01-01

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

DOE PAGES

Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; ...

2017-03-05

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

A non-iterative extension of the multivariate random effects meta-analysis.

PubMed

Makambi, Kepher H; Seung, Hyunuk

2015-01-01

Multivariate methods in meta-analysis are becoming popular and more accepted in biomedical research despite computational issues in some of the techniques. A number of approaches, both iterative and non-iterative, have been proposed including the multivariate DerSimonian and Laird method by Jackson et al. (2010), which is non-iterative. In this study, we propose an extension of the method by Hartung and Makambi (2002) and Makambi (2001) to multivariate situations. A comparison of the bias and mean square error from a simulation study indicates that, in some circumstances, the proposed approach perform better than the multivariate DerSimonian-Laird approach. An example is presented to demonstrate the application of the proposed approach.

Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

PubMed Central

Song, Junqiang; Leng, Hongze; Lu, Fengshun

2014-01-01

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303

Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

PubMed

Hudson, H M; Ma, J; Green, P

1994-01-01

Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

Validation and application of auxiliary density perturbation theory and non-iterative approximation to coupled-perturbed Kohn-Sham approach for calculation of dipole-quadrupole polarizability

NASA Astrophysics Data System (ADS)

Shedge, Sapana V.; Pal, Sourav; Köster, Andreas M.

2011-07-01

Recently, two non-iterative approaches have been proposed to calculate response properties within density functional theory (DFT). These approaches are auxiliary density perturbation theory (ADPT) and the non-iterative approach to the coupled-perturbed Kohn-Sham (NIA-CPKS) method. Though both methods are non-iterative, they use different techniques to obtain the perturbed Kohn-Sham matrix. In this Letter, for the first time, both of these two independent methods have been used for the calculation of dipole-quadrupole polarizabilities. To validate these methods, three tetrahedral molecules viz., P4,CH4 and adamantane (C10H16) have been used as examples. The comparison with MP2 and CCSD proves the reliability of the methodology.

On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

NASA Technical Reports Server (NTRS)

Brand, J. C.

1985-01-01

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

Iterative methods for elliptic finite element equations on general meshes

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.; Choudhury, Shenaz

1986-01-01

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jing Yanfei, E-mail: yanfeijing@uestc.edu.c; Huang Tingzhu, E-mail: tzhuang@uestc.edu.c; Duan Yong, E-mail: duanyong@yahoo.c

This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods to some extent when applied to the problems and reveal the competitiveness of our recently proposed Lanczos biconjugate A-orthonormalization methods to other classic and popular iterative methods. By the way, experiment results also indicate that application specific preconditioners may be mandatory and required for accelerating convergence.

Edge turbulence effect on ultra-fast swept reflectometry core measurements in tokamak plasmas

NASA Astrophysics Data System (ADS)

Zadvitskiy, G. V.; Heuraux, S.; Lechte, C.; Hacquin, S.; Sabot, R.

2018-02-01

Ultra-fast frequency-swept reflectometry (UFSR) enables one to provide information about the turbulence radial wave-number spectrum and perturbation amplitude with good spatial and temporal resolutions. However, a data interpretation of USFR is quiet tricky. An iterative algorithm to solve this inverse problem was used in past works, Gerbaud (2006 Rev. Sci. Instrum. 77 10E928). For a direct solution, a fast 1D Helmholtz solver was used. Two-dimensional effects are strong and should be taken into account during data interpretation. As 2D full-wave codes are still too time consuming for systematic application, fast 2D approaches based on the Born approximation are of prime interest. Such methods gives good results in the case of small turbulence levels. However in tokamak plasmas, edge turbulence is usually very strong and can distort and broaden the probing beam Sysoeva et al (2015 Nucl. Fusion 55 033016). It was shown that this can change reflectometer phase response from the plasma core. Comparison between 2D full wave computation and the simplified Born approximation was done. The approximated method can provide a right spectral shape, but it is unable to describe a change of the spectral amplitude with an edge turbulence level. Computation for the O-mode wave with the linear density profile in the slab geometry and for realistic Tore-Supra density profile, based on the experimental data turbulence amplitude and spectrum, were performed to investigate the role of strong edge turbulence. It is shown that the spectral peak in the signal amplitude variation spectrum which rises with edge turbulence can be a signature of strong edge turbulence. Moreover, computations for misaligned receiving and emitting antennas were performed. It was found that the signal amplitude variation peak changes its position with a receiving antenna poloidal displacement.

Multiple Revolution Solutions for the Perturbed Lambert Problem using the Method of Particular Solutions and Picard Iteration

NASA Astrophysics Data System (ADS)

Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.

2017-12-01

We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.

Fast projection/backprojection and incremental methods applied to synchrotron light tomographic reconstruction.

PubMed

de Lima, Camila; Salomão Helou, Elias

2018-01-01

Iterative methods for tomographic image reconstruction have the computational cost of each iteration dominated by the computation of the (back)projection operator, which take roughly O(N 3 ) floating point operations (flops) for N × N pixels images. Furthermore, classical iterative algorithms may take too many iterations in order to achieve acceptable images, thereby making the use of these techniques unpractical for high-resolution images. Techniques have been developed in the literature in order to reduce the computational cost of the (back)projection operator to O(N 2 logN) flops. Also, incremental algorithms have been devised that reduce by an order of magnitude the number of iterations required to achieve acceptable images. The present paper introduces an incremental algorithm with a cost of O(N 2 logN) flops per iteration and applies it to the reconstruction of very large tomographic images obtained from synchrotron light illuminated data.

MO-DE-207A-07: Filtered Iterative Reconstruction (FIR) Via Proximal Forward-Backward Splitting: A Synergy of Analytical and Iterative Reconstruction Method for CT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, H

Purpose: This work is to develop a general framework, namely filtered iterative reconstruction (FIR) method, to incorporate analytical reconstruction (AR) method into iterative reconstruction (IR) method, for enhanced CT image quality. Methods: FIR is formulated as a combination of filtered data fidelity and sparsity regularization, and then solved by proximal forward-backward splitting (PFBS) algorithm. As a result, the image reconstruction decouples data fidelity and image regularization with a two-step iterative scheme, during which an AR-projection step updates the filtered data fidelity term, while a denoising solver updates the sparsity regularization term. During the AR-projection step, the image is projected tomore » the data domain to form the data residual, and then reconstructed by certain AR to a residual image which is in turn weighted together with previous image iterate to form next image iterate. Since the eigenvalues of AR-projection operator are close to the unity, PFBS based FIR has a fast convergence. Results: The proposed FIR method is validated in the setting of circular cone-beam CT with AR being FDK and total-variation sparsity regularization, and has improved image quality from both AR and IR. For example, AIR has improved visual assessment and quantitative measurement in terms of both contrast and resolution, and reduced axial and half-fan artifacts. Conclusion: FIR is proposed to incorporate AR into IR, with an efficient image reconstruction algorithm based on PFBS. The CBCT results suggest that FIR synergizes AR and IR with improved image quality and reduced axial and half-fan artifacts. The authors was partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000), and the Shanghai Pujiang Talent Program (#14PJ1404500).« less

Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace.

PubMed

Zhang, Cheng; Lai, Chun-Liang; Pettitt, B Montgomery

The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM and the closely-related multiple Bennett acceptance ratio (MBAR) method can be improved by using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

Improved Savitzky-Golay-method-based fluorescence subtraction algorithm for rapid recovery of Raman spectra.

PubMed

Chen, Kun; Zhang, Hongyuan; Wei, Haoyun; Li, Yan

2014-08-20

In this paper, we propose an improved subtraction algorithm for rapid recovery of Raman spectra that can substantially reduce the computation time. This algorithm is based on an improved Savitzky-Golay (SG) iterative smoothing method, which involves two key novel approaches: (a) the use of the Gauss-Seidel method and (b) the introduction of a relaxation factor into the iterative procedure. By applying a novel successive relaxation (SG-SR) iterative method to the relaxation factor, additional improvement in the convergence speed over the standard Savitzky-Golay procedure is realized. The proposed improved algorithm (the RIA-SG-SR algorithm), which uses SG-SR-based iteration instead of Savitzky-Golay iteration, has been optimized and validated with a mathematically simulated Raman spectrum, as well as experimentally measured Raman spectra from non-biological and biological samples. The method results in a significant reduction in computing cost while yielding consistent rejection of fluorescence and noise for spectra with low signal-to-fluorescence ratios and varied baselines. In the simulation, RIA-SG-SR achieved 1 order of magnitude improvement in iteration number and 2 orders of magnitude improvement in computation time compared with the range-independent background-subtraction algorithm (RIA). Furthermore the computation time of the experimentally measured raw Raman spectrum processing from skin tissue decreased from 6.72 to 0.094 s. In general, the processing of the SG-SR method can be conducted within dozens of milliseconds, which can provide a real-time procedure in practical situations.

Multiscale optical simulation settings: challenging applications handled with an iterative ray-tracing FDTD interface method.

PubMed

Leiner, Claude; Nemitz, Wolfgang; Schweitzer, Susanne; Kuna, Ladislav; Wenzl, Franz P; Hartmann, Paul; Satzinger, Valentin; Sommer, Christian

2016-03-20

We show that with an appropriate combination of two optical simulation techniques-classical ray-tracing and the finite difference time domain method-an optical device containing multiple diffractive and refractive optical elements can be accurately simulated in an iterative simulation approach. We compare the simulation results with experimental measurements of the device to discuss the applicability and accuracy of our iterative simulation procedure.

Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

NASA Astrophysics Data System (ADS)

Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

2017-10-01

This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

Continuous analog of multiplicative algebraic reconstruction technique for computed tomography

NASA Astrophysics Data System (ADS)

Tateishi, Kiyoko; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Kojima, Takeshi; Yoshinaga, Tetsuya

2016-03-01

We propose a hybrid dynamical system as a continuous analog to the block-iterative multiplicative algebraic reconstruction technique (BI-MART), which is a well-known iterative image reconstruction algorithm for computed tomography. The hybrid system is described by a switched nonlinear system with a piecewise smooth vector field or differential equation and, for consistent inverse problems, the convergence of non-negatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem. Namely, we can prove theoretically that a weighted Kullback-Leibler divergence measure can be a common Lyapunov function for the switched system. We show that discretizing the differential equation by using the first-order approximation (Euler's method) based on the geometric multiplicative calculus leads to the same iterative formula of the BI-MART with the scaling parameter as a time-step of numerical discretization. The present paper is the first to reveal that a kind of iterative image reconstruction algorithm is constructed by the discretization of a continuous-time dynamical system for solving tomographic inverse problems. Iterative algorithms with not only the Euler method but also the Runge-Kutta methods of lower-orders applied for discretizing the continuous-time system can be used for image reconstruction. A numerical example showing the characteristics of the discretized iterative methods is presented.

Solving large mixed linear models using preconditioned conjugate gradient iteration.

PubMed

Strandén, I; Lidauer, M

1999-12-01

Continuous evaluation of dairy cattle with a random regression test-day model requires a fast solving method and algorithm. A new computing technique feasible in Jacobi and conjugate gradient based iterative methods using iteration on data is presented. In the new computing technique, the calculations in multiplication of a vector by a matrix were recorded to three steps instead of the commonly used two steps. The three-step method was implemented in a general mixed linear model program that used preconditioned conjugate gradient iteration. Performance of this program in comparison to other general solving programs was assessed via estimation of breeding values using univariate, multivariate, and random regression test-day models. Central processing unit time per iteration with the new three-step technique was, at best, one-third that needed with the old technique. Performance was best with the test-day model, which was the largest and most complex model used. The new program did well in comparison to other general software. Programs keeping the mixed model equations in random access memory required at least 20 and 435% more time to solve the univariate and multivariate animal models, respectively. Computations of the second best iteration on data took approximately three and five times longer for the animal and test-day models, respectively, than did the new program. Good performance was due to fast computing time per iteration and quick convergence to the final solutions. Use of preconditioned conjugate gradient based methods in solving large breeding value problems is supported by our findings.

A heuristic statistical stopping rule for iterative reconstruction in emission tomography.

PubMed

Ben Bouallègue, F; Crouzet, J F; Mariano-Goulart, D

2013-01-01

We propose a statistical stopping criterion for iterative reconstruction in emission tomography based on a heuristic statistical description of the reconstruction process. The method was assessed for MLEM reconstruction. Based on Monte-Carlo numerical simulations and using a perfectly modeled system matrix, our method was compared with classical iterative reconstruction followed by low-pass filtering in terms of Euclidian distance to the exact object, noise, and resolution. The stopping criterion was then evaluated with realistic PET data of a Hoffman brain phantom produced using the GATE platform for different count levels. The numerical experiments showed that compared with the classical method, our technique yielded significant improvement of the noise-resolution tradeoff for a wide range of counting statistics compatible with routine clinical settings. When working with realistic data, the stopping rule allowed a qualitatively and quantitatively efficient determination of the optimal image. Our method appears to give a reliable estimation of the optimal stopping point for iterative reconstruction. It should thus be of practical interest as it produces images with similar or better quality than classical post-filtered iterative reconstruction with a mastered computation time.

A Method to Solve Interior and Exterior Camera Calibration Parameters for Image Resection

NASA Technical Reports Server (NTRS)

Samtaney, Ravi

1999-01-01

An iterative method is presented to solve the internal and external camera calibration parameters, given model target points and their images from one or more camera locations. The direct linear transform formulation was used to obtain a guess for the iterative method, and herein lies one of the strengths of the present method. In all test cases, the method converged to the correct solution. In general, an overdetermined system of nonlinear equations is solved in the least-squares sense. The iterative method presented is based on Newton-Raphson for solving systems of nonlinear algebraic equations. The Jacobian is analytically derived and the pseudo-inverse of the Jacobian is obtained by singular value decomposition.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

Solving coupled groundwater flow systems using a Jacobian Free Newton Krylov method

NASA Astrophysics Data System (ADS)

Mehl, S.

2012-12-01

Jacobian Free Newton Kyrlov (JFNK) methods can have several advantages for simulating coupled groundwater flow processes versus conventional methods. Conventional methods are defined here as those based on an iterative coupling (rather than a direct coupling) and/or that use Picard iteration rather than Newton iteration. In an iterative coupling, the systems are solved separately, coupling information is updated and exchanged between the systems, and the systems are re-solved, etc., until convergence is achieved. Trusted simulators, such as Modflow, are based on these conventional methods of coupling and work well in many cases. An advantage of the JFNK method is that it only requires calculation of the residual vector of the system of equations and thus can make use of existing simulators regardless of how the equations are formulated. This opens the possibility of coupling different process models via augmentation of a residual vector by each separate process, which often requires substantially fewer changes to the existing source code than if the processes were directly coupled. However, appropriate perturbation sizes need to be determined for accurate approximations of the Frechet derivative, which is not always straightforward. Furthermore, preconditioning is necessary for reasonable convergence of the linear solution required at each Kyrlov iteration. Existing preconditioners can be used and applied separately to each process which maximizes use of existing code and robust preconditioners. In this work, iteratively coupled parent-child local grid refinement models of groundwater flow and groundwater flow models with nonlinear exchanges to streams are used to demonstrate the utility of the JFNK approach for Modflow models. Use of incomplete Cholesky preconditioners with various levels of fill are examined on a suite of nonlinear and linear models to analyze the effect of the preconditioner. Comparisons of convergence and computer simulation time are made using conventional iteratively coupled methods and those based on Picard iteration to those formulated with JFNK to gain insights on the types of nonlinearities and system features that make one approach advantageous. Results indicate that nonlinearities associated with stream/aquifer exchanges are more problematic than those resulting from unconfined flow.

Modules and methods for all photonic computing

DOEpatents

Schultz, David R.; Ma, Chao Hung

2001-01-01

A method for all photonic computing, comprising the steps of: encoding a first optical/electro-optical element with a two dimensional mathematical function representing input data; illuminating the first optical/electro-optical element with a collimated beam of light; illuminating a second optical/electro-optical element with light from the first optical/electro-optical element, the second optical/electro-optical element having a characteristic response corresponding to an iterative algorithm useful for solving a partial differential equation; iteratively recirculating the signal through the second optical/electro-optical element with light from the second optical/electro-optical element for a predetermined number of iterations; and, after the predetermined number of iterations, optically and/or electro-optically collecting output data representing an iterative optical solution from the second optical/electro-optical element.

Convergence Results on Iteration Algorithms to Linear Systems

PubMed Central

Wang, Zhuande; Yang, Chuansheng; Yuan, Yubo

2014-01-01

In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods. PMID:24991640

Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

PubMed

Wei, Qinglai; Liu, Derong; Lin, Hanquan

2016-03-01

In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

The two-phase method for finding a great number of eigenpairs of the symmetric or weakly non-symmetric large eigenvalue problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dul, F.A.; Arczewski, K.

1994-03-01

Although it has been stated that [open quotes]an attempt to solve (very large problems) by subspace iterations seems futile[close quotes], we will show that the statement is not true, especially for extremely large eigenproblems. In this paper a new two-phase subspace iteration/Rayleigh quotient/conjugate gradient method for generalized, large, symmetric eigenproblems Ax = [lambda]Bx is presented. It has the ability of solving extremely large eigenproblems, N = 216,000, for example, and finding a large number of leftmost or rightmost eigenpairs, up to 1000 or more. Multiple eigenpairs, even those with multiplicity 100, can be easily found. The use of the proposedmore » method for solving the big full eigenproblems (N [approximately] 10[sup 3]), as well as for large weakly non-symmetric eigenproblems, have been considered also. The proposed method is fully iterative; thus the factorization of matrices ins avoided. The key idea consists in joining two methods: subspace and Rayleigh quotient iterations. The systems of indefinite and almost singular linear equations (a - [sigma]B)x = By are solved by various iterative conjugate gradient method can be used without danger of breaking down due to its property that may be called [open quotes]self-correction towards the eigenvector,[close quotes] discovered recently by us. The use of various preconditioners (SSOR and IC) has also been considered. The main features of the proposed method have been analyzed in detail. Comparisons with other methods, such as, accelerated subspace iteration, Lanczos, Davidson, TLIME, TRACMN, and SRQMCG, are presented. The results of numerical tests for various physical problems (acoustic, vibrations of structures, quantum chemistry) are presented as well. 40 refs., 12 figs., 2 tabs.« less

Hierarchical Coarse-Graining Via a Generalized Yvon-Born Green Framework: Many-Body Correlations, Mappings, and Structural Accuracy

NASA Astrophysics Data System (ADS)

Rudzinski, Joseph F.

Atomically-detailed molecular dynamics simulations have emerged as one of the most powerful theoretic tools for studying complex, condensed-phase systems. Despite their ability to provide incredible molecular insight, these simulations are insufficient for investigating complex biological processes, e.g., protein folding or molecular aggregation, on relevant length and time scales. The increasing scope and sophistication of atomically-detailed models has motivated the development of "hierarchical" approaches, which parameterize a low resolution, coarse-grained (CG) model based on simulations of an atomically-detailed model. The utility of hierarchical CG models depends on their ability to accurately incorporate the correct physics of the underlying model. One approach for ensuring this "consistency" between the models is to parameterize the CG model to reproduce the structural ensemble generated by the high resolution model. The many-body potential of mean force is the proper CG energy function for reproducing all structural distributions of the atomically-detailed model, at the CG level of resolution. However, this CG potential is a configuration-dependent free energy function that is generally too complicated to represent or simulate. The multiscale coarse-graining (MS-CG) method employs a generalized Yvon-Born-Green (g-YBG) relation to directly determine a variationally optimal approximation to the many-body potential of mean force. The MS-CG/g-YBG method provides a convenient and transparent framework for investigating the equilibrium structure of the system, at the CG level of resolution. In this work, we investigate the fundamental limitations and approximations of the MS-CG/g-YBG method. Throughout the work, we propose several theoretic constructs to directly relate the MS-CG/g-YBG method to other popular structure-based CG approaches. We investigate the physical interpretation of the MS-CG/g-YBG correlation matrix, the quantity responsible for disentangling the various contributions to the average force on a CG site. We then employ an iterative extension of the MS-CG/g-YBG method that improves the accuracy of a particular set of low order correlation functions relative to the original MS-CG/g-YBG model. We demonstrate that this method provides a powerful framework for identifying the precise source of error in an MS-CG/g-YBG model. We then propose a method for identifying an optimal CG representation, prior to the development of the CG model. We employ these techniques together to demonstrate that in the cases where the MS-CG/g-YBG method fails to determine an accurate model, a fundamental problem likely exists with the chosen CG representation or interaction set. Additionally, we explicitly demonstrate that while the iterative model successfully improves the accuracy of the low order structure, it does so by distorting the higher order structural correlations relative to the underlying model. Finally, we apply these methods to investigate the utility of the MS-CG/g- YBG method for developing models for systems with complex intramolecular structure. Overall, our results demonstrate the power of the g-YBG framework for developing accurate CG models and for investigating the driving forces of equilibrium structures for complex condensed-phase systems. This work also explicitly motivates future development of bottom-up CG methods and highlights some outstanding problems in the field. iii.

Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection

PubMed Central

2010-01-01

The aim of this study was to compare iterative and direct solvers for estimation of marker effects in genomic selection. One iterative and two direct methods were used: Gauss-Seidel with Residual Update, Cholesky Decomposition and Gentleman-Givens rotations. For resembling different scenarios with respect to number of markers and of genotyped animals, a simulated data set divided into 25 subsets was used. Number of markers ranged from 1,200 to 5,925 and number of animals ranged from 1,200 to 5,865. Methods were also applied to real data comprising 3081 individuals genotyped for 45181 SNPs. Results from simulated data showed that the iterative solver was substantially faster than direct methods for larger numbers of markers. Use of a direct solver may allow for computing (co)variances of SNP effects. When applied to real data, performance of the iterative method varied substantially, depending on the level of ill-conditioning of the coefficient matrix. From results with real data, Gentleman-Givens rotations would be the method of choice in this particular application as it provided an exact solution within a fairly reasonable time frame (less than two hours). It would indeed be the preferred method whenever computer resources allow its use. PMID:21637627

Shading correction assisted iterative cone-beam CT reconstruction

NASA Astrophysics Data System (ADS)

Yang, Chunlin; Wu, Pengwei; Gong, Shutao; Wang, Jing; Lyu, Qihui; Tang, Xiangyang; Niu, Tianye

2017-11-01

Recent advances in total variation (TV) technology enable accurate CT image reconstruction from highly under-sampled and noisy projection data. The standard iterative reconstruction algorithms, which work well in conventional CT imaging, fail to perform as expected in cone beam CT (CBCT) applications, wherein the non-ideal physics issues, including scatter and beam hardening, are more severe. These physics issues result in large areas of shading artifacts and cause deterioration to the piecewise constant property assumed in reconstructed images. To overcome this obstacle, we incorporate a shading correction scheme into low-dose CBCT reconstruction and propose a clinically acceptable and stable three-dimensional iterative reconstruction method that is referred to as the shading correction assisted iterative reconstruction. In the proposed method, we modify the TV regularization term by adding a shading compensation image to the reconstructed image to compensate for the shading artifacts while leaving the data fidelity term intact. This compensation image is generated empirically, using image segmentation and low-pass filtering, and updated in the iterative process whenever necessary. When the compensation image is determined, the objective function is minimized using the fast iterative shrinkage-thresholding algorithm accelerated on a graphic processing unit. The proposed method is evaluated using CBCT projection data of the Catphan© 600 phantom and two pelvis patients. Compared with the iterative reconstruction without shading correction, the proposed method reduces the overall CT number error from around 200 HU to be around 25 HU and increases the spatial uniformity by a factor of 20 percent, given the same number of sparsely sampled projections. A clinically acceptable and stable iterative reconstruction algorithm for CBCT is proposed in this paper. Differing from the existing algorithms, this algorithm incorporates a shading correction scheme into the low-dose CBCT reconstruction and achieves more stable optimization path and more clinically acceptable reconstructed image. The method proposed by us does not rely on prior information and thus is practically attractive to the applications of low-dose CBCT imaging in the clinic.

Development of an iterative reconstruction method to overcome 2D detector low resolution limitations in MLC leaf position error detection for 3D dose verification in IMRT.

PubMed

Visser, R; Godart, J; Wauben, D J L; Langendijk, J A; Van't Veld, A A; Korevaar, E W

2016-05-21

The objective of this study was to introduce a new iterative method to reconstruct multi leaf collimator (MLC) positions based on low resolution ionization detector array measurements and to evaluate its error detection performance. The iterative reconstruction method consists of a fluence model, a detector model and an optimizer. Expected detector response was calculated using a radiotherapy treatment plan in combination with the fluence model and detector model. MLC leaf positions were reconstructed by minimizing differences between expected and measured detector response. The iterative reconstruction method was evaluated for an Elekta SLi with 10.0 mm MLC leafs in combination with the COMPASS system and the MatriXX Evolution (IBA Dosimetry) detector with a spacing of 7.62 mm. The detector was positioned in such a way that each leaf pair of the MLC was aligned with one row of ionization chambers. Known leaf displacements were introduced in various field geometries ranging from  -10.0 mm to 10.0 mm. Error detection performance was tested for MLC leaf position dependency relative to the detector position, gantry angle dependency, monitor unit dependency, and for ten clinical intensity modulated radiotherapy (IMRT) treatment beams. For one clinical head and neck IMRT treatment beam, influence of the iterative reconstruction method on existing 3D dose reconstruction artifacts was evaluated. The described iterative reconstruction method was capable of individual MLC leaf position reconstruction with millimeter accuracy, independent of the relative detector position within the range of clinically applied MU's for IMRT. Dose reconstruction artifacts in a clinical IMRT treatment beam were considerably reduced as compared to the current dose verification procedure. The iterative reconstruction method allows high accuracy 3D dose verification by including actual MLC leaf positions reconstructed from low resolution 2D measurements.

Evaluation of integration methods for hybrid simulation of complex structural systems through collapse

NASA Astrophysics Data System (ADS)

Del Carpio R., Maikol; Hashemi, M. Javad; Mosqueda, Gilberto

2017-10-01

This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration (iterative) and the operator-splitting (non-iterative) is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom (SDOF) cantilever column with replaceable steel coupons that provides repeatable highlynonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1:2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model of a 1:2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.

Calibration and Data Analysis of the MC-130 Air Balance

NASA Technical Reports Server (NTRS)

Booth, Dennis; Ulbrich, N.

2012-01-01

Design, calibration, calibration analysis, and intended use of the MC-130 air balance are discussed. The MC-130 balance is an 8.0 inch diameter force balance that has two separate internal air flow systems and one external bellows system. The manual calibration of the balance consisted of a total of 1854 data points with both unpressurized and pressurized air flowing through the balance. A subset of 1160 data points was chosen for the calibration data analysis. The regression analysis of the subset was performed using two fundamentally different analysis approaches. First, the data analysis was performed using a recently developed extension of the Iterative Method. This approach fits gage outputs as a function of both applied balance loads and bellows pressures while still allowing the application of the iteration scheme that is used with the Iterative Method. Then, for comparison, the axial force was also analyzed using the Non-Iterative Method. This alternate approach directly fits loads as a function of measured gage outputs and bellows pressures and does not require a load iteration. The regression models used by both the extended Iterative and Non-Iterative Method were constructed such that they met a set of widely accepted statistical quality requirements. These requirements lead to reliable regression models and prevent overfitting of data because they ensure that no hidden near-linear dependencies between regression model terms exist and that only statistically significant terms are included. Finally, a comparison of the axial force residuals was performed. Overall, axial force estimates obtained from both methods show excellent agreement as the differences of the standard deviation of the axial force residuals are on the order of 0.001 % of the axial force capacity.

Application of the perturbation iteration method to boundary layer type problems.

PubMed

Pakdemirli, Mehmet

2016-01-01

The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

Spotting the difference in molecular dynamics simulations of biomolecules

NASA Astrophysics Data System (ADS)

Sakuraba, Shun; Kono, Hidetoshi

2016-08-01

Comparing two trajectories from molecular simulations conducted under different conditions is not a trivial task. In this study, we apply a method called Linear Discriminant Analysis with ITERative procedure (LDA-ITER) to compare two molecular simulation results by finding the appropriate projection vectors. Because LDA-ITER attempts to determine a projection such that the projections of the two trajectories do not overlap, the comparison does not suffer from a strong anisotropy, which is an issue in protein dynamics. LDA-ITER is applied to two test cases: the T4 lysozyme protein simulation with or without a point mutation and the allosteric protein PDZ2 domain of hPTP1E with or without a ligand. The projection determined by the method agrees with the experimental data and previous simulations. The proposed procedure, which complements existing methods, is a versatile analytical method that is specialized to find the "difference" between two trajectories.

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Several improvements to the mixed-element USM3D discretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frinks, Neal T.

2016-01-01

Several improvements to the mixed-elementUSM3Ddiscretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Investigation of iterative image reconstruction in three-dimensional optoacoustic tomography

PubMed Central

Wang, Kun; Su, Richard; Oraevsky, Alexander A; Anastasio, Mark A

2012-01-01

Iterative image reconstruction algorithms for optoacoustic tomography (OAT), also known as photoacoustic tomography, have the ability to improve image quality over analytic algorithms due to their ability to incorporate accurate models of the imaging physics, instrument response, and measurement noise. However, to date, there have been few reported attempts to employ advanced iterative image reconstruction algorithms for improving image quality in three-dimensional (3D) OAT. In this work, we implement and investigate two iterative image reconstruction methods for use with a 3D OAT small animal imager: namely, a penalized least-squares (PLS) method employing a quadratic smoothness penalty and a PLS method employing a total variation norm penalty. The reconstruction algorithms employ accurate models of the ultrasonic transducer impulse responses. Experimental data sets are employed to compare the performances of the iterative reconstruction algorithms to that of a 3D filtered backprojection (FBP) algorithm. By use of quantitative measures of image quality, we demonstrate that the iterative reconstruction algorithms can mitigate image artifacts and preserve spatial resolution more effectively than FBP algorithms. These features suggest that the use of advanced image reconstruction algorithms can improve the effectiveness of 3D OAT while reducing the amount of data required for biomedical applications. PMID:22864062

Efficient Iterative Methods Applied to the Solution of Transonic Flows

NASA Astrophysics Data System (ADS)

Wissink, Andrew M.; Lyrintzis, Anastasios S.; Chronopoulos, Anthony T.

1996-02-01

We investigate the use of an inexact Newton's method to solve the potential equations in the transonic regime. As a test case, we solve the two-dimensional steady transonic small disturbance equation. Approximate factorization/ADI techniques have traditionally been employed for implicit solutions of this nonlinear equation. Instead, we apply Newton's method using an exact analytical determination of the Jacobian with preconditioned conjugate gradient-like iterative solvers for solution of the linear systems in each Newton iteration. Two iterative solvers are tested; a block s-step version of the classical Orthomin(k) algorithm called orthogonal s-step Orthomin (OSOmin) and the well-known GMRES method. The preconditioner is a vectorizable and parallelizable version of incomplete LU (ILU) factorization. Efficiency of the Newton-Iterative method on vector and parallel computer architectures is the main issue addressed. In vectorized tests on a single processor of the Cray C-90, the performance of Newton-OSOmin is superior to Newton-GMRES and a more traditional monotone AF/ADI method (MAF) for a variety of transonic Mach numbers and mesh sizes. Newton-GMRES is superior to MAF for some cases. The parallel performance of the Newton method is also found to be very good on multiple processors of the Cray C-90 and on the massively parallel thinking machine CM-5, where very fast execution rates (up to 9 Gflops) are found for large problems.

On a new iterative method for solving linear systems and comparison results

NASA Astrophysics Data System (ADS)

Jing, Yan-Fei; Huang, Ting-Zhu

2008-10-01

In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a different approach is established, which is both theoretically and numerically proven to be better than (at least the same as) Ujevic's. As the presented numerical examples show, in most cases, the convergence rate is more than one and a half that of Ujevic.

A Novel Iterative Scheme for the Very Fast and Accurate Solution of Non-LTE Radiative Transfer Problems

NASA Astrophysics Data System (ADS)

Trujillo Bueno, J.; Fabiani Bendicho, P.

1995-12-01

Iterative schemes based on Gauss-Seidel (G-S) and optimal successive over-relaxation (SOR) iteration are shown to provide a dramatic increase in the speed with which non-LTE radiation transfer (RT) problems can be solved. The convergence rates of these new RT methods are identical to those of upper triangular nonlocal approximate operator splitting techniques, but the computing time per iteration and the memory requirements are similar to those of a local operator splitting method. In addition to these properties, both methods are particularly suitable for multidimensional geometry, since they neither require the actual construction of nonlocal approximate operators nor the application of any matrix inversion procedure. Compared with the currently used Jacobi technique, which is based on the optimal local approximate operator (see Olson, Auer, & Buchler 1986), the G-S method presented here is faster by a factor 2. It gives excellent smoothing of the high-frequency error components, which makes it the iterative scheme of choice for multigrid radiative transfer. This G-S method can also be suitably combined with standard acceleration techniques to achieve even higher performance. Although the convergence rate of the optimal SOR scheme developed here for solving non-LTE RT problems is much higher than G-S, the computing time per iteration is also minimal, i.e., virtually identical to that of a local operator splitting method. While the conventional optimal local operator scheme provides the converged solution after a total CPU time (measured in arbitrary units) approximately equal to the number n of points per decade of optical depth, the time needed by this new method based on the optimal SOR iterations is only √n/2√2. This method is competitive with those that result from combining the above-mentioned Jacobi and G-S schemes with the best acceleration techniques. Contrary to what happens with the local operator splitting strategy currently in use, these novel methods remain effective even under extreme non-LTE conditions in very fine grids.

Non-homogeneous updates for the iterative coordinate descent algorithm

NASA Astrophysics Data System (ADS)

Yu, Zhou; Thibault, Jean-Baptiste; Bouman, Charles A.; Sauer, Ken D.; Hsieh, Jiang

2007-02-01

Statistical reconstruction methods show great promise for improving resolution, and reducing noise and artifacts in helical X-ray CT. In fact, statistical reconstruction seems to be particularly valuable in maintaining reconstructed image quality when the dosage is low and the noise is therefore high. However, high computational cost and long reconstruction times remain as a barrier to the use of statistical reconstruction in practical applications. Among the various iterative methods that have been studied for statistical reconstruction, iterative coordinate descent (ICD) has been found to have relatively low overall computational requirements due to its fast convergence. This paper presents a novel method for further speeding the convergence of the ICD algorithm, and therefore reducing the overall reconstruction time for statistical reconstruction. The method, which we call nonhomogeneous iterative coordinate descent (NH-ICD) uses spatially non-homogeneous updates to speed convergence by focusing computation where it is most needed. Experimental results with real data indicate that the method speeds reconstruction by roughly a factor of two for typical 3D multi-slice geometries.

Matrix completion-based reconstruction for undersampled magnetic resonance fingerprinting data.

PubMed

Doneva, Mariya; Amthor, Thomas; Koken, Peter; Sommer, Karsten; Börnert, Peter

2017-09-01

An iterative reconstruction method for undersampled magnetic resonance fingerprinting data is presented. The method performs the reconstruction entirely in k-space and is related to low rank matrix completion methods. A low dimensional data subspace is estimated from a small number of k-space locations fully sampled in the temporal direction and used to reconstruct the missing k-space samples before MRF dictionary matching. Performing the iterations in k-space eliminates the need for applying a forward and an inverse Fourier transform in each iteration required in previously proposed iterative reconstruction methods for undersampled MRF data. A projection onto the low dimensional data subspace is performed as a matrix multiplication instead of a singular value thresholding typically used in low rank matrix completion, further reducing the computational complexity of the reconstruction. The method is theoretically described and validated in phantom and in-vivo experiments. The quality of the parameter maps can be significantly improved compared to direct matching on undersampled data. Copyright © 2017 Elsevier Inc. All rights reserved.

Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields.

DTIC Science & Technology

perturbation formulas of Groebner (1960) and Alexseev (1961) for the solution of ordinary differential equations. These formulas are generalized and...iteration methods are given, which include the Methods of Picard, Groebner -Knapp, Poincare, Chen, as special cases. Chapter 3 generalizes an iterated

Convergence characteristics of nonlinear vortex-lattice methods for configuration aerodynamics

NASA Technical Reports Server (NTRS)

Seginer, A.; Rusak, Z.; Wasserstrom, E.

1983-01-01

Nonlinear panel methods have no proof for the existence and uniqueness of their solutions. The convergence characteristics of an iterative, nonlinear vortex-lattice method are, therefore, carefully investigated. The effects of several parameters, including (1) the surface-paneling method, (2) an integration method of the trajectories of the wake vortices, (3) vortex-grid refinement, and (4) the initial conditions for the first iteration on the computed aerodynamic coefficients and on the flow-field details are presented. The convergence of the iterative-solution procedure is usually rapid. The solution converges with grid refinement to a constant value, but the final value is not unique and varies with the wing surface-paneling and wake-discretization methods within some range in the vicinity of the experimental result.

Iterative load-balancing method with multigrid level relaxation for particle simulation with short-range interactions

NASA Astrophysics Data System (ADS)

Furuichi, Mikito; Nishiura, Daisuke

2017-10-01

We developed dynamic load-balancing algorithms for Particle Simulation Methods (PSM) involving short-range interactions, such as Smoothed Particle Hydrodynamics (SPH), Moving Particle Semi-implicit method (MPS), and Discrete Element method (DEM). These are needed to handle billions of particles modeled in large distributed-memory computer systems. Our method utilizes flexible orthogonal domain decomposition, allowing the sub-domain boundaries in the column to be different for each row. The imbalances in the execution time between parallel logical processes are treated as a nonlinear residual. Load-balancing is achieved by minimizing the residual within the framework of an iterative nonlinear solver, combined with a multigrid technique in the local smoother. Our iterative method is suitable for adjusting the sub-domain frequently by monitoring the performance of each computational process because it is computationally cheaper in terms of communication and memory costs than non-iterative methods. Numerical tests demonstrated the ability of our approach to handle workload imbalances arising from a non-uniform particle distribution, differences in particle types, or heterogeneous computer architecture which was difficult with previously proposed methods. We analyzed the parallel efficiency and scalability of our method using Earth simulator and K-computer supercomputer systems.

Solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators.

PubMed

Zhao, Jing; Zong, Haili

2018-01-01

In this paper, we propose parallel and cyclic iterative algorithms for solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators. We also combine the process of cyclic and parallel iterative methods and propose two mixed iterative algorithms. Our several algorithms do not need any prior information about the operator norms. Under mild assumptions, we prove weak convergence of the proposed iterative sequences in Hilbert spaces. As applications, we obtain several iterative algorithms to solve the multiple-set split equality problem.

Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

2014-03-01

We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ɛ(r) is close to one everywhere inside the protein. The Gaussian widths σi of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σi. A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua.

Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description.

PubMed

Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

2014-03-14

We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ(i) of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ(i). A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua.

The preconditioned Gauss-Seidel method faster than the SOR method

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Kohno, Toshiyuki; Morimoto, Munenori

2008-09-01

In recent years, a number of preconditioners have been applied to linear systems [A.D. Gunawardena, S.K. Jain, L. Snyder, Modified iterative methods for consistent linear systems, Linear Algebra Appl. 154-156 (1991) 123-143; T. Kohno, H. Kotakemori, H. Niki, M. Usui, Improving modified Gauss-Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997) 113-123; H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner (I+Smax), J. Comput. Appl. Math. 145 (2002) 373-378; H. Kotakemori, H. Niki, N. Okamoto, Accelerated iteration method for Z-matrices, J. Comput. Appl. Math. 75 (1996) 87-97; M. Usui, H. Niki, T.Kohno, Adaptive Gauss-Seidel method for linear systems, Internat. J. Comput. Math. 51(1994)119-125 [10

Sometimes "Newton's Method" Always "Cycles"

ERIC Educational Resources Information Center

Latulippe, Joe; Switkes, Jennifer

2012-01-01

Are there functions for which Newton's method cycles for all non-trivial initial guesses? We construct and solve a differential equation whose solution is a real-valued function that two-cycles under Newton iteration. Higher-order cycles of Newton's method iterates are explored in the complex plane using complex powers of "x." We find a class of…

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

DOE PAGES

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

2015-12-01

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Gauss-Seidel Iterative Method as a Real-Time Pile-Up Solver of Scintillation Pulses

NASA Astrophysics Data System (ADS)

Novak, Roman; Vencelj, Matja¿

2009-12-01

The pile-up rejection in nuclear spectroscopy has been confronted recently by several pile-up correction schemes that compensate for distortions of the signal and subsequent energy spectra artifacts as the counting rate increases. We study here a real-time capability of the event-by-event correction method, which at the core translates to solving many sets of linear equations. Tight time limits and constrained front-end electronics resources make well-known direct solvers inappropriate. We propose a novel approach based on the Gauss-Seidel iterative method, which turns out to be a stable and cost-efficient solution to improve spectroscopic resolution in the front-end electronics. We show the method convergence properties for a class of matrices that emerge in calorimetric processing of scintillation detector signals and demonstrate the ability of the method to support the relevant resolutions. The sole iteration-based error component can be brought below the sliding window induced errors in a reasonable number of iteration steps, thus allowing real-time operation. An area-efficient hardware implementation is proposed that fully utilizes the method's inherent parallelism.

Iterative optimization method for design of quantitative magnetization transfer imaging experiments.

PubMed

Levesque, Ives R; Sled, John G; Pike, G Bruce

2011-09-01

Quantitative magnetization transfer imaging (QMTI) using spoiled gradient echo sequences with pulsed off-resonance saturation can be a time-consuming technique. A method is presented for selection of an optimum experimental design for quantitative magnetization transfer imaging based on the iterative reduction of a discrete sampling of the Z-spectrum. The applicability of the technique is demonstrated for human brain white matter imaging at 1.5 T and 3 T, and optimal designs are produced to target specific model parameters. The optimal number of measurements and the signal-to-noise ratio required for stable parameter estimation are also investigated. In vivo imaging results demonstrate that this optimal design approach substantially improves parameter map quality. The iterative method presented here provides an advantage over free form optimal design methods, in that pragmatic design constraints are readily incorporated. In particular, the presented method avoids clustering and repeated measures in the final experimental design, an attractive feature for the purpose of magnetization transfer model validation. The iterative optimal design technique is general and can be applied to any method of quantitative magnetization transfer imaging. Copyright © 2011 Wiley-Liss, Inc.

Multiple zeros of polynomials

NASA Technical Reports Server (NTRS)

Wood, C. A.

1974-01-01

For polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is, either they fail to converge to some or all of the zeros, or they converge to very bad approximations of the polynomial's zeros. This material introduces two new methods, the greatest common divisor (G.C.D.) method and the repeated greatest common divisor (repeated G.C.D.) method, which are superior methods for numerically approximating the zeros of a polynomial having multiple zeros. These methods were programmed in FORTRAN 4 and comparisons in time and accuracy are given.

Finding the Optimal Guidance for Enhancing Anchored Instruction

ERIC Educational Resources Information Center

Zydney, Janet Mannheimer; Bathke, Arne; Hasselbring, Ted S.

2014-01-01

This study investigated the effect of different methods of guidance with anchored instruction on students' mathematical problem-solving performance. The purpose of this research was to iteratively design a learning environment to find the optimal level of guidance. Two iterations of the software were compared. The first iteration used explicit…

Numerical Grid Generation and Potential Airfoil Analysis and Design

DTIC Science & Technology

1988-01-01

Gauss- Seidel , SOR and ADI iterative methods e JACOBI METHOD In the Jacobi method each new value of a function is computed entirely from old values...preceding iteration and adding the inhomogeneous (boundary condition) term. * GAUSS- SEIDEL METHOD When we compute I in a Jacobi method, we have already...Gauss- Seidel method. Sufficient condition for p convergence of the Gauss- Seidel method is diagonal-dominance of [A].9W e SUCESSIVE OVER-RELAXATION (SOR

Influence of Primary Gage Sensitivities on the Convergence of Balance Load Iterations

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred

2012-01-01

The connection between the convergence of wind tunnel balance load iterations and the existence of the primary gage sensitivities of a balance is discussed. First, basic elements of two load iteration equations that the iterative method uses in combination with results of a calibration data analysis for the prediction of balance loads are reviewed. Then, the connection between the primary gage sensitivities, the load format, the gage output format, and the convergence characteristics of the load iteration equation choices is investigated. A new criterion is also introduced that may be used to objectively determine if the primary gage sensitivity of a balance gage exists. Then, it is shown that both load iteration equations will converge as long as a suitable regression model is used for the analysis of the balance calibration data, the combined influence of non linear terms of the regression model is very small, and the primary gage sensitivities of all balance gages exist. The last requirement is fulfilled, e.g., if force balance calibration data is analyzed in force balance format. Finally, it is demonstrated that only one of the two load iteration equation choices, i.e., the iteration equation used by the primary load iteration method, converges if one or more primary gage sensitivities are missing. This situation may occur, e.g., if force balance calibration data is analyzed in direct read format using the original gage outputs. Data from the calibration of a six component force balance is used to illustrate the connection between the convergence of the load iteration equation choices and the existence of the primary gage sensitivities.

Block Gauss elimination followed by a classical iterative method for the solution of linear systems

NASA Astrophysics Data System (ADS)

Alanelli, Maria; Hadjidimos, Apostolos

2004-02-01

In the last two decades many papers have appeared in which the application of an iterative method for the solution of a linear system is preceded by a step of the Gauss elimination process in the hope that this will increase the rates of convergence of the iterative method. This combination of methods has been proven successful especially when the matrix A of the system is an M-matrix. The purpose of this paper is to extend the idea of one to more Gauss elimination steps, consider other classes of matrices A, e.g., p-cyclic consistently ordered, and generalize and improve the asymptotic convergence rates of some of the methods known so far.

Development of generalized pressure velocity coupling scheme for the analysis of compressible and incompressible combusting flows

NASA Technical Reports Server (NTRS)

Chen, C. P.; Wu, S. T.

1992-01-01

The objective of this investigation has been to develop an algorithm (or algorithms) for the improvement of the accuracy and efficiency of the computer fluid dynamics (CFD) models to study the fundamental physics of combustion chamber flows, which are necessary ultimately for the design of propulsion systems such as SSME and STME. During this three year study (May 19, 1978 - May 18, 1992), a unique algorithm was developed for all speed flows. This newly developed algorithm basically consists of two pressure-based algorithms (i.e. PISOC and MFICE). This PISOC is a non-iterative scheme and the FICE is an iterative scheme where PISOC has the characteristic advantages on low and high speed flows and the modified FICE has shown its efficiency and accuracy to compute the flows in the transonic region. A new algorithm is born from a combination of these two algorithms. This newly developed algorithm has general application in both time-accurate and steady state flows, and also was tested extensively for various flow conditions, such as turbulent flows, chemically reacting flows, and multiphase flows.

Modified conjugate gradient method for diagonalizing large matrices.

PubMed

Jie, Quanlin; Liu, Dunhuan

2003-11-01

We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

NASA Astrophysics Data System (ADS)

Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2018-06-01

In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

DOE PAGES

Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; ...

2012-01-01

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less

Efficient iterative methods applied to the solution of transonic flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wissink, A.M.; Lyrintzis, A.S.; Chronopoulos, A.T.

1996-02-01

We investigate the use of an inexact Newton`s method to solve the potential equations in the transonic regime. As a test case, we solve the two-dimensional steady transonic small disturbance equation. Approximate factorization/ADI techniques have traditionally been employed for implicit solutions of this nonlinear equation. Instead, we apply Newton`s method using an exact analytical determination of the Jacobian with preconditioned conjugate gradient-like iterative solvers for solution of the linear systems in each Newton iteration. Two iterative solvers are tested; a block s-step version of the classical Orthomin(k) algorithm called orthogonal s-step Orthomin (OSOmin) and the well-known GIVIRES method. The preconditionermore » is a vectorizable and parallelizable version of incomplete LU (ILU) factorization. Efficiency of the Newton-Iterative method on vector and parallel computer architectures is the main issue addressed. In vectorized tests on a single processor of the Cray C-90, the performance of Newton-OSOmin is superior to Newton-GMRES and a more traditional monotone AF/ADI method (MAF) for a variety of transonic Mach numbers and mesh sizes. Newton- GIVIRES is superior to MAF for some cases. The parallel performance of the Newton method is also found to be very good on multiple processors of the Cray C-90 and on the massively parallel thinking machine CM-5, where very fast execution rates (up to 9 Gflops) are found for large problems. 38 refs., 14 figs., 7 tabs.« less

Sparse magnetic resonance imaging reconstruction using the bregman iteration

NASA Astrophysics Data System (ADS)

Lee, Dong-Hoon; Hong, Cheol-Pyo; Lee, Man-Woo

2013-01-01

Magnetic resonance imaging (MRI) reconstruction needs many samples that are sequentially sampled by using phase encoding gradients in a MRI system. It is directly connected to the scan time for the MRI system and takes a long time. Therefore, many researchers have studied ways to reduce the scan time, especially, compressed sensing (CS), which is used for sparse images and reconstruction for fewer sampling datasets when the k-space is not fully sampled. Recently, an iterative technique based on the bregman method was developed for denoising. The bregman iteration method improves on total variation (TV) regularization by gradually recovering the fine-scale structures that are usually lost in TV regularization. In this study, we studied sparse sampling image reconstruction using the bregman iteration for a low-field MRI system to improve its temporal resolution and to validate its usefulness. The image was obtained with a 0.32 T MRI scanner (Magfinder II, SCIMEDIX, Korea) with a phantom and an in-vivo human brain in a head coil. We applied random k-space sampling, and we determined the sampling ratios by using half the fully sampled k-space. The bregman iteration was used to generate the final images based on the reduced data. We also calculated the root-mean-square-error (RMSE) values from error images that were obtained using various numbers of bregman iterations. Our reconstructed images using the bregman iteration for sparse sampling images showed good results compared with the original images. Moreover, the RMSE values showed that the sparse reconstructed phantom and the human images converged to the original images. We confirmed the feasibility of sparse sampling image reconstruction methods using the bregman iteration with a low-field MRI system and obtained good results. Although our results used half the sampling ratio, this method will be helpful in increasing the temporal resolution at low-field MRI systems.

Comparison of different eigensolvers for calculating vibrational spectra using low-rank, sum-of-product basis functions

NASA Astrophysics Data System (ADS)

Leclerc, Arnaud; Thomas, Phillip S.; Carrington, Tucker

2017-08-01

Vibrational spectra and wavefunctions of polyatomic molecules can be calculated at low memory cost using low-rank sum-of-product (SOP) decompositions to represent basis functions generated using an iterative eigensolver. Using a SOP tensor format does not determine the iterative eigensolver. The choice of the interative eigensolver is limited by the need to restrict the rank of the SOP basis functions at every stage of the calculation. We have adapted, implemented and compared different reduced-rank algorithms based on standard iterative methods (block-Davidson algorithm, Chebyshev iteration) to calculate vibrational energy levels and wavefunctions of the 12-dimensional acetonitrile molecule. The effect of using low-rank SOP basis functions on the different methods is analysed and the numerical results are compared with those obtained with the reduced rank block power method. Relative merits of the different algorithms are presented, showing that the advantage of using a more sophisticated method, although mitigated by the use of reduced-rank SOP functions, is noticeable in terms of CPU time.

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

NASA Technical Reports Server (NTRS)

Gaonkar, Gopal H.; Achar, N. S.

1992-01-01

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Multilevel acceleration of scattering-source iterations with application to electron transport

DOE PAGES

Drumm, Clif; Fan, Wesley

2017-08-18

Acceleration/preconditioning strategies available in the SCEPTRE radiation transport code are described. A flexible transport synthetic acceleration (TSA) algorithm that uses a low-order discrete-ordinates (S N) or spherical-harmonics (P N) solve to accelerate convergence of a high-order S N source-iteration (SI) solve is described. Convergence of the low-order solves can be further accelerated by applying off-the-shelf incomplete-factorization or algebraic-multigrid methods. Also available is an algorithm that uses a generalized minimum residual (GMRES) iterative method rather than SI for convergence, using a parallel sweep-based solver to build up a Krylov subspace. TSA has been applied as a preconditioner to accelerate the convergencemore » of the GMRES iterations. The methods are applied to several problems involving electron transport and problems with artificial cross sections with large scattering ratios. These methods were compared and evaluated by considering material discontinuities and scattering anisotropy. Observed accelerations obtained are highly problem dependent, but speedup factors around 10 have been observed in typical applications.« less

Evaluating user reputation in online rating systems via an iterative group-based ranking method

NASA Astrophysics Data System (ADS)

Gao, Jian; Zhou, Tao

2017-05-01

Reputation is a valuable asset in online social lives and it has drawn increased attention. Due to the existence of noisy ratings and spamming attacks, how to evaluate user reputation in online rating systems is especially significant. However, most of the previous ranking-based methods either follow a debatable assumption or have unsatisfied robustness. In this paper, we propose an iterative group-based ranking method by introducing an iterative reputation-allocation process into the original group-based ranking method. More specifically, the reputation of users is calculated based on the weighted sizes of the user rating groups after grouping all users by their rating similarities, and the high reputation users' ratings have larger weights in dominating the corresponding user rating groups. The reputation of users and the user rating group sizes are iteratively updated until they become stable. Results on two real data sets with artificial spammers suggest that the proposed method has better performance than the state-of-the-art methods and its robustness is considerably improved comparing with the original group-based ranking method. Our work highlights the positive role of considering users' grouping behaviors towards a better online user reputation evaluation.

Computation of nonlinear ultrasound fields using a linearized contrast source method.

PubMed

Verweij, Martin D; Demi, Libertario; van Dongen, Koen W A

2013-08-01

Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic (lossy, inhomogeneous) media. The Iterative Nonlinear Contrast Source (INCS) method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods. This full wave method considers the nonlinear term of the Westervelt equation as a nonlinear contrast source, and solves the equivalent integral equation via the Neumann iterative solution. Recently, the method has been extended with a contrast source that accounts for spatially varying attenuation. The current paper addresses the problem that the Neumann iterative solution converges badly for strong contrast sources. The remedy is linearization of the nonlinear contrast source, combined with application of more advanced methods for solving the resulting integral equation. Numerical results show that linearization in combination with a Bi-Conjugate Gradient Stabilized method allows the INCS method to deal with fairly strong, inhomogeneous attenuation, while the error due to the linearization can be eliminated by restarting the iterative scheme.

Compensation for the phase-type spatial periodic modulation of the near-field beam at 1053 nm

NASA Astrophysics Data System (ADS)

Gao, Yaru; Liu, Dean; Yang, Aihua; Tang, Ruyu; Zhu, Jianqiang

2017-10-01

A phase-only spatial light modulator is used to provide and compensate for the spatial periodic modulation (SPM) of the near-field beam at the near infrared at 1053nm wavelength with an improved iterative weight-based method. The transmission characteristics of the incident beam has been changed by a spatial light modulator (SLM) to shape the spatial intensity of the output beam. The propagation and reverse propagation of the light in free space are two important processes in the iterative process. The based theory is the beam angular spectrum transmit formula (ASTF) and the principle of the iterative weight-based method. We have made two improvements to the originally proposed iterative weight-based method. We select the appropriate parameter by choosing the minimum value of the output beam contrast degree and use the MATLAB built-in angle function to acquire the corresponding phase of the light wave function. The required phase that compensates for the intensity distribution of the incident SPM beam is iterated by this algorithm, which can decrease the magnitude of the SPM of the intensity on the observation plane. The experimental results show that the phase-type SPM of the near-field beam is subject to a certain restriction. We have also analyzed some factors that make the results imperfect. The experiment results verifies the possible applicability of this iterative weight-based method to compensate for the SPM of the near-field beam.

An iterative method for the localization of a neutron source in a large box (container)

NASA Astrophysics Data System (ADS)

Dubinski, S.; Presler, O.; Alfassi, Z. B.

2007-12-01

The localization of an unknown neutron source in a bulky box was studied. This can be used for the inspection of cargo, to prevent the smuggling of neutron and α emitters. It is important to localize the source from the outside for safety reasons. Source localization is necessary in order to determine its activity. A previous study showed that, by using six detectors, three on each parallel face of the box (460×420×200 mm 3), the location of the source can be found with an average distance of 4.73 cm between the real source position and the calculated one and a maximal distance of about 9 cm. Accuracy was improved in this work by applying an iteration method based on four fixed detectors and the successive iteration of positioning of an external calibrating source. The initial positioning of the calibrating source is the plane of detectors 1 and 2. This method finds the unknown source location with an average distance of 0.78 cm between the real source position and the calculated one and a maximum distance of 3.66 cm for the same box. For larger boxes, localization without iterations requires an increase in the number of detectors, while localization with iterations requires only an increase in the number of iteration steps. In addition to source localization, two methods for determining the activity of the unknown source were also studied.

A comparison between progressive extension method (PEM) and iterative method (IM) for magnetic field extrapolations in the solar atmosphere

NASA Technical Reports Server (NTRS)

Wu, S. T.; Sun, M. T.; Sakurai, Takashi

1990-01-01

This paper presents a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, viz the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized, and the accuracy and numerical instability are discussed. On the basis of this investigation, it is claimed that the two methods do resemble each other qualitatively.

Computational trigonometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gustafson, K.

1994-12-31

By means of the author`s earlier theory of antieigenvalues and antieigenvectors, a new computational approach to iterative methods is presented. This enables an explicit trigonometric understanding of iterative convergence and provides new insights into the sharpness of error bounds. Direct applications to Gradient descent, Conjugate gradient, GCR(k), Orthomin, CGN, GMRES, CGS, and other matrix iterative schemes will be given.

Effect of contrast enhancement prior to iteration procedure on image correction for soft x-ray projection microscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jamsranjav, Erdenetogtokh, E-mail: ja.erdenetogtokh@gmail.com; Shiina, Tatsuo, E-mail: shiina@faculity.chiba-u.jp; Kuge, Kenichi

2016-01-28

Soft X-ray microscopy is well recognized as a powerful tool of high-resolution imaging for hydrated biological specimens. Projection type of it has characteristics of easy zooming function, simple optical layout and so on. However the image is blurred by the diffraction of X-rays, leading the spatial resolution to be worse. In this study, the blurred images have been corrected by an iteration procedure, i.e., Fresnel and inverse Fresnel transformations repeated. This method was confirmed by earlier studies to be effective. Nevertheless it was not enough to some images showing too low contrast, especially at high magnification. In the present study,more » we tried a contrast enhancement method to make the diffraction fringes clearer prior to the iteration procedure. The method was effective to improve the images which were not successful by iteration procedure only.« less

A fast method to emulate an iterative POCS image reconstruction algorithm.

PubMed

Zeng, Gengsheng L

2017-10-01

Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering. The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter. The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms. © 2017 American Association of Physicists in Medicine.

Generalized Pattern Search methods for a class of nonsmooth optimization problems with structure

NASA Astrophysics Data System (ADS)

Bogani, C.; Gasparo, M. G.; Papini, A.

2009-07-01

We propose a Generalized Pattern Search (GPS) method to solve a class of nonsmooth minimization problems, where the set of nondifferentiability is included in the union of known hyperplanes and, therefore, is highly structured. Both unconstrained and linearly constrained problems are considered. At each iteration the set of poll directions is enforced to conform to the geometry of both the nondifferentiability set and the boundary of the feasible region, near the current iterate. This is the key issue to guarantee the convergence of certain subsequences of iterates to points which satisfy first-order optimality conditions. Numerical experiments on some classical problems validate the method.

Harmonics analysis of the ITER poloidal field converter based on a piecewise method

NASA Astrophysics Data System (ADS)

Xudong, WANG; Liuwei, XU; Peng, FU; Ji, LI; Yanan, WU

2017-12-01

Poloidal field (PF) converters provide controlled DC voltage and current to PF coils. The many harmonics generated by the PF converter flow into the power grid and seriously affect power systems and electric equipment. Due to the complexity of the system, the traditional integral operation in Fourier analysis is complicated and inaccurate. This paper presents a piecewise method to calculate the harmonics of the ITER PF converter. The relationship between the grid input current and the DC output current of the ITER PF converter is deduced. The grid current is decomposed into the sum of some simple functions. By calculating simple function harmonics based on the piecewise method, the harmonics of the PF converter under different operation modes are obtained. In order to examine the validity of the method, a simulation model is established based on Matlab/Simulink and a relevant experiment is implemented in the ITER PF integration test platform. Comparative results are given. The calculated results are found to be consistent with simulation and experiment. The piecewise method is proved correct and valid for calculating the system harmonics.

RF Pulse Design using Nonlinear Gradient Magnetic Fields

PubMed Central

Kopanoglu, Emre; Constable, R. Todd

2014-01-01

Purpose An iterative k-space trajectory and radio-frequency (RF) pulse design method is proposed for Excitation using Nonlinear Gradient Magnetic fields (ENiGMa). Theory and Methods The spatial encoding functions (SEFs) generated by nonlinear gradient fields (NLGFs) are linearly dependent in Cartesian-coordinates. Left uncorrected, this may lead to flip-angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a Matching-Pursuit algorithm, and the RF pulse is designed using a Conjugate-Gradient algorithm. Three variants of the proposed approach are given: the full-algorithm, a computationally-cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. Results The method is compared to other iterative (Matching-Pursuit and Conjugate Gradient) and non-iterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity significantly. Conclusion An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. PMID:25203286

Iterative electromagnetic Born inversion applied to earth conductivity imaging

NASA Astrophysics Data System (ADS)

Alumbaugh, D. L.

1993-08-01

This thesis investigates the use of a fast imaging technique to deduce the spatial conductivity distribution in the earth from low frequency (less than 1 MHz), cross well electromagnetic (EM) measurements. The theory embodied in this work is the extension of previous strategies and is based on the Born series approximation to solve both the forward and inverse problem. Nonlinear integral equations are employed to derive the series expansion which accounts for the scattered magnetic fields that are generated by inhomogeneities embedded in either a homogenous or a layered earth. A sinusoidally oscillating, vertically oriented magnetic dipole is employed as a source, and it is assumed that the scattering bodies are azimuthally symmetric about the source dipole axis. The use of this model geometry reduces the 3-D vector problem to a more manageable 2-D scalar form. The validity of the cross well EM method is tested by applying the imaging scheme to two sets of field data. Images of the data collected at the Devine, Texas test site show excellent correlation with the well logs. Unfortunately there is a drift error present in the data that limits the accuracy of the results. A more complete set of data collected at the Richmond field station in Richmond, California demonstrates that cross well EM can be successfully employed to monitor the position of an injected mass of salt water. Both the data and the resulting images clearly indicate the plume migrates toward the north-northwest. The plausibility of these conclusions is verified by applying the imaging code to synthetic data generated by a 3-D sheet model.

A comparison of several methods of solving nonlinear regression groundwater flow problems

USGS Publications Warehouse

Cooley, Richard L.

1985-01-01

Computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear-regression steady state groundwater flow problems. The fastest methods were the Marquardt and quasi-linearization methods, which required almost identical computer times and numbers of iterations; the next fastest was the quasi-Newton method, and last was the Fletcher-Reeves method, which did not converge in 100 iterations for two of the problems. The fastest method per iteration was the Fletcher-Reeves method, and this was followed closely by the quasi-Newton method. The Marquardt and quasi-linearization methods were slower. For all four methods the speed per iteration was directly related to the number of parameters in the model. However, this effect was much more pronounced for the Marquardt and quasi-linearization methods than for the other two. Hence the quasi-Newton (and perhaps Fletcher-Reeves) method might be more efficient than either the Marquardt or quasi-linearization methods if the number of parameters in a particular model were large, although this remains to be proven. The Marquardt method required somewhat less central memory than the quasi-linearization metilod for three of the four problems. For all four problems the quasi-Newton method required roughly two thirds to three quarters of the memory required by the Marquardt method, and the Fletcher-Reeves method required slightly less memory than the quasi-Newton method. Memory requirements were not excessive for any of the four methods.

Adaptively Tuned Iterative Low Dose CT Image Denoising

PubMed Central

Hashemi, SayedMasoud; Paul, Narinder S.; Beheshti, Soosan; Cobbold, Richard S. C.

2015-01-01

Improving image quality is a critical objective in low dose computed tomography (CT) imaging and is the primary focus of CT image denoising. State-of-the-art CT denoising algorithms are mainly based on iterative minimization of an objective function, in which the performance is controlled by regularization parameters. To achieve the best results, these should be chosen carefully. However, the parameter selection is typically performed in an ad hoc manner, which can cause the algorithms to converge slowly or become trapped in a local minimum. To overcome these issues a noise confidence region evaluation (NCRE) method is used, which evaluates the denoising residuals iteratively and compares their statistics with those produced by additive noise. It then updates the parameters at the end of each iteration to achieve a better match to the noise statistics. By combining NCRE with the fundamentals of block matching and 3D filtering (BM3D) approach, a new iterative CT image denoising method is proposed. It is shown that this new denoising method improves the BM3D performance in terms of both the mean square error and a structural similarity index. Moreover, simulations and patient results show that this method preserves the clinically important details of low dose CT images together with a substantial noise reduction. PMID:26089972

Anderson acceleration and application to the three-temperature energy equations

NASA Astrophysics Data System (ADS)

An, Hengbin; Jia, Xiaowei; Walker, Homer F.

2017-10-01

The Anderson acceleration method is an algorithm for accelerating the convergence of fixed-point iterations, including the Picard method. Anderson acceleration was first proposed in 1965 and, for some years, has been used successfully to accelerate the convergence of self-consistent field iterations in electronic-structure computations. Recently, the method has attracted growing attention in other application areas and among numerical analysts. Compared with a Newton-like method, an advantage of Anderson acceleration is that there is no need to form the Jacobian matrix. Thus the method is easy to implement. In this paper, an Anderson-accelerated Picard method is employed to solve the three-temperature energy equations, which are a type of strong nonlinear radiation-diffusion equations. Two strategies are used to improve the robustness of the Anderson acceleration method. One strategy is to adjust the iterates when necessary to satisfy the physical constraint. Another strategy is to monitor and, if necessary, reduce the matrix condition number of the least-squares problem in the Anderson-acceleration implementation so that numerical stability can be guaranteed. Numerical results show that the Anderson-accelerated Picard method can solve the three-temperature energy equations efficiently. Compared with the Picard method without acceleration, Anderson acceleration can reduce the number of iterations by at least half. A comparison between a Jacobian-free Newton-Krylov method, the Picard method, and the Anderson-accelerated Picard method is conducted in this paper.

Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

NASA Astrophysics Data System (ADS)

Lavery, N.; Taylor, C.

1999-07-01

Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright

Improved evaluation of optical depth components from Langley plot data

NASA Technical Reports Server (NTRS)

Biggar, S. F.; Gellman, D. I.; Slater, P. N.

1990-01-01

A simple, iterative procedure to determine the optical depth components of the extinction optical depth measured by a solar radiometer is presented. Simulated data show that the iterative procedure improves the determination of the exponent of a Junge law particle size distribution. The determination of the optical depth due to aerosol scattering is improved as compared to a method which uses only two points from the extinction data. The iterative method was used to determine spectral optical depth components for June 11-13, 1988 during the MAC III experiment.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Walker, H. F.

1975-01-01

A general iterative procedure is given for determining the consistent maximum likelihood estimates of normal distributions. In addition, a local maximum of the log-likelihood function, Newtons's method, a method of scoring, and modifications of these procedures are discussed.

A study on Marangoni convection by the variational iteration method

NASA Astrophysics Data System (ADS)

Karaoǧlu, Onur; Oturanç, Galip

2012-09-01

In this paper, we will consider the use of the variational iteration method and Padé approximant for finding approximate solutions for a Marangoni convection induced flow over a free surface due to an imposed temperature gradient. The solutions are compared with the numerical (fourth-order Runge Kutta) solutions.

Iteration of ultrasound aberration correction methods

NASA Astrophysics Data System (ADS)

Maasoey, Svein-Erik; Angelsen, Bjoern; Varslot, Trond

2004-05-01

Aberration in ultrasound medical imaging is usually modeled by time-delay and amplitude variations concentrated on the transmitting/receiving array. This filter process is here denoted a TDA filter. The TDA filter is an approximation to the physical aberration process, which occurs over an extended part of the human body wall. Estimation of the TDA filter, and performing correction on transmit and receive, has proven difficult. It has yet to be shown that this method works adequately for severe aberration. Estimation of the TDA filter can be iterated by retransmitting a corrected signal and re-estimate until a convergence criterion is fulfilled (adaptive imaging). Two methods for estimating time-delay and amplitude variations in receive signals from random scatterers have been developed. One method correlates each element signal with a reference signal. The other method use eigenvalue decomposition of the receive cross-spectrum matrix, based upon a receive energy-maximizing criterion. Simulations of iterating aberration correction with a TDA filter have been investigated to study its convergence properties. A weak and strong human-body wall model generated aberration. Both emulated the human abdominal wall. Results after iteration improve aberration correction substantially, and both estimation methods converge, even for the case of strong aberration.

Flexible Method for Developing Tactics, Techniques, and Procedures for Future Capabilities

DTIC Science & Technology

2009-02-01

levels of ability, military experience, and motivation, (b) number and type of significant events, and (c) other sources of natural variability...research has developed a number of specific instruments designed to aid in this process. Second, the iterative, feed-forward nature of the method allows...FLEX method), but still lack the structured KE approach and iterative, feed-forward nature of the FLEX method. To facilitate decision making

An iterative method for the Helmholtz equation

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1983-01-01

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

An iterative method for obtaining the optimum lightning location on a spherical surface

NASA Technical Reports Server (NTRS)

Chao, Gao; Qiming, MA

1991-01-01

A brief introduction to the basic principles of an eigen method used to obtain the optimum source location of lightning is presented. The location of the optimum source is obtained by using multiple direction finders (DF's) on a spherical surface. An improvement of this method, which takes the distance of source-DF's as a constant, is presented. It is pointed out that using a weight factor of signal strength is not the most ideal method because of the inexact inverse signal strength-distance relation and the inaccurate signal amplitude. An iterative calculation method is presented using the distance from the source to the DF as a weight factor. This improved method has higher accuracy and needs only a little more calculation time. Some computer simulations for a 4DF system are presented to show the improvement of location through use of the iterative method.

On iterative algorithms for quantitative photoacoustic tomography in the radiative transport regime

NASA Astrophysics Data System (ADS)

Wang, Chao; Zhou, Tie

2017-11-01

In this paper, we present a numerical reconstruction method for quantitative photoacoustic tomography (QPAT), based on the radiative transfer equation (RTE), which models light propagation more accurately than diffusion approximation (DA). We investigate the reconstruction of absorption coefficient and scattering coefficient of biological tissues. An improved fixed-point iterative method to retrieve the absorption coefficient, given the scattering coefficient, is proposed for its cheap computational cost; the convergence of this method is also proved. The Barzilai-Borwein (BB) method is applied to retrieve two coefficients simultaneously. Since the reconstruction of optical coefficients involves the solutions of original and adjoint RTEs in the framework of optimization, an efficient solver with high accuracy is developed from Gao and Zhao (2009 Transp. Theory Stat. Phys. 38 149-92). Simulation experiments illustrate that the improved fixed-point iterative method and the BB method are competitive methods for QPAT in the relevant cases.

An analytically iterative method for solving problems of cosmic-ray modulation

NASA Astrophysics Data System (ADS)

Kolesnyk, Yuriy L.; Bobik, Pavol; Shakhov, Boris A.; Putis, Marian

2017-09-01

The development of an analytically iterative method for solving steady-state as well as unsteady-state problems of cosmic-ray (CR) modulation is proposed. Iterations for obtaining the solutions are constructed for the spherically symmetric form of the CR propagation equation. The main solution of the considered problem consists of the zero-order solution that is obtained during the initial iteration and amendments that may be obtained by subsequent iterations. The finding of the zero-order solution is based on the CR isotropy during propagation in the space, whereas the anisotropy is taken into account when finding the next amendments. To begin with, the method is applied to solve the problem of CR modulation where the diffusion coefficient κ and the solar wind speed u are constants with an Local Interstellar Spectra (LIS) spectrum. The solution obtained with two iterations was compared with an analytical solution and with numerical solutions. Finally, solutions that have only one iteration for two problems of CR modulation with u = constant and the same form of LIS spectrum were obtained and tested against numerical solutions. For the first problem, κ is proportional to the momentum of the particle p, so it has the form κ = k0η, where η =p/m_0c. For the second problem, the diffusion coefficient is given in the form κ = k0βη, where β =v/c is the particle speed relative to the speed of light. There was a good matching of the obtained solutions with the numerical solutions as well as with the analytical solution for the problem where κ = constant.

Nonnegative least-squares image deblurring: improved gradient projection approaches

NASA Astrophysics Data System (ADS)

Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.

2010-02-01

The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.

Physics Model-Based Scatter Correction in Multi-Source Interior Computed Tomography.

PubMed

Gong, Hao; Li, Bin; Jia, Xun; Cao, Guohua

2018-02-01

Multi-source interior computed tomography (CT) has a great potential to provide ultra-fast and organ-oriented imaging at low radiation dose. However, X-ray cross scattering from multiple simultaneously activated X-ray imaging chains compromises imaging quality. Previously, we published two hardware-based scatter correction methods for multi-source interior CT. Here, we propose a software-based scatter correction method, with the benefit of no need for hardware modifications. The new method is based on a physics model and an iterative framework. The physics model was derived analytically, and was used to calculate X-ray scattering signals in both forward direction and cross directions in multi-source interior CT. The physics model was integrated to an iterative scatter correction framework to reduce scatter artifacts. The method was applied to phantom data from both Monte Carlo simulations and physical experimentation that were designed to emulate the image acquisition in a multi-source interior CT architecture recently proposed by our team. The proposed scatter correction method reduced scatter artifacts significantly, even with only one iteration. Within a few iterations, the reconstructed images fast converged toward the "scatter-free" reference images. After applying the scatter correction method, the maximum CT number error at the region-of-interests (ROIs) was reduced to 46 HU in numerical phantom dataset and 48 HU in physical phantom dataset respectively, and the contrast-noise-ratio at those ROIs increased by up to 44.3% and up to 19.7%, respectively. The proposed physics model-based iterative scatter correction method could be useful for scatter correction in dual-source or multi-source CT.

Unsupervised iterative detection of land mines in highly cluttered environments.

PubMed

Batman, Sinan; Goutsias, John

2003-01-01

An unsupervised iterative scheme is proposed for land mine detection in heavily cluttered scenes. This scheme is based on iterating hybrid multispectral filters that consist of a decorrelating linear transform coupled with a nonlinear morphological detector. Detections extracted from the first pass are used to improve results in subsequent iterations. The procedure stops after a predetermined number of iterations. The proposed scheme addresses several weaknesses associated with previous adaptations of morphological approaches to land mine detection. Improvement in detection performance, robustness with respect to clutter inhomogeneities, a completely unsupervised operation, and computational efficiency are the main highlights of the method. Experimental results reveal excellent performance.

Analysis of Anderson Acceleration on a Simplified Neutronics/Thermal Hydraulics System

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toth, Alex; Kelley, C. T.; Slattery, Stuart R

ABSTRACT A standard method for solving coupled multiphysics problems in light water reactors is Picard iteration, which sequentially alternates between solving single physics applications. This solution approach is appealing due to simplicity of implementation and the ability to leverage existing software packages to accurately solve single physics applications. However, there are several drawbacks in the convergence behavior of this method; namely slow convergence and the necessity of heuristically chosen damping factors to achieve convergence in many cases. Anderson acceleration is a method that has been seen to be more robust and fast converging than Picard iteration for many problems, withoutmore » significantly higher cost per iteration or complexity of implementation, though its effectiveness in the context of multiphysics coupling is not well explored. In this work, we develop a one-dimensional model simulating the coupling between the neutron distribution and fuel and coolant properties in a single fuel pin. We show that this model generally captures the convergence issues noted in Picard iterations which couple high-fidelity physics codes. We then use this model to gauge potential improvements with regard to rate of convergence and robustness from utilizing Anderson acceleration as an alternative to Picard iteration.« less

Development of an efficient multigrid method for the NEM form of the multigroup neutron diffusion equation

NASA Astrophysics Data System (ADS)

Al-Chalabi, Rifat M. Khalil

1997-09-01

Development of an improvement to the computational efficiency of the existing nested iterative solution strategy of the Nodal Exapansion Method (NEM) nodal based neutron diffusion code NESTLE is presented. The improvement in the solution strategy is the result of developing a multilevel acceleration scheme that does not suffer from the numerical stalling associated with a number of iterative solution methods. The acceleration scheme is based on the multigrid method, which is specifically adapted for incorporation into the NEM nonlinear iterative strategy. This scheme optimizes the computational interplay between the spatial discretization and the NEM nonlinear iterative solution process through the use of the multigrid method. The combination of the NEM nodal method, calculation of the homogenized, neutron nodal balance coefficients (i.e. restriction operator), efficient underlying smoothing algorithm (power method of NESTLE), and the finer mesh reconstruction algorithm (i.e. prolongation operator), all operating on a sequence of coarser spatial nodes, constitutes the multilevel acceleration scheme employed in this research. Two implementations of the multigrid method into the NESTLE code were examined; the Imbedded NEM Strategy and the Imbedded CMFD Strategy. The main difference in implementation between the two methods is that in the Imbedded NEM Strategy, the NEM solution is required at every MG level. Numerical tests have shown that the Imbedded NEM Strategy suffers from divergence at coarse- grid levels, hence all the results for the different benchmarks presented here were obtained using the Imbedded CMFD Strategy. The novelties in the developed MG method are as follows: the formulation of the restriction and prolongation operators, and the selection of the relaxation method. The restriction operator utilizes a variation of the reactor physics, consistent homogenization technique. The prolongation operator is based upon a variant of the pin power reconstruction methodology. The relaxation method, which is the power method, utilizes a constant coefficient matrix within the NEM non-linear iterative strategy. The choice of the MG nesting within the nested iterative strategy enables the incorporation of other non-linear effects with no additional coding effort. In addition, if an eigenvalue problem is being solved, it remains an eigenvalue problem at all grid levels, simplifying coding implementation. The merit of the developed MG method was tested by incorporating it into the NESTLE iterative solver, and employing it to solve four different benchmark problems. In addition to the base cases, three different sensitivity studies are performed, examining the effects of number of MG levels, homogenized coupling coefficients correction (i.e. restriction operator), and fine-mesh reconstruction algorithm (i.e. prolongation operator). The multilevel acceleration scheme developed in this research provides the foundation for developing adaptive multilevel acceleration methods for steady-state and transient NEM nodal neutron diffusion equations. (Abstract shortened by UMI.)

Anderson Acceleration for Fixed-Point Iterations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walker, Homer F.

The purpose of this grant was to support research on acceleration methods for fixed-point iterations, with applications to computational frameworks and simulation problems that are of interest to DOE.

Modeling design iteration in product design and development and its solution by a novel artificial bee colony algorithm.

PubMed

Chen, Tinggui; Xiao, Renbin

2014-01-01

Due to fierce market competition, how to improve product quality and reduce development cost determines the core competitiveness of enterprises. However, design iteration generally causes increases of product cost and delays of development time as well, so how to identify and model couplings among tasks in product design and development has become an important issue for enterprises to settle. In this paper, the shortcomings existing in WTM model are discussed and tearing approach as well as inner iteration method is used to complement the classic WTM model. In addition, the ABC algorithm is also introduced to find out the optimal decoupling schemes. In this paper, firstly, tearing approach and inner iteration method are analyzed for solving coupled sets. Secondly, a hybrid iteration model combining these two technologies is set up. Thirdly, a high-performance swarm intelligence algorithm, artificial bee colony, is adopted to realize problem-solving. Finally, an engineering design of a chemical processing system is given in order to verify its reasonability and effectiveness.

C–IBI: Targeting cumulative coordination within an iterative protocol to derive coarse-grained models of (multi-component) complex fluids

DOE PAGES

de Oliveira, Tiago E.; Netz, Paulo A.; Kremer, Kurt; ...

2016-05-03

We present a coarse-graining strategy that we test for aqueous mixtures. The method uses pair-wise cumulative coordination as a target function within an iterative Boltzmann inversion (IBI) like protocol. We name this method coordination iterative Boltzmann inversion (C–IBI). While the underlying coarse-grained model is still structure based and, thus, preserves pair-wise solution structure, our method also reproduces solvation thermodynamics of binary and/or ternary mixtures. In addition, we observe much faster convergence within C–IBI compared to IBI. To validate the robustness, we apply C–IBI to study test cases of solvation thermodynamics of aqueous urea and a triglycine solvation in aqueous urea.

Multiple solution of linear algebraic systems by an iterative method with recomputed preconditioner in the analysis of microstrip structures

NASA Astrophysics Data System (ADS)

Ahunov, Roman R.; Kuksenko, Sergey P.; Gazizov, Talgat R.

2016-06-01

A multiple solution of linear algebraic systems with dense matrix by iterative methods is considered. To accelerate the process, the recomputing of the preconditioning matrix is used. A priory condition of the recomputing based on change of the arithmetic mean of the current solution time during the multiple solution is proposed. To confirm the effectiveness of the proposed approach, the numerical experiments using iterative methods BiCGStab and CGS for four different sets of matrices on two examples of microstrip structures are carried out. For solution of 100 linear systems the acceleration up to 1.6 times, compared to the approach without recomputing, is obtained.

Iterative-method performance evaluation for multiple vectors associated with a large-scale sparse matrix

NASA Astrophysics Data System (ADS)

Imamura, Seigo; Ono, Kenji; Yokokawa, Mitsuo

2016-07-01

Ensemble computing, which is an instance of capacity computing, is an effective computing scenario for exascale parallel supercomputers. In ensemble computing, there are multiple linear systems associated with a common coefficient matrix. We improve the performance of iterative solvers for multiple vectors by solving them at the same time, that is, by solving for the product of the matrices. We implemented several iterative methods and compared their performance. The maximum performance on Sparc VIIIfx was 7.6 times higher than that of a naïve implementation. Finally, to deal with the different convergence processes of linear systems, we introduced a control method to eliminate the calculation of already converged vectors.

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fahimian, Benjamin P.; Zhao Yunzhe; Huang Zhifeng

Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). Inmore » each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Results: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. Conclusions: A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.« less

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction

PubMed Central

Fahimian, Benjamin P.; Zhao, Yunzhe; Huang, Zhifeng; Fung, Russell; Mao, Yu; Zhu, Chun; Khatonabadi, Maryam; DeMarco, John J.; Osher, Stanley J.; McNitt-Gray, Michael F.; Miao, Jianwei

2013-01-01

Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Results: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. Conclusions: A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method. PMID:23464329

Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule

NASA Astrophysics Data System (ADS)

Jin, Qinian; Wang, Wei

2018-03-01

The iteratively regularized Gauss-Newton method is one of the most prominent regularization methods for solving nonlinear ill-posed inverse problems when the data is corrupted by noise. In order to produce a useful approximate solution, this iterative method should be terminated properly. The existing a priori and a posteriori stopping rules require accurate information on the noise level, which may not be available or reliable in practical applications. In this paper we propose a heuristic selection rule for this regularization method, which requires no information on the noise level. By imposing certain conditions on the noise, we derive a posteriori error estimates on the approximate solutions under various source conditions. Furthermore, we establish a convergence result without using any source condition. Numerical results are presented to illustrate the performance of our heuristic selection rule.

Single-step reinitialization and extending algorithms for level-set based multi-phase flow simulations

NASA Astrophysics Data System (ADS)

Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-12-01

We propose efficient single-step formulations for reinitialization and extending algorithms, which are critical components of level-set based interface-tracking methods. The level-set field is reinitialized with a single-step (non iterative) "forward tracing" algorithm. A minimum set of cells is defined that describes the interface, and reinitialization employs only data from these cells. Fluid states are extrapolated or extended across the interface by a single-step "backward tracing" algorithm. Both algorithms, which are motivated by analogy to ray-tracing, avoid multiple block-boundary data exchanges that are inevitable for iterative reinitialization and extending approaches within a parallel-computing environment. The single-step algorithms are combined with a multi-resolution conservative sharp-interface method and validated by a wide range of benchmark test cases. We demonstrate that the proposed reinitialization method achieves second-order accuracy in conserving the volume of each phase. The interface location is invariant to reapplication of the single-step reinitialization. Generally, we observe smaller absolute errors than for standard iterative reinitialization on the same grid. The computational efficiency is higher than for the standard and typical high-order iterative reinitialization methods. We observe a 2- to 6-times efficiency improvement over the standard method for serial execution. The proposed single-step extending algorithm, which is commonly employed for assigning data to ghost cells with ghost-fluid or conservative interface interaction methods, shows about 10-times efficiency improvement over the standard method while maintaining same accuracy. Despite their simplicity, the proposed algorithms offer an efficient and robust alternative to iterative reinitialization and extending methods for level-set based multi-phase simulations.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

NASA Astrophysics Data System (ADS)

Koleva, M. N.

2011-11-01

In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

Domain decomposition preconditioners for the spectral collocation method

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio; Sacchilandriani, Giovanni

1988-01-01

Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.

Single image super-resolution based on approximated Heaviside functions and iterative refinement

PubMed Central

Wang, Xin-Yu; Huang, Ting-Zhu; Deng, Liang-Jian

2018-01-01

One method of solving the single-image super-resolution problem is to use Heaviside functions. This has been done previously by making a binary classification of image components as “smooth” and “non-smooth”, describing these with approximated Heaviside functions (AHFs), and iteration including l1 regularization. We now introduce a new method in which the binary classification of image components is extended to different degrees of smoothness and non-smoothness, these components being represented by various classes of AHFs. Taking into account the sparsity of the non-smooth components, their coefficients are l1 regularized. In addition, to pick up more image details, the new method uses an iterative refinement for the residuals between the original low-resolution input and the downsampled resulting image. Experimental results showed that the new method is superior to the original AHF method and to four other published methods. PMID:29329298

Construction, classification and parametrization of complex Hadamard matrices

NASA Astrophysics Data System (ADS)

Szöllősi, Ferenc

To improve the design of nuclear systems, high-fidelity neutron fluxes are required. Leadership-class machines provide platforms on which very large problems can be solved. Computing such fluxes efficiently requires numerical methods with good convergence properties and algorithms that can scale to hundreds of thousands of cores. Many 3-D deterministic transport codes are decomposable in space and angle only, limiting them to tens of thousands of cores. Most codes rely on methods such as Gauss Seidel for fixed source problems and power iteration for eigenvalue problems, which can be slow to converge for challenging problems like those with highly scattering materials or high dominance ratios. Three methods have been added to the 3-D SN transport code Denovo that are designed to improve convergence and enable the full use of cutting-edge computers. The first is a multigroup Krylov solver that converges more quickly than Gauss Seidel and parallelizes the code in energy such that Denovo can use hundreds of thousand of cores effectively. The second is Rayleigh quotient iteration (RQI), an old method applied in a new context. This eigenvalue solver finds the dominant eigenvalue in a mathematically optimal way and should converge in fewer iterations than power iteration. RQI creates energy-block-dense equations that the new Krylov solver treats efficiently. However, RQI can have convergence problems because it creates poorly conditioned systems. This can be overcome with preconditioning. The third method is a multigrid-in-energy preconditioner. The preconditioner takes advantage of the new energy decomposition because the grids are in energy rather than space or angle. The preconditioner greatly reduces iteration count for many problem types and scales well in energy. It also allows RQI to be successful for problems it could not solve otherwise. The methods added to Denovo accomplish the goals of this work. They converge in fewer iterations than traditional methods and enable the use of hundreds of thousands of cores. Each method can be used individually, with the multigroup Krylov solver and multigrid-in-energy preconditioner being particularly successful on their own. The largest benefit, though, comes from using these methods in concert.

A non-iterative twin image elimination method with two in-line digital holograms

NASA Astrophysics Data System (ADS)

Kim, Jongwu; Lee, Heejung; Jeon, Philjun; Kim, Dug Young

2018-02-01

We propose a simple non-iterative in-line holographic measurement method which can effectively eliminate a twin image in digital holographic 3D imaging. It is shown that a twin image can be effectively eliminated with only two measured holograms by using a simple numerical propagation algorithm and arithmetic calculations.

A Probabilistic Collocation Based Iterative Kalman Filter for Landfill Data Assimilation

NASA Astrophysics Data System (ADS)

Qiang, Z.; Zeng, L.; Wu, L.

2016-12-01

Due to the strong spatial heterogeneity of landfill, uncertainty is ubiquitous in gas transport process in landfill. To accurately characterize the landfill properties, the ensemble Kalman filter (EnKF) has been employed to assimilate the measurements, e.g., the gas pressure. As a Monte Carlo (MC) based method, the EnKF usually requires a large ensemble size, which poses a high computational cost for large scale problems. In this work, we propose a probabilistic collocation based iterative Kalman filter (PCIKF) to estimate permeability in a liquid-gas coupling model. This method employs polynomial chaos expansion (PCE) to represent and propagate the uncertainties of model parameters and states, and an iterative form of Kalman filter to assimilate the current gas pressure data. To further reduce the computation cost, the functional ANOVA (analysis of variance) decomposition is conducted, and only the first order ANOVA components are remained for PCE. Illustrated with numerical case studies, this proposed method shows significant superiority in computation efficiency compared with the traditional MC based iterative EnKF. The developed method has promising potential in reliable prediction and management of landfill gas production.

Parallel iterative solution for h and p approximations of the shallow water equations

USGS Publications Warehouse

Barragy, E.J.; Walters, R.A.

1998-01-01

A p finite element scheme and parallel iterative solver are introduced for a modified form of the shallow water equations. The governing equations are the three-dimensional shallow water equations. After a harmonic decomposition in time and rearrangement, the resulting equations are a complex Helmholz problem for surface elevation, and a complex momentum equation for the horizontal velocity. Both equations are nonlinear and the resulting system is solved using the Picard iteration combined with a preconditioned biconjugate gradient (PBCG) method for the linearized subproblems. A subdomain-based parallel preconditioner is developed which uses incomplete LU factorization with thresholding (ILUT) methods within subdomains, overlapping ILUT factorizations for subdomain boundaries and under-relaxed iteration for the resulting block system. The method builds on techniques successfully applied to linear elements by introducing ordering and condensation techniques to handle uniform p refinement. The combined methods show good performance for a range of p (element order), h (element size), and N (number of processors). Performance and scalability results are presented for a field scale problem where up to 512 processors are used. ?? 1998 Elsevier Science Ltd. All rights reserved.

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

NASA Astrophysics Data System (ADS)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

Error analysis applied to several inversion techniques used for the retrieval of middle atmospheric constituents from limb-scanning MM-wave spectroscopic measurements

NASA Technical Reports Server (NTRS)

Puliafito, E.; Bevilacqua, R.; Olivero, J.; Degenhardt, W.

1992-01-01

The formal retrieval error analysis of Rodgers (1990) allows the quantitative determination of such retrieval properties as measurement error sensitivity, resolution, and inversion bias. This technique was applied to five numerical inversion techniques and two nonlinear iterative techniques used for the retrieval of middle atmospheric constituent concentrations from limb-scanning millimeter-wave spectroscopic measurements. It is found that the iterative methods have better vertical resolution, but are slightly more sensitive to measurement error than constrained matrix methods. The iterative methods converge to the exact solution, whereas two of the matrix methods under consideration have an explicit constraint, the sensitivity of the solution to the a priori profile. Tradeoffs of these retrieval characteristics are presented.

An improved 3D MoF method based on analytical partial derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2016-12-01

MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

Strongly Coupled Fluid-Body Dynamics in the Immersed Boundary Projection Method

NASA Astrophysics Data System (ADS)

Wang, Chengjie; Eldredge, Jeff D.

2014-11-01

A computational algorithm is developed to simulate dynamically coupled interaction between fluid and rigid bodies. The basic computational framework is built upon a multi-domain immersed boundary method library, whirl, developed in previous work. In this library, the Navier-Stokes equations for incompressible flow are solved on a uniform Cartesian grid by the vorticity-based immersed boundary projection method of Colonius and Taira. A solver for the dynamics of rigid-body systems is also included. The fluid and rigid-body solvers are strongly coupled with an iterative approach based on the block Gauss-Seidel method. Interfacial force, with its intimate connection with the Lagrange multipliers used in the fluid solver, is used as the primary iteration variable. Relaxation, developed from a stability analysis of the iterative scheme, is used to achieve convergence in only 2-4 iterations per time step. Several two- and three-dimensional numerical tests are conducted to validate and demonstrate the method, including flapping of flexible wings, self-excited oscillations of a system of linked plates and three-dimensional propulsion of flexible fluked tail. This work has been supported by AFOSR, under Award FA9550-11-1-0098.

Analytic Evolution of Singular Distribution Amplitudes in QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tandogan Kunkel, Asli

2014-08-01

Distribution amplitudes (DAs) are the basic functions that contain information about the quark momentum. DAs are necessary to describe hard exclusive processes in quantum chromodynamics. We describe a method of analytic evolution of DAs that have singularities such as nonzero values at the end points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a at (constant) DA, antisymmetric at DA, and then use the method for evolution of the two-photon generalized distribution amplitude. Our approach to DA evolution has advantages over the standardmore » method of expansion in Gegenbauer polynomials [1, 2] and over a straightforward iteration of an initial distribution with evolution kernel. Expansion in Gegenbauer polynomials requires an infinite number of terms in order to accurately reproduce functions in the vicinity of singular points. Straightforward iteration of an initial distribution produces logarithmically divergent terms at each iteration. In our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve. Afterwards, in order to get precise results, only one or two iterations are needed.« less

Conjugate gradient coupled with multigrid for an indefinite problem

NASA Technical Reports Server (NTRS)

Gozani, J.; Nachshon, A.; Turkel, E.

1984-01-01

An iterative algorithm for the Helmholtz equation is presented. This scheme was based on the preconditioned conjugate gradient method for the normal equations. The preconditioning is one cycle of a multigrid method for the discrete Laplacian. The smoothing algorithm is red-black Gauss-Seidel and is constructed so it is a symmetric operator. The total number of iterations needed by the algorithm is independent of h. By varying the number of grids, the number of iterations depends only weakly on k when k(3)h(2) is constant. Comparisons with a SSOR preconditioner are presented.

Iterative method of construction of a bifurcation diagram of autorotation motions for a system with one degree of freedom

NASA Astrophysics Data System (ADS)

Klimina, L. A.

2018-05-01

The modification of the Picard approach is suggested that is targeted to the construction of a bifurcation diagram of 2π -periodic motions of mechanical system with a cylindrical phase space. Each iterative step is based on principles of averaging and energy balance similar to the Poincare-Pontryagin approach. If the iterative procedure converges, it provides the periodic trajectory of the system depending on the bifurcation parameter of the model. The method is applied to describe self-sustained rotations in the model of an aerodynamic pendulum.

Optimized iterative decoding method for TPC coded CPM

NASA Astrophysics Data System (ADS)

Ma, Yanmin; Lai, Penghui; Wang, Shilian; Xie, Shunqin; Zhang, Wei

2018-05-01

Turbo Product Code (TPC) coded Continuous Phase Modulation (CPM) system (TPC-CPM) has been widely used in aeronautical telemetry and satellite communication. This paper mainly investigates the improvement and optimization on the TPC-CPM system. We first add the interleaver and deinterleaver to the TPC-CPM system, and then establish an iterative system to iteratively decode. However, the improved system has a poor convergence ability. To overcome this issue, we use the Extrinsic Information Transfer (EXIT) analysis to find the optimal factors for the system. The experiments show our method is efficient to improve the convergence performance.

An Efficient Algorithm for Perturbed Orbit Integration Combining Analytical Continuation and Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Elgohary, T.; Kim, D.; Turner, J.; Junkins, J.

2014-09-01

Several methods exist for integrating the motion in high order gravity fields. Some recent methods use an approximate starting orbit, and an efficient method is needed for generating warm starts that account for specific low order gravity approximations. By introducing two scalar Lagrange-like invariants and employing Leibniz product rule, the perturbed motion is integrated by a novel recursive formulation. The Lagrange-like invariants allow exact arbitrary order time derivatives. Restricting attention to the perturbations due to the zonal harmonics J2 through J6, we illustrate an idea. The recursively generated vector-valued time derivatives for the trajectory are used to develop a continuation series-based solution for propagating position and velocity. Numerical comparisons indicate performance improvements of ~ 70X over existing explicit Runge-Kutta methods while maintaining mm accuracy for the orbit predictions. The Modified Chebyshev Picard Iteration (MCPI) is an iterative path approximation method to solve nonlinear ordinary differential equations. The MCPI utilizes Picard iteration with orthogonal Chebyshev polynomial basis functions to recursively update the states. The key advantages of the MCPI are as follows: 1) Large segments of a trajectory can be approximated by evaluating the forcing function at multiple nodes along the current approximation during each iteration. 2) It can readily handle general gravity perturbations as well as non-conservative forces. 3) Parallel applications are possible. The Picard sequence converges to the solution over large time intervals when the forces are continuous and differentiable. According to the accuracy of the starting solutions, however, the MCPI may require significant number of iterations and function evaluations compared to other integrators. In this work, we provide an efficient methodology to establish good starting solutions from the continuation series method; this warm start improves the performance of the MCPI significantly and will likely be useful for other applications where efficiently computed approximate orbit solutions are needed.

Data-driven Green's function retrieval and application to imaging with multidimensional deconvolution

NASA Astrophysics Data System (ADS)

Broggini, Filippo; Wapenaar, Kees; van der Neut, Joost; Snieder, Roel

2014-01-01

An iterative method is presented that allows one to retrieve the Green's function originating from a virtual source located inside a medium using reflection data measured only at the acquisition surface. In addition to the reflection response, an estimate of the travel times corresponding to the direct arrivals is required. However, no detailed information about the heterogeneities in the medium is needed. The iterative scheme generalizes the Marchenko equation for inverse scattering to the seismic reflection problem. To give insight in the mechanism of the iterative method, its steps for a simple layered medium are analyzed using physical arguments based on the stationary phase method. The retrieved Green's wavefield is shown to correctly contain the multiples due to the inhomogeneities present in the medium. Additionally, a variant of the iterative scheme enables decomposition of the retrieved wavefield into its downgoing and upgoing components. These wavefields then enable creation of a ghost-free image of the medium with either cross correlation or multidimensional deconvolution, presenting an advantage over standard prestack migration.

LDPC-based iterative joint source-channel decoding for JPEG2000.

PubMed

Pu, Lingling; Wu, Zhenyu; Bilgin, Ali; Marcellin, Michael W; Vasic, Bane

2007-02-01

A framework is proposed for iterative joint source-channel decoding of JPEG2000 codestreams. At the encoder, JPEG2000 is used to perform source coding with certain error-resilience (ER) modes, and LDPC codes are used to perform channel coding. During decoding, the source decoder uses the ER modes to identify corrupt sections of the codestream and provides this information to the channel decoder. Decoding is carried out jointly in an iterative fashion. Experimental results indicate that the proposed method requires fewer iterations and improves overall system performance.

Application of a dual-resolution voxelization scheme to compressed-sensing (CS)-based iterative reconstruction in digital tomosynthesis (DTS)

NASA Astrophysics Data System (ADS)

Park, S. Y.; Kim, G. A.; Cho, H. S.; Park, C. K.; Lee, D. Y.; Lim, H. W.; Lee, H. W.; Kim, K. S.; Kang, S. Y.; Park, J. E.; Kim, W. S.; Jeon, D. H.; Je, U. K.; Woo, T. H.; Oh, J. E.

2018-02-01

In recent digital tomosynthesis (DTS), iterative reconstruction methods are often used owing to the potential to provide multiplanar images of superior image quality to conventional filtered-backprojection (FBP)-based methods. However, they require enormous computational cost in the iterative process, which has still been an obstacle to put them to practical use. In this work, we propose a new DTS reconstruction method incorporated with a dual-resolution voxelization scheme in attempt to overcome these difficulties, in which the voxels outside a small region-of-interest (ROI) containing target diagnosis are binned by 2 × 2 × 2 while the voxels inside the ROI remain unbinned. We considered a compressed-sensing (CS)-based iterative algorithm with a dual-constraint strategy for more accurate DTS reconstruction. We implemented the proposed algorithm and performed a systematic simulation and experiment to demonstrate its viability. Our results indicate that the proposed method seems to be effective for reducing computational cost considerably in iterative DTS reconstruction, keeping the image quality inside the ROI not much degraded. A binning size of 2 × 2 × 2 required only about 31.9% computational memory and about 2.6% reconstruction time, compared to those for no binning case. The reconstruction quality was evaluated in terms of the root-mean-square error (RMSE), the contrast-to-noise ratio (CNR), and the universal-quality index (UQI).

Iterated unscented Kalman filter for phase unwrapping of interferometric fringes.

PubMed

Xie, Xianming

2016-08-22

A fresh phase unwrapping algorithm based on iterated unscented Kalman filter is proposed to estimate unambiguous unwrapped phase of interferometric fringes. This method is the result of combining an iterated unscented Kalman filter with a robust phase gradient estimator based on amended matrix pencil model, and an efficient quality-guided strategy based on heap sort. The iterated unscented Kalman filter that is one of the most robust methods under the Bayesian theorem frame in non-linear signal processing so far, is applied to perform simultaneously noise suppression and phase unwrapping of interferometric fringes for the first time, which can simplify the complexity and the difficulty of pre-filtering procedure followed by phase unwrapping procedure, and even can remove the pre-filtering procedure. The robust phase gradient estimator is used to efficiently and accurately obtain phase gradient information from interferometric fringes, which is needed for the iterated unscented Kalman filtering phase unwrapping model. The efficient quality-guided strategy is able to ensure that the proposed method fast unwraps wrapped pixels along the path from the high-quality area to the low-quality area of wrapped phase images, which can greatly improve the efficiency of phase unwrapping. Results obtained from synthetic data and real data show that the proposed method can obtain better solutions with an acceptable time consumption, with respect to some of the most used algorithms.

Using the surface panel method to predict the steady performance of ducted propellers

NASA Astrophysics Data System (ADS)

Cai, Hao-Peng; Su, Yu-Min; Li, Xin; Shen, Hai-Long

2009-12-01

A new numerical method was developed for predicting the steady hydrodynamic performance of ducted propellers. A potential based surface panel method was applied both to the duct and the propeller, and the interaction between them was solved by an induced velocity potential iterative method. Compared with the induced velocity iterative method, the method presented can save programming and calculating time. Numerical results for a JD simplified ducted propeller series showed that the method presented is effective for predicting the steady hydrodynamic performance of ducted propellers.

Numerical Model of Multiple Scattering and Emission from Layering Snowpack for Microwave Remote Sensing

NASA Astrophysics Data System (ADS)

Jin, Y.; Liang, Z.

2002-12-01

The vector radiative transfer (VRT) equation is an integral-deferential equation to describe multiple scattering, absorption and transmission of four Stokes parameters in random scatter media. From the integral formal solution of VRT equation, the lower order solutions, such as the first-order scattering for a layer medium or the second order scattering for a half space, can be obtained. The lower order solutions are usually good at low frequency when high-order scattering is negligible. It won't be feasible to continue iteration for obtaining high order scattering solution because too many folds integration would be involved. In the space-borne microwave remote sensing, for example, the DMSP (Defense Meterological Satellite Program) SSM/I (Special Sensor Microwave/Imager) employed seven channels of 19, 22, 37 and 85GHz. Multiple scattering from the terrain surfaces such as snowpack cannot be neglected at these channels. The discrete ordinate and eigen-analysis method has been studied to take into account for multiple scattering and applied to remote sensing of atmospheric precipitation, snowpack etc. Snowpack was modeled as a layer of dense spherical particles, and the VRT for a layer of uniformly dense spherical particles has been numerically studied by the discrete ordinate method. However, due to surface melting and refrozen crusts, the snowpack undergoes stratifying to form inhomegeneous profiles of the ice grain size, fractional volume and physical temperature etc. It becomes necessary to study multiple scattering and emission from stratified snowpack of dense ice grains. But, the discrete ordinate and eigen-analysis method cannot be simply applied to multi-layers model, because numerically solving a set of multi-equations of VRT is difficult. Stratifying the inhomogeneous media into multi-slabs and employing the first order Mueller matrix of each thin slab, this paper developed an iterative method to derive high orders scattering solutions of whole scatter media. High order scattering and emission from inhomogeneous stratifying media of dense spherical particles are numerically obtained. The brightness temperature at low frequency such as 5.3 GHz without high order scattering and at SSM/I channels with high order scattering are obtained. This approach is also compared with the conventional discrete ordinate method for an uniform layer model. Numerical simulation for inhomogeneous snowpack is also compared with the measurements of microwave remote sensing.

An Accurate Method for Measuring Airplane-Borne Conformal Antenna's Radar Cross Section

NASA Astrophysics Data System (ADS)

Guo, Shuxia; Zhang, Lei; Wang, Yafeng; Hu, Chufeng

2016-09-01

The airplane-borne conformal antenna attaches itself tightly with the airplane skin, so the conventional measurement method cannot determine the contribution of the airplane-borne conformal antenna to its radar cross section (RCS). This paper uses the 2D microwave imaging to isolate and extract the distribution of the reflectivity of the airplane-borne conformal antenna. It obtains the 2D spatial spectra of the conformal antenna through the wave spectral transform between the 2D spatial image and the 2D spatial spectrum. After the interpolation from the rectangular coordinate domain to the polar coordinate domain, the spectral domain data for the variation of the scatter of the conformal antenna with frequency and angle is obtained. The experimental results show that the measurement method proposed in this paper greatly enhances the airplane-borne conformal antenna's RCS measurement accuracy, essentially eliminates the influences caused by the airplane skin and more accurately reveals the airplane-borne conformal antenna's RCS scatter properties.

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction.

PubMed

Fahimian, Benjamin P; Zhao, Yunzhe; Huang, Zhifeng; Fung, Russell; Mao, Yu; Zhu, Chun; Khatonabadi, Maryam; DeMarco, John J; Osher, Stanley J; McNitt-Gray, Michael F; Miao, Jianwei

2013-03-01

A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.

The solution of linear systems of equations with a structural analysis code on the NAS CRAY-2

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Overman, Andrea L.

1988-01-01

Two methods for solving linear systems of equations on the NAS Cray-2 are described. One is a direct method; the other is an iterative method. Both methods exploit the architecture of the Cray-2, particularly the vectorization, and are aimed at structural analysis applications. To demonstrate and evaluate the methods, they were installed in a finite element structural analysis code denoted the Computational Structural Mechanics (CSM) Testbed. A description of the techniques used to integrate the two solvers into the Testbed is given. Storage schemes, memory requirements, operation counts, and reformatting procedures are discussed. Finally, results from the new methods are compared with results from the initial Testbed sparse Choleski equation solver for three structural analysis problems. The new direct solvers described achieve the highest computational rates of the methods compared. The new iterative methods are not able to achieve as high computation rates as the vectorized direct solvers but are best for well conditioned problems which require fewer iterations to converge to the solution.

An Automated Baseline Correction Method Based on Iterative Morphological Operations.

PubMed

Chen, Yunliang; Dai, Liankui

2018-05-01

Raman spectra usually suffer from baseline drift caused by fluorescence or other reasons. Therefore, baseline correction is a necessary and crucial step that must be performed before subsequent processing and analysis of Raman spectra. An automated baseline correction method based on iterative morphological operations is proposed in this work. The method can adaptively determine the structuring element first and then gradually remove the spectral peaks during iteration to get an estimated baseline. Experiments on simulated data and real-world Raman data show that the proposed method is accurate, fast, and flexible for handling different kinds of baselines in various practical situations. The comparison of the proposed method with some state-of-the-art baseline correction methods demonstrates its advantages over the existing methods in terms of accuracy, adaptability, and flexibility. Although only Raman spectra are investigated in this paper, the proposed method is hopefully to be used for the baseline correction of other analytical instrumental signals, such as IR spectra and chromatograms.

Three dimensional iterative beam propagation method for optical waveguide devices

NASA Astrophysics Data System (ADS)

Ma, Changbao; Van Keuren, Edward

2006-10-01

The finite difference beam propagation method (FD-BPM) is an effective model for simulating a wide range of optical waveguide structures. The classical FD-BPMs are based on the Crank-Nicholson scheme, and in tridiagonal form can be solved using the Thomas method. We present a different type of algorithm for 3-D structures. In this algorithm, the wave equation is formulated into a large sparse matrix equation which can be solved using iterative methods. The simulation window shifting scheme and threshold technique introduced in our earlier work are utilized to overcome the convergence problem of iterative methods for large sparse matrix equation and wide-angle simulations. This method enables us to develop higher-order 3-D wide-angle (WA-) BPMs based on Pade approximant operators and the multistep method, which are commonly used in WA-BPMs for 2-D structures. Simulations using the new methods will be compared to the analytical results to assure its effectiveness and applicability.

SU-E-I-33: Initial Evaluation of Model-Based Iterative CT Reconstruction Using Standard Image Quality Phantoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gingold, E; Dave, J

2014-06-01

Purpose: The purpose of this study was to compare a new model-based iterative reconstruction with existing reconstruction methods (filtered backprojection and basic iterative reconstruction) using quantitative analysis of standard image quality phantom images. Methods: An ACR accreditation phantom (Gammex 464) and a CATPHAN600 phantom were scanned using 3 routine clinical acquisition protocols (adult axial brain, adult abdomen, and pediatric abdomen) on a Philips iCT system. Each scan was acquired using default conditions and 75%, 50% and 25% dose levels. Images were reconstructed using standard filtered backprojection (FBP), conventional iterative reconstruction (iDose4) and a prototype model-based iterative reconstruction (IMR). Phantom measurementsmore » included CT number accuracy, contrast to noise ratio (CNR), modulation transfer function (MTF), low contrast detectability (LCD), and noise power spectrum (NPS). Results: The choice of reconstruction method had no effect on CT number accuracy, or MTF (p<0.01). The CNR of a 6 HU contrast target was improved by 1–67% with iDose4 relative to FBP, while IMR improved CNR by 145–367% across all protocols and dose levels. Within each scan protocol, the CNR improvement from IMR vs FBP showed a general trend of greater improvement at lower dose levels. NPS magnitude was greatest for FBP and lowest for IMR. The NPS of the IMR reconstruction showed a pronounced decrease with increasing spatial frequency, consistent with the unusual noise texture seen in IMR images. Conclusion: Iterative Model Reconstruction reduces noise and improves contrast-to-noise ratio without sacrificing spatial resolution in CT phantom images. This offers the possibility of radiation dose reduction and improved low contrast detectability compared with filtered backprojection or conventional iterative reconstruction.« less

Udzawa-type iterative method with parareal preconditioner for a parabolic optimal control problem

NASA Astrophysics Data System (ADS)

Lapin, A.; Romanenko, A.

2016-11-01

The article deals with the optimal control problem with the parabolic equation as state problem. There are point-wise constraints on the state and control functions. The objective functional involves the observation given in the domain at each moment. The conditions for convergence Udzawa's type iterative method are given. The parareal method to inverse preconditioner is given. The results of calculations are presented.

Leveraging Anderson Acceleration for improved convergence of iterative solutions to transport systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Willert, Jeffrey; Taitano, William T.; Knoll, Dana

In this note we demonstrate that using Anderson Acceleration (AA) in place of a standard Picard iteration can not only increase the convergence rate but also make the iteration more robust for two transport applications. We also compare the convergence acceleration provided by AA to that provided by moment-based acceleration methods. Additionally, we demonstrate that those two acceleration methods can be used together in a nested fashion. We begin by describing the AA algorithm. At this point, we will describe two application problems, one from neutronics and one from plasma physics, on which we will apply AA. We provide computationalmore » results which highlight the benefits of using AA, namely that we can compute solutions using fewer function evaluations, larger time-steps, and achieve a more robust iteration.« less

Parallel solution of the symmetric tridiagonal eigenproblem. Research report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jessup, E.R.

1989-10-01

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed-memory Multiple Instruction, Multiple Data multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speed up, and accuracy. Experiments on an IPSC hypercube multiprocessor reveal that Cuppen's method ismore » the most accurate approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effect of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptions of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.« less

Parallel solution of the symmetric tridiagonal eigenproblem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jessup, E.R.

1989-01-01

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed memory MIMD multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues, and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speedup, and accuracy. Experiments on an iPSC hyper-cube multiprocessor reveal that Cuppen's method is the most accuratemore » approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effects of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptations of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.« less

An iterative method for systems of nonlinear hyperbolic equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1989-01-01

An iterative algorithm for the efficient solution of systems of nonlinear hyperbolic equations is presented. Parallelism is evident at several levels. In the formation of the iteration, the equations are decoupled, thereby providing large grain parallelism. Parallelism may also be exploited within the solves for each equation. Convergence of the interation is established via a bounding function argument. Experimental results in two-dimensions are presented.

Accelerated iterative beam angle selection in IMRT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bangert, Mark, E-mail: m.bangert@dkfz.de; Unkelbach, Jan

2016-03-15

Purpose: Iterative methods for beam angle selection (BAS) for intensity-modulated radiation therapy (IMRT) planning sequentially construct a beneficial ensemble of beam directions. In a naïve implementation, the nth beam is selected by adding beam orientations one-by-one from a discrete set of candidates to an existing ensemble of (n − 1) beams. The best beam orientation is identified in a time consuming process by solving the fluence map optimization (FMO) problem for every candidate beam and selecting the beam that yields the largest improvement to the objective function value. This paper evaluates two alternative methods to accelerate iterative BAS based onmore » surrogates for the FMO objective function value. Methods: We suggest to select candidate beams not based on the FMO objective function value after convergence but (1) based on the objective function value after five FMO iterations of a gradient based algorithm and (2) based on a projected gradient of the FMO problem in the first iteration. The performance of the objective function surrogates is evaluated based on the resulting objective function values and dose statistics in a treatment planning study comprising three intracranial, three pancreas, and three prostate cases. Furthermore, iterative BAS is evaluated for an application in which a small number of noncoplanar beams complement a set of coplanar beam orientations. This scenario is of practical interest as noncoplanar setups may require additional attention of the treatment personnel for every couch rotation. Results: Iterative BAS relying on objective function surrogates yields similar results compared to naïve BAS with regard to the objective function values and dose statistics. At the same time, early stopping of the FMO and using the projected gradient during the first iteration enable reductions in computation time by approximately one to two orders of magnitude. With regard to the clinical delivery of noncoplanar IMRT treatments, we could show that optimized beam ensembles using only a few noncoplanar beam orientations often approach the plan quality of fully noncoplanar ensembles. Conclusions: We conclude that iterative BAS in combination with objective function surrogates can be a viable option to implement automated BAS at clinically acceptable computation times.« less

Radiative transfer theory for active remote sensing of a layer of small ellipsoidal scatterers. [of vegetation

NASA Technical Reports Server (NTRS)

Tsang, L.; Kubacsi, M. C.; Kong, J. A.

1981-01-01

The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.

Using an Iterative Mixed-Methods Research Design to Investigate Schools Facing Exceptionally Challenging Circumstances within Trinidad and Tobago

ERIC Educational Resources Information Center

De Lisle, Jerome; Seunarinesingh, Krishna; Mohammed, Rhoda; Lee-Piggott, Rinnelle

2017-01-01

In this study, methodology and theory were linked to explicate the nature of education practice within schools facing exceptionally challenging circumstances (SFECC) in Trinidad and Tobago. The research design was an iterative quan>QUAL-quan>qual multi-method research programme, consisting of 3 independent projects linked together by overall…

A Study of Morrison's Iterative Noise Removal Method. Final Report M. S. Thesis

NASA Technical Reports Server (NTRS)

Ioup, G. E.; Wright, K. A. R.

1985-01-01

Morrison's iterative noise removal method is studied by characterizing its effect upon systems of differing noise level and response function. The nature of data acquired from a linear shift invariant instrument is discussed so as to define the relationship between the input signal, the instrument response function, and the output signal. Fourier analysis is introduced, along with several pertinent theorems, as a tool to more thorough understanding of the nature of and difficulties with deconvolution. In relation to such difficulties the necessity of a noise removal process is discussed. Morrison's iterative noise removal method and the restrictions upon its application are developed. The nature of permissible response functions is discussed, as is the choice of the response functions used.

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations.

PubMed

Aviat, Félix; Levitt, Antoine; Stamm, Benjamin; Maday, Yvon; Ren, Pengyu; Ponder, Jay W; Lagardère, Louis; Piquemal, Jean-Philip

2017-01-10

We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration ("peek"), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations.

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations

PubMed Central

2016-01-01

We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration (“peek”), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations. PMID:28068773

A method for reducing the largest relative errors in Monte Carlo iterated-fission-source calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hunter, J. L.; Sutton, T. M.

2013-07-01

In Monte Carlo iterated-fission-source calculations relative uncertainties on local tallies tend to be larger in lower-power regions and smaller in higher-power regions. Reducing the largest uncertainties to an acceptable level simply by running a larger number of neutron histories is often prohibitively expensive. The uniform fission site method has been developed to yield a more spatially-uniform distribution of relative uncertainties. This is accomplished by biasing the density of fission neutron source sites while not biasing the solution. The method is integrated into the source iteration process, and does not require any auxiliary forward or adjoint calculations. For a given amountmore » of computational effort, the use of the method results in a reduction of the largest uncertainties relative to the standard algorithm. Two variants of the method have been implemented and tested. Both have been shown to be effective. (authors)« less

Subsonic panel method for designing wing surfaces from pressure distribution

NASA Technical Reports Server (NTRS)

Bristow, D. R.; Hawk, J. D.

1983-01-01

An iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical distribution of pressure. The calculations are initialized by using a surface panel method to analyze a baseline wing or wing-fuselage configuration. A first-order expansion to the baseline panel method equations is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter. In every iteration cycle, the matrix is used both to calculate the geometry perturbation and to analyze the perturbed geometry. The distribution of potential on the perturbed geometry is established by simple linear extrapolation from the baseline solution. The extrapolated potential is converted to pressure by Bernoulli's equation. Not only is the accuracy of the approach good for very large perturbations, but the computing cost of each complete iteration cycle is substantially less than one analysis solution by a conventional panel method.

Improved Diffuse Foreground Subtraction with the ILC Method: CMB Map and Angular Power Spectrum Using Planck and WMAP Observations

NASA Astrophysics Data System (ADS)

Sudevan, Vipin; Aluri, Pavan K.; Yadav, Sarvesh Kumar; Saha, Rajib; Souradeep, Tarun

2017-06-01

We report an improved technique for diffuse foreground minimization from Cosmic Microwave Background (CMB) maps using a new multiphase iterative harmonic space internal-linear-combination (HILC) approach. Our method nullifies a foreground leakage that was present in the old and usual iterative HILC method. In phase 1 of the multiphase technique, we obtain an initial cleaned map using the single iteration HILC approach over the desired portion of the sky. In phase 2, we obtain a final CMB map using the iterative HILC approach; however, now, to nullify the leakage, during each iteration, some of the regions of the sky that are not being cleaned in the current iteration are replaced by the corresponding cleaned portions of the phase 1 map. We bring all input frequency maps to a common and maximum possible beam and pixel resolution at the beginning of the analysis, which significantly reduces data redundancy, memory usage, and computational cost, and avoids, during the HILC weight calculation, the deconvolution of partial sky harmonic coefficients by the azimuthally symmetric beam and pixel window functions, which in a strict mathematical sense, are not well defined. Using WMAP 9 year and Planck 2015 frequency maps, we obtain foreground-cleaned CMB maps and a CMB angular power spectrum for the multipole range 2≤slant {\\ell }≤slant 2500. Our power spectrum matches the published Planck results with some differences at different multipole ranges. We validate our method by performing Monte Carlo simulations. Finally, we show that the weights for HILC foreground minimization have the intrinsic characteristic that they also tend to produce a statistically isotropic CMB map.

Analytic approximations of Von Kármán plate under arbitrary uniform pressure—equations in integral form

NASA Astrophysics Data System (ADS)

Zhong, XiaoXu; Liao, ShiJun

2018-01-01

Analytic approximations of the Von Kármán's plate equations in integral form for a circular plate under external uniform pressure to arbitrary magnitude are successfully obtained by means of the homotopy analysis method (HAM), an analytic approximation technique for highly nonlinear problems. Two HAM-based approaches are proposed for either a given external uniform pressure Q or a given central deflection, respectively. Both of them are valid for uniform pressure to arbitrary magnitude by choosing proper values of the so-called convergence-control parameters c 1 and c 2 in the frame of the HAM. Besides, it is found that the HAM-based iteration approaches generally converge much faster than the interpolation iterative method. Furthermore, we prove that the interpolation iterative method is a special case of the first-order HAM iteration approach for a given external uniform pressure Q when c 1 = - θ and c 2 = -1, where θ denotes the interpolation iterative parameter. Therefore, according to the convergence theorem of Zheng and Zhou about the interpolation iterative method, the HAM-based approaches are valid for uniform pressure to arbitrary magnitude at least in the special case c 1 = - θ and c 2 = -1. In addition, we prove that the HAM approach for the Von Kármán's plate equations in differential form is just a special case of the HAM for the Von Kármán's plate equations in integral form mentioned in this paper. All of these illustrate the validity and great potential of the HAM for highly nonlinear problems, and its superiority over perturbation techniques.

The sexual and reproductive health of foreign-born women in the United States.

PubMed

Tapales, Athena; Douglas-Hall, Ayana; Whitehead, Hannah

2018-02-14

To explore the sexual and reproductive health (SRH) behaviors, health insurance coverage and use of SRH services of women in the United States (U.S.) by nativity, disaggregated by race and ethnicity. We analyzed publicly available and restricted data from the National Survey of Family Growth to assess differences and similarities between foreign-born and U.S.-born women, both overall and within Hispanic, non-Hispanic (NH) white, NH black and NH Asian groups. A larger proportion of foreign-born women than U.S.-born women lacked health insurance coverage. Foreign-born women utilized SRH services at lower rates than U.S.-born women; this effect diminished at the multivariate level, although race and ethnicity differences remained. Overall, foreign-born women were less likely to pay for SRH services with private insurance than U.S.-born women. Foreign-born women were less likely to use the most effective contraceptive methods than U.S.-born women, with some variation across race and ethnicity: NH white and NH black foreign-born women were less likely to use highly effective contraceptive methods than their U.S.-born counterparts, but among Hispanic women, the reverse was true. Our findings demonstrate that the SRH behaviors, needs and outcomes of foreign-born women differ from those of U.S-born women within the same race/ethnic group. This paper contributes to the emergent literature on immigrants in the U.S. by laying the foundation for further research on the SRH of the foreign-born population in the country, which is critical for developing public health policies and programs to understand better and serve this growing and diverse population. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

Quickprop method to speed up learning process of Artificial Neural Network in money's nominal value recognition case

NASA Astrophysics Data System (ADS)

Swastika, Windra

2017-03-01

A money's nominal value recognition system has been developed using Artificial Neural Network (ANN). ANN with Back Propagation has one disadvantage. The learning process is very slow (or never reach the target) in the case of large number of iteration, weight and samples. One way to speed up the learning process is using Quickprop method. Quickprop method is based on Newton's method and able to speed up the learning process by assuming that the weight adjustment (E) is a parabolic function. The goal is to minimize the error gradient (E'). In our system, we use 5 types of money's nominal value, i.e. 1,000 IDR, 2,000 IDR, 5,000 IDR, 10,000 IDR and 50,000 IDR. One of the surface of each nominal were scanned and digitally processed. There are 40 patterns to be used as training set in ANN system. The effectiveness of Quickprop method in the ANN system was validated by 2 factors, (1) number of iterations required to reach error below 0.1; and (2) the accuracy to predict nominal values based on the input. Our results shows that the use of Quickprop method is successfully reduce the learning process compared to Back Propagation method. For 40 input patterns, Quickprop method successfully reached error below 0.1 for only 20 iterations, while Back Propagation method required 2000 iterations. The prediction accuracy for both method is higher than 90%.

A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position.

PubMed

Zhou, Wenjie; Wei, Xuesong; Wang, Leqin; Wu, Guangkuan

2017-05-01

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

NASA Astrophysics Data System (ADS)

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M. N.; Head-Gordon, Teresa; Skylaris, Chris-Kriton

2017-03-01

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory.

PubMed

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M N; Head-Gordon, Teresa; Skylaris, Chris-Kriton

2017-03-28

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes-in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

DOE PAGES

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; ...

2017-03-28

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less

Gauss Seidel-type methods for energy states of a multi-component Bose Einstein condensate

NASA Astrophysics Data System (ADS)

Chang, Shu-Ming; Lin, Wen-Wei; Shieh, Shih-Feng

2005-01-01

In this paper, we propose two iterative methods, a Jacobi-type iteration (JI) and a Gauss-Seidel-type iteration (GSI), for the computation of energy states of the time-independent vector Gross-Pitaevskii equation (VGPE) which describes a multi-component Bose-Einstein condensate (BEC). A discretization of the VGPE leads to a nonlinear algebraic eigenvalue problem (NAEP). We prove that the GSI method converges locally and linearly to a solution of the NAEP if and only if the associated minimized energy functional problem has a strictly local minimum. The GSI method can thus be used to compute ground states and positive bound states, as well as the corresponding energies of a multi-component BEC. Numerical experience shows that the GSI converges much faster than JI and converges globally within 10-20 steps.

Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Yunfeng, E-mail: yfcai@math.pku.edu.cn; Department of Computer Science, University of California, Davis 95616; Bai, Zhaojun, E-mail: bai@cs.ucdavis.edu

2013-12-15

The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for ab initio electronic structure calculations. We propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative diagonalization of such eigenvalue problems. In partition-of-unity finite-element (PUFE) pseudopotential density-functional calculations, employing a nonorthogonal basis, we show that the hybrid preconditioned block steepest descent method is a cost-effective eigensolver, outperforming current state-of-the-art global preconditioning schemes, and comparably efficient for the ill-conditioned generalized eigenvalue problems produced by PUFE as the locally optimal blockmore » preconditioned conjugate-gradient method for the well-conditioned standard eigenvalue problems produced by planewave methods.« less

Quality measures in applications of image restoration.

PubMed

Kriete, A; Naim, M; Schafer, L

2001-01-01

We describe a new method for the estimation of image quality in image restoration applications. We demonstrate this technique on a simulated data set of fluorescent beads, in comparison with restoration by three different deconvolution methods. Both the number of iterations and a regularisation factor are varied to enforce changes in the resulting image quality. First, the data sets are directly compared by an accuracy measure. These values serve to validate the image quality descriptor, which is developed on the basis of optical information theory. This most general measure takes into account the spectral energies and the noise, weighted in a logarithmic fashion. It is demonstrated that this method is particularly helpful as a user-oriented method to control the output of iterative image restorations and to eliminate the guesswork in choosing a suitable number of iterations.

Progress in Development of the ITER Plasma Control System Simulation Platform

NASA Astrophysics Data System (ADS)

Walker, Michael; Humphreys, David; Sammuli, Brian; Ambrosino, Giuseppe; de Tommasi, Gianmaria; Mattei, Massimiliano; Raupp, Gerhard; Treutterer, Wolfgang; Winter, Axel

2017-10-01

We report on progress made and expected uses of the Plasma Control System Simulation Platform (PCSSP), the primary test environment for development of the ITER Plasma Control System (PCS). PCSSP will be used for verification and validation of the ITER PCS Final Design for First Plasma, to be completed in 2020. We discuss the objectives of PCSSP, its overall structure, selected features, application to existing devices, and expected evolution over the lifetime of the ITER PCS. We describe an archiving solution for simulation results, methods for incorporating physics models of the plasma and physical plant (tokamak, actuator, and diagnostic systems) into PCSSP, and defining characteristics of models suitable for a plasma control development environment such as PCSSP. Applications of PCSSP simulation models including resistive plasma equilibrium evolution are demonstrated. PCSSP development supported by ITER Organization under ITER/CTS/6000000037. Resistive evolution code developed under General Atomics' Internal funding. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization.

A new Newton-like method for solving nonlinear equations.

PubMed

Saheya, B; Chen, Guo-Qing; Sui, Yun-Kang; Wu, Cai-Ying

2016-01-01

This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.

Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

DOE PAGES

Till, Andrew T.; Warsa, James S.; Morel, Jim E.

2018-06-15

The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a group-dependent state size but may be formulated without inner iterations in the presence ofmore » scattering, while ARF has a group-independent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.« less

Modeling Design Iteration in Product Design and Development and Its Solution by a Novel Artificial Bee Colony Algorithm

PubMed Central

2014-01-01

Due to fierce market competition, how to improve product quality and reduce development cost determines the core competitiveness of enterprises. However, design iteration generally causes increases of product cost and delays of development time as well, so how to identify and model couplings among tasks in product design and development has become an important issue for enterprises to settle. In this paper, the shortcomings existing in WTM model are discussed and tearing approach as well as inner iteration method is used to complement the classic WTM model. In addition, the ABC algorithm is also introduced to find out the optimal decoupling schemes. In this paper, firstly, tearing approach and inner iteration method are analyzed for solving coupled sets. Secondly, a hybrid iteration model combining these two technologies is set up. Thirdly, a high-performance swarm intelligence algorithm, artificial bee colony, is adopted to realize problem-solving. Finally, an engineering design of a chemical processing system is given in order to verify its reasonability and effectiveness. PMID:25431584

Fast non-interferometric iterative phase retrieval for holographic data storage.

PubMed

Lin, Xiao; Huang, Yong; Shimura, Tsutomu; Fujimura, Ryushi; Tanaka, Yoshito; Endo, Masao; Nishimoto, Hajimu; Liu, Jinpeng; Li, Yang; Liu, Ying; Tan, Xiaodi

2017-12-11

Fast non-interferometric phase retrieval is a very important technique for phase-encoded holographic data storage and other phase based applications due to its advantage of easy implementation, simple system setup, and robust noise tolerance. Here we present an iterative non-interferometric phase retrieval for 4-level phase encoded holographic data storage based on an iterative Fourier transform algorithm and known portion of the encoded data, which increases the storage code rate to two-times that of an amplitude based method. Only a single image at the Fourier plane of the beam is captured for the iterative reconstruction. Since beam intensity at the Fourier plane of the reconstructed beam is more concentrated than the reconstructed beam itself, the requirement of diffractive efficiency of the recording media is reduced, which will improve the dynamic range of recording media significantly. The phase retrieval only requires 10 iterations to achieve a less than 5% phase data error rate, which is successfully demonstrated by recording and reconstructing a test image data experimentally. We believe our method will further advance the holographic data storage technique in the era of big data.

Validation of the thermal transport model used for ITER startup scenario predictions with DIII-D experimental data

DOE PAGES

Casper, T. A.; Meyer, W. H.; Jackson, G. L.; ...

2010-12-08

We are exploring characteristics of ITER startup scenarios in similarity experiments conducted on the DIII-D Tokamak. In these experiments, we have validated scenarios for the ITER current ramp up to full current and developed methods to control the plasma parameters to achieve stability. Predictive simulations of ITER startup using 2D free-boundary equilibrium and 1D transport codes rely on accurate estimates of the electron and ion temperature profiles that determine the electrical conductivity and pressure profiles during the current rise. Here we present results of validation studies that apply the transport model used by the ITER team to DIII-D discharge evolutionmore » and comparisons with data from our similarity experiments.« less

A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position

PubMed Central

Zhou, Wenjie; Wei, Xuesong; Wang, Leqin

2017-01-01

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method—twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length. PMID:28572997

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

A stopping criterion for the iterative solution of partial differential equations

NASA Astrophysics Data System (ADS)

Rao, Kaustubh; Malan, Paul; Perot, J. Blair

2018-01-01

A stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead. The proposed criterion uses information from prior solution changes to estimate the error. When the solution changes are noisy or stagnating it reverts to a less accurate but more robust, low-cost singular value estimate to approximate the error given the residual. This estimator can also be applied to iterative linear matrix solvers such as Krylov subspace or multigrid methods. Examples of the stopping criterion's ability to accurately estimate the non-linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics.

Economic costs of alcohol use in Sri Lanka

PubMed Central

Ranaweera, Sajeeva; Amarasinghe, Hemantha; Thavorncharoensap, Montarat; Ranasinghe, Thushara; Karunaratna, Sumudu; Santatiwongchai, Benjarin; Chaikledkaew, Usa; Abeykoon, Palitha; De Silva, Amala

2018-01-01

Aim Alcohol related disease conditions are responsible for a significant proportion of morbidity and mortality in Sri Lanka. This study quantified the economic cost of selected alcohol related disease conditions in Sri Lanka in 2015. Methods This study uses the prevalence-based cost of illness methodology specified by the World Health Organization, and uses the gross costing approach. The direct costs includes the costs of curative care (inpatient and outpatient care borne by the state and out of pocket expenditure borne by patients) for alcohol related diseases, weighted by the respective population attributable fractions. Indirect costs consist of lost earnings due to absenteeism of the patient and carers due to seeking care and recuperation, and the loss of income due to mortality. Data form the Ministry of Health, Registrar General’s Department, Department of Census and Statistics and the National Cancer Registry was used. Systemic and house costs and population attributable fractions were obtained from research studies. Economists, Public Health Experts, Medical Administrators and Clinical Specialists were iteratively consulted during the estimation and validation of the costs and the results. Results The estimated present value of current and future economic cost of the alcohol-related conditions for Sri Lanka in 2015 was USD 885.86 million, 1.07% of the GDP of that year. The direct cost of alcohol related disease conditions was USD 388.35 million, which was 44% of the total cost, while the indirect cost was USD 497.50 million, which was 66% of the total cost. Road Injury cost was the highest cost category among the conditions studied. Conclusion Addressing alcohol use and its harms through effective implementation of evidence-based polices and interventions is urgently required to address the economic costs of alcohol use in Sri Lanka as it imposes a significant burden to the country. PMID:29879178

Iterative computation of generalized inverses, with an application to CMG steering laws

NASA Technical Reports Server (NTRS)

Steincamp, J. W.

1971-01-01

A cubically convergent iterative method for computing the generalized inverse of an arbitrary M X N matrix A is developed and a FORTRAN subroutine by which the method was implemented for real matrices on a CDC 3200 is given, with a numerical example to illustrate accuracy. Application to a redundant single-gimbal CMG assembly steering law is discussed.

A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Jameson, Antony

1986-01-01

A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.

Iterative methods used in overlap astrometric reduction techniques do not always converge

NASA Astrophysics Data System (ADS)

Rapaport, M.; Ducourant, C.; Colin, J.; Le Campion, J. F.

1993-04-01

In this paper we prove that the classical Gauss-Seidel type iterative methods used for the solution of the reduced normal equations occurring in overlapping reduction methods of astrometry do not always converge. We exhibit examples of divergence. We then analyze an alternative algorithm proposed by Wang (1985). We prove the consistency of this algorithm and verify that it can be convergent while the Gauss-Seidel method is divergent. We conjecture the convergence of Wang method for the solution of astrometric problems using overlap techniques.

Iterative Methods to Solve Linear RF Fields in Hot Plasma

NASA Astrophysics Data System (ADS)

Spencer, Joseph; Svidzinski, Vladimir; Evstatiev, Evstati; Galkin, Sergei; Kim, Jin-Soo

2014-10-01

Most magnetic plasma confinement devices use radio frequency (RF) waves for current drive and/or heating. Numerical modeling of RF fields is an important part of performance analysis of such devices and a predictive tool aiding design and development of future devices. Prior attempts at this modeling have mostly used direct solvers to solve the formulated linear equations. Full wave modeling of RF fields in hot plasma with 3D nonuniformities is mostly prohibited, with memory demands of a direct solver placing a significant limitation on spatial resolution. Iterative methods can significantly increase spatial resolution. We explore the feasibility of using iterative methods in 3D full wave modeling. The linear wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel (which includes a nonlocal dielectric response) is calculated by integrating along test particle orbits. The wave equation is discretized using a finite difference approach. The initial guess is important in iterative methods, and we examine different initial guesses including the solution to the cold plasma wave equation. Work is supported by the U.S. DOE SBIR program.

Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

NASA Technical Reports Server (NTRS)

Bramble, James H.; Kwak, Do Y.; Pasciak, Joseph E.

1993-01-01

In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).

Low-memory iterative density fitting.

PubMed

Grajciar, Lukáš

2015-07-30

A new low-memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix-vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15-fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12-core CPU workstation. © 2015 Wiley Periodicals, Inc.

2D and 3D registration methods for dual-energy contrast-enhanced digital breast tomosynthesis

NASA Astrophysics Data System (ADS)

Lau, Kristen C.; Roth, Susan; Maidment, Andrew D. A.

2014-03-01

Contrast-enhanced digital breast tomosynthesis (CE-DBT) uses an iodinated contrast agent to image the threedimensional breast vasculature. The University of Pennsylvania is conducting a CE-DBT clinical study in patients with known breast cancers. The breast is compressed continuously and imaged at four time points (1 pre-contrast; 3 postcontrast). A hybrid subtraction scheme is proposed. First, dual-energy (DE) images are obtained by a weighted logarithmic subtraction of the high-energy and low-energy image pairs. Then, post-contrast DE images are subtracted from the pre-contrast DE image. This hybrid temporal subtraction of DE images is performed to analyze iodine uptake, but suffers from motion artifacts. Employing image registration further helps to correct for motion, enhancing the evaluation of vascular kinetics. Registration using ANTS (Advanced Normalization Tools) is performed in an iterative manner. Mutual information optimization first corrects large-scale motions. Normalized cross-correlation optimization then iteratively corrects fine-scale misalignment. Two methods have been evaluated: a 2D method using a slice-by-slice approach, and a 3D method using a volumetric approach to account for out-of-plane breast motion. Our results demonstrate that iterative registration qualitatively improves with each iteration (five iterations total). Motion artifacts near the edge of the breast are corrected effectively and structures within the breast (e.g. blood vessels, surgical clip) are better visualized. Statistical and clinical evaluations of registration accuracy in the CE-DBT images are ongoing.

On the inversion of geodetic integrals defined over the sphere using 1-D FFT

NASA Astrophysics Data System (ADS)

García, R. V.; Alejo, C. A.

2005-08-01

An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine’s integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.

Cosmic Microwave Background Mapmaking with a Messenger Field

NASA Astrophysics Data System (ADS)

Huffenberger, Kevin M.; Næss, Sigurd K.

2018-01-01

We apply a messenger field method to solve the linear minimum-variance mapmaking equation in the context of Cosmic Microwave Background (CMB) observations. In simulations, the method produces sky maps that converge significantly faster than those from a conjugate gradient descent algorithm with a diagonal preconditioner, even though the computational cost per iteration is similar. The messenger method recovers large scales in the map better than conjugate gradient descent, and yields a lower overall χ2. In the single, pencil beam approximation, each iteration of the messenger mapmaking procedure produces an unbiased map, and the iterations become more optimal as they proceed. A variant of the method can handle differential data or perform deconvolution mapmaking. The messenger method requires no preconditioner, but a high-quality solution needs a cooling parameter to control the convergence. We study the convergence properties of this new method and discuss how the algorithm is feasible for the large data sets of current and future CMB experiments.

Run-time parallelization and scheduling of loops

NASA Technical Reports Server (NTRS)

Saltz, Joel H.; Mirchandaney, Ravi; Crowley, Kay

1991-01-01

Run-time methods are studied to automatically parallelize and schedule iterations of a do loop in certain cases where compile-time information is inadequate. The methods presented involve execution time preprocessing of the loop. At compile-time, these methods set up the framework for performing a loop dependency analysis. At run-time, wavefronts of concurrently executable loop iterations are identified. Using this wavefront information, loop iterations are reordered for increased parallelism. Symbolic transformation rules are used to produce: inspector procedures that perform execution time preprocessing, and executors or transformed versions of source code loop structures. These transformed loop structures carry out the calculations planned in the inspector procedures. Performance results are presented from experiments conducted on the Encore Multimax. These results illustrate that run-time reordering of loop indexes can have a significant impact on performance.

Improving the efficiency of molecular replacement by utilizing a new iterative transform phasing algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Hongxing; Fang, Hengrui; Miller, Mitchell D.

2016-07-15

An iterative transform algorithm is proposed to improve the conventional molecular-replacement method for solving the phase problem in X-ray crystallography. Several examples of successful trial calculations carried out with real diffraction data are presented. An iterative transform method proposed previously for direct phasing of high-solvent-content protein crystals is employed for enhancing the molecular-replacement (MR) algorithm in protein crystallography. Target structures that are resistant to conventional MR due to insufficient similarity between the template and target structures might be tractable with this modified phasing method. Trial calculations involving three different structures are described to test and illustrate the methodology. The relationshipmore » of the approach to PHENIX Phaser-MR and MR-Rosetta is discussed.« less

Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods

PubMed Central

Ramani, Sathish; Liu, Zhihao; Rosen, Jeffrey; Nielsen, Jon-Fredrik; Fessler, Jeffrey A.

2012-01-01

Regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values. We focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive (possibly complex) Gaussian noise. Generalized cross-validation (GCV) and (weighted) mean-squared error (MSE) approaches (based on Stein's Unbiased Risk Estimate— SURE) need the Jacobian matrix of the nonlinear reconstruction operator (representative of the iterative algorithm) with respect to the data. We derive the desired Jacobian matrix for two types of nonlinear iterative algorithms: a fast variant of the standard iterative reweighted least-squares method and the contemporary split-Bregman algorithm, both of which can accommodate a wide variety of analysis- and synthesis-type regularizers. The proposed approach iteratively computes two weighted SURE-type measures: Predicted-SURE and Projected-SURE (that require knowledge of noise variance σ2), and GCV (that does not need σ2) for these algorithms. We apply the methods to image restoration and to magnetic resonance image (MRI) reconstruction using total variation (TV) and an analysis-type ℓ1-regularization. We demonstrate through simulations and experiments with real data that minimizing Predicted-SURE and Projected-SURE consistently lead to near-MSE-optimal reconstructions. We also observed that minimizing GCV yields reconstruction results that are near-MSE-optimal for image restoration and slightly sub-optimal for MRI. Theoretical derivations in this work related to Jacobian matrix evaluations can be extended, in principle, to other types of regularizers and reconstruction algorithms. PMID:22531764

The fractal geometry of Hartree-Fock

NASA Astrophysics Data System (ADS)

Theel, Friethjof; Karamatskou, Antonia; Santra, Robin

2017-12-01

The Hartree-Fock method is an important approximation for the ground-state electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The Hartree-Fock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the Hartree-Fock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals. The focus is put on the convergence behavior of the dynamical system as a function of a suitable control parameter. In our case, a complex parameter λ controls the strength of the electron-electron interaction. An investigation of the convergence behavior depending on the parameter λ is performed for helium, neon, and argon. We observe fractal structures in the complex λ-plane, which resemble the well-known Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well.

Iterative pass optimization of sequence data

NASA Technical Reports Server (NTRS)

Wheeler, Ward C.

2003-01-01

The problem of determining the minimum-cost hypothetical ancestral sequences for a given cladogram is known to be NP-complete. This "tree alignment" problem has motivated the considerable effort placed in multiple sequence alignment procedures. Wheeler in 1996 proposed a heuristic method, direct optimization, to calculate cladogram costs without the intervention of multiple sequence alignment. This method, though more efficient in time and more effective in cladogram length than many alignment-based procedures, greedily optimizes nodes based on descendent information only. In their proposal of an exact multiple alignment solution, Sankoff et al. in 1976 described a heuristic procedure--the iterative improvement method--to create alignments at internal nodes by solving a series of median problems. The combination of a three-sequence direct optimization with iterative improvement and a branch-length-based cladogram cost procedure, provides an algorithm that frequently results in superior (i.e., lower) cladogram costs. This iterative pass optimization is both computation and memory intensive, but economies can be made to reduce this burden. An example in arthropod systematics is discussed. c2003 The Willi Hennig Society. Published by Elsevier Science (USA). All rights reserved.

FBILI method for multi-level line transfer

NASA Astrophysics Data System (ADS)

Kuzmanovska, O.; Atanacković, O.; Faurobert, M.

2017-07-01

Efficient non-LTE multilevel radiative transfer calculations are needed for a proper interpretation of astrophysical spectra. In particular, realistic simulations of time-dependent processes or multi-dimensional phenomena require that the iterative method used to solve such non-linear and non-local problem is as fast as possible. There are several multilevel codes based on efficient iterative schemes that provide a very high convergence rate, especially when combined with mathematical acceleration techniques. The Forth-and-Back Implicit Lambda Iteration (FBILI) developed by Atanacković-Vukmanović et al. [1] is a Gauss-Seidel-type iterative scheme that is characterized by a very high convergence rate without the need of complementing it with additional acceleration techniques. In this paper we make the implementation of the FBILI method to the multilevel atom line transfer in 1D more explicit. We also consider some of its variants and investigate their convergence properties by solving the benchmark problem of CaII line formation in the solar atmosphere. Finally, we compare our solutions with results obtained with the well known code MULTI.

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

NASA Astrophysics Data System (ADS)

Shao, Meiyue; Aktulga, H. Metin; Yang, Chao; Ng, Esmond G.; Maris, Pieter; Vary, James P.

2018-01-01

We describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. The use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. We also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.

1990-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. D., Jr.

1992-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number od operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

Analytical and quasi-Bayesian methods as development of the iterative approach for mixed radiation biodosimetry.

PubMed

Słonecka, Iwona; Łukasik, Krzysztof; Fornalski, Krzysztof W

2018-06-04

The present paper proposes two methods of calculating components of the dose absorbed by the human body after exposure to a mixed neutron and gamma radiation field. The article presents a novel approach to replace the common iterative method in its analytical form, thus reducing the calculation time. It also shows a possibility of estimating the neutron and gamma doses when their ratio in a mixed beam is not precisely known.

Demons deformable registration of CT and cone-beam CT using an iterative intensity matching approach.

PubMed

Nithiananthan, Sajendra; Schafer, Sebastian; Uneri, Ali; Mirota, Daniel J; Stayman, J Webster; Zbijewski, Wojciech; Brock, Kristy K; Daly, Michael J; Chan, Harley; Irish, Jonathan C; Siewerdsen, Jeffrey H

2011-04-01

A method of intensity-based deformable registration of CT and cone-beam CT (CBCT) images is described, in which intensity correction occurs simultaneously within the iterative registration process. The method preserves the speed and simplicity of the popular Demons algorithm while providing robustness and accuracy in the presence of large mismatch between CT and CBCT voxel values ("intensity"). A variant of the Demons algorithm was developed in which an estimate of the relationship between CT and CBCT intensity values for specific materials in the image is computed at each iteration based on the set of currently overlapping voxels. This tissue-specific intensity correction is then used to estimate the registration output for that iteration and the process is repeated. The robustness of the method was tested in CBCT images of a cadaveric head exhibiting a broad range of simulated intensity variations associated with x-ray scatter, object truncation, and/or errors in the reconstruction algorithm. The accuracy of CT-CBCT registration was also measured in six real cases, exhibiting deformations ranging from simple to complex during surgery or radiotherapy guided by a CBCT-capable C-arm or linear accelerator, respectively. The iterative intensity matching approach was robust against all levels of intensity variation examined, including spatially varying errors in voxel value of a factor of 2 or more, as can be encountered in cases of high x-ray scatter. Registration accuracy without intensity matching degraded severely with increasing magnitude of intensity error and introduced image distortion. A single histogram match performed prior to registration alleviated some of these effects but was also prone to image distortion and was quantifiably less robust and accurate than the iterative approach. Within the six case registration accuracy study, iterative intensity matching Demons reduced mean TRE to (2.5 +/- 2.8) mm compared to (3.5 +/- 3.0) mm with rigid registration. A method was developed to iteratively correct CT-CBCT intensity disparity during Demons registration, enabling fast, intensity-based registration in CBCT-guided procedures such as surgery and radiotherapy, in which CBCT voxel values may be inaccurate. Accurate CT-CBCT registration in turn facilitates registration of multimodality preoperative image and planning data to intraoperative CBCT by way of the preoperative CT, thereby linking the intraoperative frame of reference to a wealth of preoperative information that could improve interventional guidance.

Demons deformable registration of CT and cone-beam CT using an iterative intensity matching approach

PubMed Central

Nithiananthan, Sajendra; Schafer, Sebastian; Uneri, Ali; Mirota, Daniel J.; Stayman, J. Webster; Zbijewski, Wojciech; Brock, Kristy K.; Daly, Michael J.; Chan, Harley; Irish, Jonathan C.; Siewerdsen, Jeffrey H.

2011-01-01

Purpose: A method of intensity-based deformable registration of CT and cone-beam CT (CBCT) images is described, in which intensity correction occurs simultaneously within the iterative registration process. The method preserves the speed and simplicity of the popular Demons algorithm while providing robustness and accuracy in the presence of large mismatch between CT and CBCT voxel values (“intensity”). Methods: A variant of the Demons algorithm was developed in which an estimate of the relationship between CT and CBCT intensity values for specific materials in the image is computed at each iteration based on the set of currently overlapping voxels. This tissue-specific intensity correction is then used to estimate the registration output for that iteration and the process is repeated. The robustness of the method was tested in CBCT images of a cadaveric head exhibiting a broad range of simulated intensity variations associated with x-ray scatter, object truncation, and∕or errors in the reconstruction algorithm. The accuracy of CT-CBCT registration was also measured in six real cases, exhibiting deformations ranging from simple to complex during surgery or radiotherapy guided by a CBCT-capable C-arm or linear accelerator, respectively. Results: The iterative intensity matching approach was robust against all levels of intensity variation examined, including spatially varying errors in voxel value of a factor of 2 or more, as can be encountered in cases of high x-ray scatter. Registration accuracy without intensity matching degraded severely with increasing magnitude of intensity error and introduced image distortion. A single histogram match performed prior to registration alleviated some of these effects but was also prone to image distortion and was quantifiably less robust and accurate than the iterative approach. Within the six case registration accuracy study, iterative intensity matching Demons reduced mean TRE to (2.5±2.8) mm compared to (3.5±3.0) mm with rigid registration. Conclusions: A method was developed to iteratively correct CT-CBCT intensity disparity during Demons registration, enabling fast, intensity-based registration in CBCT-guided procedures such as surgery and radiotherapy, in which CBCT voxel values may be inaccurate. Accurate CT-CBCT registration in turn facilitates registration of multimodality preoperative image and planning data to intraoperative CBCT by way of the preoperative CT, thereby linking the intraoperative frame of reference to a wealth of preoperative information that could improve interventional guidance. PMID:21626913

Demons deformable registration of CT and cone-beam CT using an iterative intensity matching approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nithiananthan, Sajendra; Schafer, Sebastian; Uneri, Ali

2011-04-15

Purpose: A method of intensity-based deformable registration of CT and cone-beam CT (CBCT) images is described, in which intensity correction occurs simultaneously within the iterative registration process. The method preserves the speed and simplicity of the popular Demons algorithm while providing robustness and accuracy in the presence of large mismatch between CT and CBCT voxel values (''intensity''). Methods: A variant of the Demons algorithm was developed in which an estimate of the relationship between CT and CBCT intensity values for specific materials in the image is computed at each iteration based on the set of currently overlapping voxels. This tissue-specificmore » intensity correction is then used to estimate the registration output for that iteration and the process is repeated. The robustness of the method was tested in CBCT images of a cadaveric head exhibiting a broad range of simulated intensity variations associated with x-ray scatter, object truncation, and/or errors in the reconstruction algorithm. The accuracy of CT-CBCT registration was also measured in six real cases, exhibiting deformations ranging from simple to complex during surgery or radiotherapy guided by a CBCT-capable C-arm or linear accelerator, respectively. Results: The iterative intensity matching approach was robust against all levels of intensity variation examined, including spatially varying errors in voxel value of a factor of 2 or more, as can be encountered in cases of high x-ray scatter. Registration accuracy without intensity matching degraded severely with increasing magnitude of intensity error and introduced image distortion. A single histogram match performed prior to registration alleviated some of these effects but was also prone to image distortion and was quantifiably less robust and accurate than the iterative approach. Within the six case registration accuracy study, iterative intensity matching Demons reduced mean TRE to (2.5{+-}2.8) mm compared to (3.5{+-}3.0) mm with rigid registration. Conclusions: A method was developed to iteratively correct CT-CBCT intensity disparity during Demons registration, enabling fast, intensity-based registration in CBCT-guided procedures such as surgery and radiotherapy, in which CBCT voxel values may be inaccurate. Accurate CT-CBCT registration in turn facilitates registration of multimodality preoperative image and planning data to intraoperative CBCT by way of the preoperative CT, thereby linking the intraoperative frame of reference to a wealth of preoperative information that could improve interventional guidance.« less

Picard Trajectory Approximation Iteration for Efficient Orbit Propagation

DTIC Science & Technology

2015-07-21

Eqn (8)) for an iterative ap- proximation of eccentric anomaly, and is transformed back to . The Lambert/ Kepler time – eccentric anomaly relationship...of Kepler motion based on spinor regulari- zation, Journal fur die Reine und Angewandt Mathematik 218, 204-219, 1965. [3] Levi-Civita T., Sur la...transformed back to  , ,x y z . The Lambert/ Kepler time – eccentric anomaly relationship is iterated by a Newton/Secant method to converge on the

Iterative-Transform Phase Retrieval Using Adaptive Diversity

NASA Technical Reports Server (NTRS)

Dean, Bruce H.

2007-01-01

A phase-diverse iterative-transform phase-retrieval algorithm enables high spatial-frequency, high-dynamic-range, image-based wavefront sensing. [The terms phase-diverse, phase retrieval, image-based, and wavefront sensing are defined in the first of the two immediately preceding articles, Broadband Phase Retrieval for Image-Based Wavefront Sensing (GSC-14899-1).] As described below, no prior phase-retrieval algorithm has offered both high dynamic range and the capability to recover high spatial-frequency components. Each of the previously developed image-based phase-retrieval techniques can be classified into one of two categories: iterative transform or parametric. Among the modifications of the original iterative-transform approach has been the introduction of a defocus diversity function (also defined in the cited companion article). Modifications of the original parametric approach have included minimizing alternative objective functions as well as implementing a variety of nonlinear optimization methods. The iterative-transform approach offers the advantage of ability to recover low, middle, and high spatial frequencies, but has disadvantage of having a limited dynamic range to one wavelength or less. In contrast, parametric phase retrieval offers the advantage of high dynamic range, but is poorly suited for recovering higher spatial frequency aberrations. The present phase-diverse iterative transform phase-retrieval algorithm offers both the high-spatial-frequency capability of the iterative-transform approach and the high dynamic range of parametric phase-recovery techniques. In implementation, this is a focus-diverse iterative-transform phaseretrieval algorithm that incorporates an adaptive diversity function, which makes it possible to avoid phase unwrapping while preserving high-spatial-frequency recovery. The algorithm includes an inner and an outer loop (see figure). An initial estimate of phase is used to start the algorithm on the inner loop, wherein multiple intensity images are processed, each using a different defocus value. The processing is done by an iterative-transform method, yielding individual phase estimates corresponding to each image of the defocus-diversity data set. These individual phase estimates are combined in a weighted average to form a new phase estimate, which serves as the initial phase estimate for either the next iteration of the iterative-transform method or, if the maximum number of iterations has been reached, for the next several steps, which constitute the outerloop portion of the algorithm. The details of the next several steps must be omitted here for the sake of brevity. The overall effect of these steps is to adaptively update the diversity defocus values according to recovery of global defocus in the phase estimate. Aberration recovery varies with differing amounts as the amount of diversity defocus is updated in each image; thus, feedback is incorporated into the recovery process. This process is iterated until the global defocus error is driven to zero during the recovery process. The amplitude of aberration may far exceed one wavelength after completion of the inner-loop portion of the algorithm, and the classical iterative transform method does not, by itself, enable recovery of multi-wavelength aberrations. Hence, in the absence of a means of off-loading the multi-wavelength portion of the aberration, the algorithm would produce a wrapped phase map. However, a special aberration-fitting procedure can be applied to the wrapped phase data to transfer at least some portion of the multi-wavelength aberration to the diversity function, wherein the data are treated as known phase values. In this way, a multiwavelength aberration can be recovered incrementally by successively applying the aberration-fitting procedure to intermediate wrapped phase maps. During recovery, as more of the aberration is transferred to the diversity function following successive iterations around the ter loop, the estimated phase ceases to wrap in places where the aberration values become incorporated as part of the diversity function. As a result, as the aberration content is transferred to the diversity function, the phase estimate resembles that of a reference flat.

Anatomical-based partial volume correction for low-dose dedicated cardiac SPECT/CT

NASA Astrophysics Data System (ADS)

Liu, Hui; Chan, Chung; Grobshtein, Yariv; Ma, Tianyu; Liu, Yaqiang; Wang, Shi; Stacy, Mitchel R.; Sinusas, Albert J.; Liu, Chi

2015-09-01

Due to the limited spatial resolution, partial volume effect has been a major degrading factor on quantitative accuracy in emission tomography systems. This study aims to investigate the performance of several anatomical-based partial volume correction (PVC) methods for a dedicated cardiac SPECT/CT system (GE Discovery NM/CT 570c) with focused field-of-view over a clinically relevant range of high and low count levels for two different radiotracer distributions. These PVC methods include perturbation geometry transfer matrix (pGTM), pGTM followed by multi-target correction (MTC), pGTM with known concentration in blood pool, the former followed by MTC and our newly proposed methods, which perform the MTC method iteratively, where the mean values in all regions are estimated and updated by the MTC-corrected images each time in the iterative process. The NCAT phantom was simulated for cardiovascular imaging with 99mTc-tetrofosmin, a myocardial perfusion agent, and 99mTc-red blood cell (RBC), a pure intravascular imaging agent. Images were acquired at six different count levels to investigate the performance of PVC methods in both high and low count levels for low-dose applications. We performed two large animal in vivo cardiac imaging experiments following injection of 99mTc-RBC for evaluation of intramyocardial blood volume (IMBV). The simulation results showed our proposed iterative methods provide superior performance than other existing PVC methods in terms of image quality, quantitative accuracy, and reproducibility (standard deviation), particularly for low-count data. The iterative approaches are robust for both 99mTc-tetrofosmin perfusion imaging and 99mTc-RBC imaging of IMBV and blood pool activity even at low count levels. The animal study results indicated the effectiveness of PVC to correct the overestimation of IMBV due to blood pool contamination. In conclusion, the iterative PVC methods can achieve more accurate quantification, particularly for low count cardiac SPECT studies, typically obtained from low-dose protocols, gated studies, and dynamic applications.

Varying face occlusion detection and iterative recovery for face recognition

NASA Astrophysics Data System (ADS)

Wang, Meng; Hu, Zhengping; Sun, Zhe; Zhao, Shuhuan; Sun, Mei

2017-05-01

In most sparse representation methods for face recognition (FR), occlusion problems were usually solved via removing the occlusion part of both query samples and training samples to perform the recognition process. This practice ignores the global feature of facial image and may lead to unsatisfactory results due to the limitation of local features. Considering the aforementioned drawback, we propose a method called varying occlusion detection and iterative recovery for FR. The main contributions of our method are as follows: (1) to detect an accurate occlusion area of facial images, an image processing and intersection-based clustering combination method is used for occlusion FR; (2) according to an accurate occlusion map, the new integrated facial images are recovered iteratively and put into a recognition process; and (3) the effectiveness on recognition accuracy of our method is verified by comparing it with three typical occlusion map detection methods. Experiments show that the proposed method has a highly accurate detection and recovery performance and that it outperforms several similar state-of-the-art methods against partial contiguous occlusion.

Quantitative PCR for Tracking the Megaplasmid-Borne Biodegradation Potential of a Model Sphingomonad

PubMed Central

Hartmann, Erica M.; Badalamenti, Jonathan P.; Krajmalnik-Brown, Rosa

2012-01-01

We developed a quantitative PCR method for tracking the dxnA1 gene, the initial, megaplasmid-borne gene in Sphingomonas wittichii RW1's dibenzo-p-dioxin degradation pathway. We used this method on complex environmental samples and report on growth of S. wittichii RW1 in landfill leachate, thus furnishing a novel tool for monitoring megaplasmid-borne, dioxygenase-encoding genes. PMID:22492441

Composition of web services using Markov decision processes and dynamic programming.

PubMed

Uc-Cetina, Víctor; Moo-Mena, Francisco; Hernandez-Ucan, Rafael

2015-01-01

We propose a Markov decision process model for solving the Web service composition (WSC) problem. Iterative policy evaluation, value iteration, and policy iteration algorithms are used to experimentally validate our approach, with artificial and real data. The experimental results show the reliability of the model and the methods employed, with policy iteration being the best one in terms of the minimum number of iterations needed to estimate an optimal policy, with the highest Quality of Service attributes. Our experimental work shows how the solution of a WSC problem involving a set of 100,000 individual Web services and where a valid composition requiring the selection of 1,000 services from the available set can be computed in the worst case in less than 200 seconds, using an Intel Core i5 computer with 6 GB RAM. Moreover, a real WSC problem involving only 7 individual Web services requires less than 0.08 seconds, using the same computational power. Finally, a comparison with two popular reinforcement learning algorithms, sarsa and Q-learning, shows that these algorithms require one or two orders of magnitude and more time than policy iteration, iterative policy evaluation, and value iteration to handle WSC problems of the same complexity.

Convergence analysis of modulus-based matrix splitting iterative methods for implicit complementarity problems.

PubMed

Wang, An; Cao, Yang; Shi, Quan

2018-01-01

In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li (Numer. Linear Algebra Appl. 23:629-641, 2016). New convergence conditions are presented when the system matrix is a positive-definite matrix and an [Formula: see text]-matrix, respectively.

TH-AB-BRA-09: Stability Analysis of a Novel Dose Calculation Algorithm for MRI Guided Radiotherapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zelyak, O; Fallone, B; Cross Cancer Institute, Edmonton, AB

2016-06-15

Purpose: To determine the iterative deterministic solution stability of the Linear Boltzmann Transport Equation (LBTE) in the presence of magnetic fields. Methods: The LBTE with magnetic fields under investigation is derived using a discrete ordinates approach. The stability analysis is performed using analytical and numerical methods. Analytically, the spectral Fourier analysis is used to obtain the convergence rate of the source iteration procedures based on finding the largest eigenvalue of the iterative operator. This eigenvalue is a function of relevant physical parameters, such as magnetic field strength and material properties, and provides essential information about the domain of applicability requiredmore » for clinically optimal parameter selection and maximum speed of convergence. The analytical results are reinforced by numerical simulations performed using the same discrete ordinates method in angle, and a discontinuous finite element spatial approach. Results: The spectral radius for the source iteration technique of the time independent transport equation with isotropic and anisotropic scattering centers inside infinite 3D medium is equal to the ratio of differential and total cross sections. The result is confirmed numerically by solving LBTE and is in full agreement with previously published results. The addition of magnetic field reveals that the convergence becomes dependent on the strength of magnetic field, the energy group discretization, and the order of anisotropic expansion. Conclusion: The source iteration technique for solving the LBTE with magnetic fields with the discrete ordinates method leads to divergent solutions in the limiting cases of small energy discretizations and high magnetic field strengths. Future investigations into non-stationary Krylov subspace techniques as an iterative solver will be performed as this has been shown to produce greater stability than source iteration. Furthermore, a stability analysis of a discontinuous finite element space-angle approach (which has been shown to provide the greatest stability) will also be investigated. Dr. B Gino Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization)« less

Experimental validation of an OSEM-type iterative reconstruction algorithm for inverse geometry computed tomography

NASA Astrophysics Data System (ADS)

David, Sabrina; Burion, Steve; Tepe, Alan; Wilfley, Brian; Menig, Daniel; Funk, Tobias

2012-03-01

Iterative reconstruction methods have emerged as a promising avenue to reduce dose in CT imaging. Another, perhaps less well-known, advance has been the development of inverse geometry CT (IGCT) imaging systems, which can significantly reduce the radiation dose delivered to a patient during a CT scan compared to conventional CT systems. Here we show that IGCT data can be reconstructed using iterative methods, thereby combining two novel methods for CT dose reduction. A prototype IGCT scanner was developed using a scanning beam digital X-ray system - an inverse geometry fluoroscopy system with a 9,000 focal spot x-ray source and small photon counting detector. 90 fluoroscopic projections or "superviews" spanning an angle of 360 degrees were acquired of an anthropomorphic phantom mimicking a 1 year-old boy. The superviews were reconstructed with a custom iterative reconstruction algorithm, based on the maximum-likelihood algorithm for transmission tomography (ML-TR). The normalization term was calculated based on flat-field data acquired without a phantom. 15 subsets were used, and a total of 10 complete iterations were performed. Initial reconstructed images showed faithful reconstruction of anatomical details. Good edge resolution and good contrast-to-noise properties were observed. Overall, ML-TR reconstruction of IGCT data collected by a bench-top prototype was shown to be viable, which may be an important milestone in the further development of inverse geometry CT.

How to Compute Labile Metal-Ligand Equilibria

ERIC Educational Resources Information Center

de Levie, Robert

2007-01-01

The different methods used for computing labile metal-ligand complexes, which are suitable for an iterative computer solution, are illustrated. The ligand function has allowed students to relegate otherwise tedious iterations to a computer, while retaining complete control over what is calculated.

Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Lin; Shao, Sihong; E, Weinan

2012-11-06

We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Ptmore » $$_{2}$$, Au$$_{2}$$, TlF, and Bi$$_{2}$$Se$$_{3}$$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.« less

More on analyzing the reflection of a laser beam by a deformed highly reflective volume Bragg grating using iteration of the beam propagation method.

PubMed

Shu, Hong; Mokhov, Sergiy; Zeldovich, Boris Ya; Bass, Michael

2009-01-01

A further extension of the iteration method for beam propagation calculation is presented that can be applied for volume Bragg gratings (VBGs) with extremely large grating strength. A reformulation of the beam propagation formulation is presented for analyzing the reflection of a laser beam by a deformed VBG. These methods will be shown to be very accurate and efficient. A VBG with generic z-dependent distortion has been analyzed using these methods.

Numerical solution of Euler's equation by perturbed functionals

NASA Technical Reports Server (NTRS)

Dey, S. K.

1985-01-01

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

Migration without migraines

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lines, L.; Burton, A.; Lu, H.X.

Accurate velocity models are a necessity for reliable migration results. Velocity analysis generally involves the use of methods such as normal moveout analysis (NMO), seismic traveltime tomography, or iterative prestack migration. These techniques can be effective, and each has its own advantage or disadvantage. Conventional NMO methods are relatively inexpensive but basically require simplifying assumptions about geology. Tomography is a more general method but requires traveltime interpretation of prestack data. Iterative prestack depth migration is very general but is computationally expensive. In some cases, there is the opportunity to estimate vertical velocities by use of well information. The well informationmore » can be used to optimize poststack migrations, thereby eliminating some of the time and expense of iterative prestack migration. The optimized poststack migration procedure defined here computes the velocity model which minimizes the depth differences between seismic images and formation depths at the well by using a least squares inversion method. The optimization methods described in this paper will hopefully produce ``migrations without migraines.``« less

An overview of NSPCG: A nonsymmetric preconditioned conjugate gradient package

NASA Astrophysics Data System (ADS)

Oppe, Thomas C.; Joubert, Wayne D.; Kincaid, David R.

1989-05-01

The most recent research-oriented software package developed as part of the ITPACK Project is called "NSPCG" since it contains many nonsymmetric preconditioned conjugate gradient procedures. It is designed to solve large sparse systems of linear algebraic equations by a variety of different iterative methods. One of the main purposes for the development of the package is to provide a common modular structure for research on iterative methods for nonsymmetric matrices. Another purpose for the development of the package is to investigate the suitability of several iterative methods for vector computers. Since the vectorizability of an iterative method depends greatly on the matrix structure, NSPCG allows great flexibility in the operator representation. The coefficient matrix can be passed in one of several different matrix data storage schemes. These sparse data formats allow matrices with a wide range of structures from highly structured ones such as those with all nonzeros along a relatively small number of diagonals to completely unstructured sparse matrices. Alternatively, the package allows the user to call the accelerators directly with user-supplied routines for performing certain matrix operations. In this case, one can use the data format from an application program and not be required to copy the matrix into one of the package formats. This is particularly advantageous when memory space is limited. Some of the basic preconditioners that are available are point methods such as Jacobi, Incomplete LU Decomposition and Symmetric Successive Overrelaxation as well as block and multicolor preconditioners. The user can select from a large collection of accelerators such as Conjugate Gradient (CG), Chebyshev (SI, for semi-iterative), Generalized Minimal Residual (GMRES), Biconjugate Gradient Squared (BCGS) and many others. The package is modular so that almost any accelerator can be used with almost any preconditioner.

Improvements to image quality using hybrid and model-based iterative reconstructions: a phantom study.

PubMed

Aurumskjöld, Marie-Louise; Ydström, Kristina; Tingberg, Anders; Söderberg, Marcus

2017-01-01

The number of computed tomography (CT) examinations is increasing and leading to an increase in total patient exposure. It is therefore important to optimize CT scan imaging conditions in order to reduce the radiation dose. The introduction of iterative reconstruction methods has enabled an improvement in image quality and a reduction in radiation dose. To investigate how image quality depends on reconstruction method and to discuss patient dose reduction resulting from the use of hybrid and model-based iterative reconstruction. An image quality phantom (Catphan® 600) and an anthropomorphic torso phantom were examined on a Philips Brilliance iCT. The image quality was evaluated in terms of CT numbers, noise, noise power spectra (NPS), contrast-to-noise ratio (CNR), low-contrast resolution, and spatial resolution for different scan parameters and dose levels. The images were reconstructed using filtered back projection (FBP) and different settings of hybrid (iDose 4 ) and model-based (IMR) iterative reconstruction methods. iDose 4 decreased the noise by 15-45% compared with FBP depending on the level of iDose 4 . The IMR reduced the noise even further, by 60-75% compared to FBP. The results are independent of dose. The NPS showed changes in the noise distribution for different reconstruction methods. The low-contrast resolution and CNR were improved with iDose 4 , and the improvement was even greater with IMR. There is great potential to reduce noise and thereby improve image quality by using hybrid or, in particular, model-based iterative reconstruction methods, or to lower radiation dose and maintain image quality. © The Foundation Acta Radiologica 2016.

A self-adapting system for the automated detection of inter-ictal epileptiform discharges.

PubMed

Lodder, Shaun S; van Putten, Michel J A M

2014-01-01

Scalp EEG remains the standard clinical procedure for the diagnosis of epilepsy. Manual detection of inter-ictal epileptiform discharges (IEDs) is slow and cumbersome, and few automated methods are used to assist in practice. This is mostly due to low sensitivities, high false positive rates, or a lack of trust in the automated method. In this study we aim to find a solution that will make computer assisted detection more efficient than conventional methods, while preserving the detection certainty of a manual search. Our solution consists of two phases. First, a detection phase finds all events similar to epileptiform activity by using a large database of template waveforms. Individual template detections are combined to form "IED nominations", each with a corresponding certainty value based on the reliability of their contributing templates. The second phase uses the ten nominations with highest certainty and presents them to the reviewer one by one for confirmation. Confirmations are used to update certainty values of the remaining nominations, and another iteration is performed where ten nominations with the highest certainty are presented. This continues until the reviewer is satisfied with what has been seen. Reviewer feedback is also used to update template accuracies globally and improve future detections. Using the described method and fifteen evaluation EEGs (241 IEDs), one third of all inter-ictal events were shown after one iteration, half after two iterations, and 74%, 90%, and 95% after 5, 10 and 15 iterations respectively. Reviewing fifteen iterations for the 20-30 min recordings 1 took approximately 5 min. The proposed method shows a practical approach for combining automated detection with visual searching for inter-ictal epileptiform activity. Further evaluation is needed to verify its clinical feasibility and measure the added value it presents.

A Kernel-free Boundary Integral Method for Elliptic Boundary Value Problems ⋆

PubMed Central

Ying, Wenjun; Henriquez, Craig S.

2013-01-01

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. PMID:23519600

A Huygens immersed-finite-element particle-in-cell method for modeling plasma-surface interactions with moving interface

NASA Astrophysics Data System (ADS)

Cao, Huijun; Cao, Yong; Chu, Yuchuan; He, Xiaoming; Lin, Tao

2018-06-01

Surface evolution is an unavoidable issue in engineering plasma applications. In this article an iterative method for modeling plasma-surface interactions with moving interface is proposed and validated. In this method, the plasma dynamics is simulated by an immersed finite element particle-in-cell (IFE-PIC) method, and the surface evolution is modeled by the Huygens wavelet method which is coupled with the iteration of the IFE-PIC method. Numerical experiments, including prototypical engineering applications, such as the erosion of Hall thruster channel wall, are presented to demonstrate features of this Huygens IFE-PIC method for simulating the dynamic plasma-surface interactions.

Dynamics of a new family of iterative processes for quadratic polynomials

NASA Astrophysics Data System (ADS)

Gutiérrez, J. M.; Hernández, M. A.; Romero, N.

2010-03-01

In this work we show the presence of the well-known Catalan numbers in the study of the convergence and the dynamical behavior of a family of iterative methods for solving nonlinear equations. In fact, we introduce a family of methods, depending on a parameter . These methods reach the order of convergence m+2 when they are applied to quadratic polynomials with different roots. Newton's and Chebyshev's methods appear as particular choices of the family appear for m=0 and m=1, respectively. We make both analytical and graphical studies of these methods, which give rise to rational functions defined in the extended complex plane. Firstly, we prove that the coefficients of the aforementioned family of iterative processes can be written in terms of the Catalan numbers. Secondly, we make an incursion into its dynamical behavior. In fact, we show that the rational maps related to these methods can be written in terms of the entries of the Catalan triangle. Next we analyze its general convergence, by including some computer plots showing the intricate structure of the Universal Julia sets associated with the methods.

Propagation-based x-ray phase contrast imaging using an iterative phase diversity technique

NASA Astrophysics Data System (ADS)

Carroll, Aidan J.; van Riessen, Grant A.; Balaur, Eugeniu; Dolbnya, Igor P.; Tran, Giang N.; Peele, Andrew G.

2018-03-01

Through the use of a phase diversity technique, we demonstrate a near-field in-line x-ray phase contrast algorithm that provides improved object reconstruction when compared to our previous iterative methods for a homogeneous sample. Like our previous methods, the new technique uses the sample refractive index distribution during the reconstruction process. The technique complements existing monochromatic and polychromatic methods and is useful in situations where experimental phase contrast data is affected by noise.

An Extension of the Krieger-Li-Iafrate Approximation to the Optimized-Effective-Potential Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wilson, B.G.

1999-11-11

The Krieger-Li-Iafrate approximation can be expressed as the zeroth order result of an unstable iterative method for solving the integral equation form of the optimized-effective-potential method. By pre-conditioning the iterate a first order correction can be obtained which recovers the bulk of quantal oscillations missing in the zeroth order approximation. A comparison of calculated total energies are given with Krieger-Li-Iafrate, Local Density Functional, and Hyper-Hartree-Fock results for non-relativistic atoms and ions.

Method for protein structure alignment

DOEpatents

Blankenbecler, Richard; Ohlsson, Mattias; Peterson, Carsten; Ringner, Markus

2005-02-22

This invention provides a method for protein structure alignment. More particularly, the present invention provides a method for identification, classification and prediction of protein structures. The present invention involves two key ingredients. First, an energy or cost function formulation of the problem simultaneously in terms of binary (Potts) assignment variables and real-valued atomic coordinates. Second, a minimization of the energy or cost function by an iterative method, where in each iteration (1) a mean field method is employed for the assignment variables and (2) exact rotation and/or translation of atomic coordinates is performed, weighted with the corresponding assignment variables.

A minimization method on the basis of embedding the feasible set and the epigraph

NASA Astrophysics Data System (ADS)

Zabotin, I. Ya; Shulgina, O. N.; Yarullin, R. S.

2016-11-01

We propose a conditional minimization method of the convex nonsmooth function which belongs to the class of cutting-plane methods. During constructing iteration points a feasible set and an epigraph of the objective function are approximated by the polyhedral sets. In this connection, auxiliary problems of constructing iteration points are linear programming problems. In optimization process there is some opportunity of updating sets which approximate the epigraph. These updates are performed by periodically dropping of cutting planes which form embedding sets. Convergence of the proposed method is proved, some realizations of the method are discussed.

Convergence of Newton's method for a single real equation

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1985-01-01

Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed.

Comparison Analysis of Recognition Algorithms of Forest-Cover Objects on Hyperspectral Air-Borne and Space-Borne Images

NASA Astrophysics Data System (ADS)

Kozoderov, V. V.; Kondranin, T. V.; Dmitriev, E. V.

2017-12-01

The basic model for the recognition of natural and anthropogenic objects using their spectral and textural features is described in the problem of hyperspectral air-borne and space-borne imagery processing. The model is based on improvements of the Bayesian classifier that is a computational procedure of statistical decision making in machine-learning methods of pattern recognition. The principal component method is implemented to decompose the hyperspectral measurements on the basis of empirical orthogonal functions. Application examples are shown of various modifications of the Bayesian classifier and Support Vector Machine method. Examples are provided of comparing these classifiers and a metrical classifier that operates on finding the minimal Euclidean distance between different points and sets in the multidimensional feature space. A comparison is also carried out with the " K-weighted neighbors" method that is close to the nonparametric Bayesian classifier.

Conjugate gradient and cross-correlation based least-square reverse time migration and its application

NASA Astrophysics Data System (ADS)

Sun, Xiao-Dong; Ge, Zhong-Hui; Li, Zhen-Chun

2017-09-01

Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration (LSRTM) (also known as linearized reflectivity inversion) aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional (4D) seismic images compared to traditional RTM and Fourier finite difference (FFD) migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.

Virtual fringe projection system with nonparallel illumination based on iteration

NASA Astrophysics Data System (ADS)

Zhou, Duo; Wang, Zhangying; Gao, Nan; Zhang, Zonghua; Jiang, Xiangqian

2017-06-01

Fringe projection profilometry has been widely applied in many fields. To set up an ideal measuring system, a virtual fringe projection technique has been studied to assist in the design of hardware configurations. However, existing virtual fringe projection systems use parallel illumination and have a fixed optical framework. This paper presents a virtual fringe projection system with nonparallel illumination. Using an iterative method to calculate intersection points between rays and reference planes or object surfaces, the proposed system can simulate projected fringe patterns and captured images. A new explicit calibration method has been presented to validate the precision of the system. Simulated results indicate that the proposed iterative method outperforms previous systems. Our virtual system can be applied to error analysis, algorithm optimization, and help operators to find ideal system parameter settings for actual measurements.

Tick-Borne Pathogen – Reversed and Conventional Discovery of Disease

PubMed Central

Tijsse-Klasen, Ellen; Koopmans, Marion P. G.; Sprong, Hein

2014-01-01

Molecular methods have increased the number of known microorganisms associated with ticks significantly. Some of these newly identified microorganisms are readily linked to human disease while others are yet unknown to cause human disease. The face of tick-borne disease discovery has changed with more diseases now being discovered in a “reversed way,” detecting disease cases only years after the tick-borne microorganism was first discovered. Compared to the conventional discovery of infectious diseases, reverse order discovery presents researchers with new challenges. Estimating public health risks of such agents is especially challenging, as case definitions and diagnostic procedures may initially be missing. We discuss the advantages and shortcomings of molecular methods, serology, and epidemiological studies that might be used to study some fundamental questions regarding newly identified tick-borne diseases. With increased tick-exposure and improved detection methods, more tick-borne microorganisms will be added to the list of pathogens causing disease in humans in the future. PMID:25072045

Improved cryoEM-Guided Iterative Molecular Dynamics–Rosetta Protein Structure Refinement Protocol for High Precision Protein Structure Prediction

PubMed Central

2016-01-01

Many excellent methods exist that incorporate cryo-electron microscopy (cryoEM) data to constrain computational protein structure prediction and refinement. Previously, it was shown that iteration of two such orthogonal sampling and scoring methods – Rosetta and molecular dynamics (MD) simulations – facilitated exploration of conformational space in principle. Here, we go beyond a proof-of-concept study and address significant remaining limitations of the iterative MD–Rosetta protein structure refinement protocol. Specifically, all parts of the iterative refinement protocol are now guided by medium-resolution cryoEM density maps, and previous knowledge about the native structure of the protein is no longer necessary. Models are identified solely based on score or simulation time. All four benchmark proteins showed substantial improvement through three rounds of the iterative refinement protocol. The best-scoring final models of two proteins had sub-Ångstrom RMSD to the native structure over residues in secondary structure elements. Molecular dynamics was most efficient in refining secondary structure elements and was thus highly complementary to the Rosetta refinement which is most powerful in refining side chains and loop regions. PMID:25883538

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

DOE PAGES

Slaybaugh, R. N.; Ramirez-Zweiger, M.; Pandya, Tara; ...

2018-02-20

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MGmore » Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.« less

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slaybaugh, R. N.; Ramirez-Zweiger, M.; Pandya, Tara

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MGmore » Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.« less

From the Rendering Equation to Stratified Light Transport Inversion

DTIC Science & Technology

2010-12-09

iteratively. These approaches relate closely to the radiosity method for diffuse global illumination in forward rendering (Hanrahan et al, 1991; Gortler et...currently simply use sparse matrices to represent T, we are also interested in exploring connections with hierar- chical and wavelet radiosity as in...Seidel iterative methods used in radiosity . 2.4 Inverse Light Transport Previous work on inverse rendering has considered inversion of the direct

Inspection Methods in Programming.

DTIC Science & Technology

1981-06-01

Counting is a a specialization of Iterative-generation in which the generating function is Oneplus ) Waters’ second category of plan building method...is Oneplus and the initial input is 1. 0 I 180 CHAPTER NINE -ta a acio f igr9-.IeaieGnrtoPln 7 -7 STEADY STATE PLANS 181 TemporalPlan counting...specializalion iterative-generation roles .action(afu nction) ,tail(counting) conslraints .action.op = oneplus A .action.input = 1 The lItcrative-application

Numerical calculation of the internal flow field in a centrifugal compressor impeller

NASA Technical Reports Server (NTRS)

Walitt, L.; Harp, J. L., Jr.; Liu, C. Y.

1975-01-01

An iterative numerical method has been developed for the calculation of steady, three-dimensional, viscous, compressible flow fields in centrifugal compressor impellers. The computer code, which embodies the method, solves the steady three dimensional, compressible Navier-Stokes equations in rotating, curvilinear coordinates. The solution takes place on blade-to-blade surfaces of revolution which move from the hub to the shroud during each iteration.

Maxwell iteration for the lattice Boltzmann method with diffusive scaling

NASA Astrophysics Data System (ADS)

Zhao, Weifeng; Yong, Wen-An

2017-03-01

In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.

Autonomous Method and System for Minimizing the Magnitude of Plasma Discharge Current Oscillations in a Hall Effect Plasma Device

NASA Technical Reports Server (NTRS)

Hruby, Vladimir (Inventor); Demmons, Nathaniel (Inventor); Ehrbar, Eric (Inventor); Pote, Bruce (Inventor); Rosenblad, Nathan (Inventor)

2014-01-01

An autonomous method for minimizing the magnitude of plasma discharge current oscillations in a Hall effect plasma device includes iteratively measuring plasma discharge current oscillations of the plasma device and iteratively adjusting the magnet current delivered to the plasma device in response to measured plasma discharge current oscillations to reduce the magnitude of the plasma discharge current oscillations.

The truncated conjugate gradient (TCG), a non-iterative/fixed-cost strategy for computing polarization in molecular dynamics: Fast evaluation of analytical forces

NASA Astrophysics Data System (ADS)

Aviat, Félix; Lagardère, Louis; Piquemal, Jean-Philip

2017-10-01

In a recent paper [F. Aviat et al., J. Chem. Theory Comput. 13, 180-190 (2017)], we proposed the Truncated Conjugate Gradient (TCG) approach to compute the polarization energy and forces in polarizable molecular simulations. The method consists in truncating the conjugate gradient algorithm at a fixed predetermined order leading to a fixed computational cost and can thus be considered "non-iterative." This gives the possibility to derive analytical forces avoiding the usual energy conservation (i.e., drifts) issues occurring with iterative approaches. A key point concerns the evaluation of the analytical gradients, which is more complex than that with a usual solver. In this paper, after reviewing the present state of the art of polarization solvers, we detail a viable strategy for the efficient implementation of the TCG calculation. The complete cost of the approach is then measured as it is tested using a multi-time step scheme and compared to timings using usual iterative approaches. We show that the TCG methods are more efficient than traditional techniques, making it a method of choice for future long molecular dynamics simulations using polarizable force fields where energy conservation matters. We detail the various steps required for the implementation of the complete method by software developers.

The truncated conjugate gradient (TCG), a non-iterative/fixed-cost strategy for computing polarization in molecular dynamics: Fast evaluation of analytical forces.

PubMed

Aviat, Félix; Lagardère, Louis; Piquemal, Jean-Philip

2017-10-28

In a recent paper [F. Aviat et al., J. Chem. Theory Comput. 13, 180-190 (2017)], we proposed the Truncated Conjugate Gradient (TCG) approach to compute the polarization energy and forces in polarizable molecular simulations. The method consists in truncating the conjugate gradient algorithm at a fixed predetermined order leading to a fixed computational cost and can thus be considered "non-iterative." This gives the possibility to derive analytical forces avoiding the usual energy conservation (i.e., drifts) issues occurring with iterative approaches. A key point concerns the evaluation of the analytical gradients, which is more complex than that with a usual solver. In this paper, after reviewing the present state of the art of polarization solvers, we detail a viable strategy for the efficient implementation of the TCG calculation. The complete cost of the approach is then measured as it is tested using a multi-time step scheme and compared to timings using usual iterative approaches. We show that the TCG methods are more efficient than traditional techniques, making it a method of choice for future long molecular dynamics simulations using polarizable force fields where energy conservation matters. We detail the various steps required for the implementation of the complete method by software developers.

Improving cluster-based missing value estimation of DNA microarray data.

PubMed

Brás, Lígia P; Menezes, José C

2007-06-01

We present a modification of the weighted K-nearest neighbours imputation method (KNNimpute) for missing values (MVs) estimation in microarray data based on the reuse of estimated data. The method was called iterative KNN imputation (IKNNimpute) as the estimation is performed iteratively using the recently estimated values. The estimation efficiency of IKNNimpute was assessed under different conditions (data type, fraction and structure of missing data) by the normalized root mean squared error (NRMSE) and the correlation coefficients between estimated and true values, and compared with that of other cluster-based estimation methods (KNNimpute and sequential KNN). We further investigated the influence of imputation on the detection of differentially expressed genes using SAM by examining the differentially expressed genes that are lost after MV estimation. The performance measures give consistent results, indicating that the iterative procedure of IKNNimpute can enhance the prediction ability of cluster-based methods in the presence of high missing rates, in non-time series experiments and in data sets comprising both time series and non-time series data, because the information of the genes having MVs is used more efficiently and the iterative procedure allows refining the MV estimates. More importantly, IKNN has a smaller detrimental effect on the detection of differentially expressed genes.

Image transmission system using adaptive joint source and channel decoding

NASA Astrophysics Data System (ADS)

Liu, Weiliang; Daut, David G.

2005-03-01

In this paper, an adaptive joint source and channel decoding method is designed to accelerate the convergence of the iterative log-dimain sum-product decoding procedure of LDPC codes as well as to improve the reconstructed image quality. Error resilience modes are used in the JPEG2000 source codec, which makes it possible to provide useful source decoded information to the channel decoder. After each iteration, a tentative decoding is made and the channel decoded bits are then sent to the JPEG2000 decoder. Due to the error resilience modes, some bits are known to be either correct or in error. The positions of these bits are then fed back to the channel decoder. The log-likelihood ratios (LLR) of these bits are then modified by a weighting factor for the next iteration. By observing the statistics of the decoding procedure, the weighting factor is designed as a function of the channel condition. That is, for lower channel SNR, a larger factor is assigned, and vice versa. Results show that the proposed joint decoding methods can greatly reduce the number of iterations, and thereby reduce the decoding delay considerably. At the same time, this method always outperforms the non-source controlled decoding method up to 5dB in terms of PSNR for various reconstructed images.

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

NASA Astrophysics Data System (ADS)

Resita Arum, Sari; A, Suparmi; C, Cari

2016-01-01

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function. Project supported by the Higher Education Project (Grant No. 698/UN27.11/PN/2015).

Explaining low mortality among US immigrants relative to native-born Americans: the role of smoking.

PubMed

Blue, Laura; Fenelon, Andrew

2011-06-01

In many developed countries, immigrants live longer-that is, have lower death rates at most or all ages-than native-born residents. This article tests whether different levels of smoking-related mortality can explain part of the 'healthy immigrant effect' in the USA, as well as part of the related 'Hispanic paradox': the tendency for US Hispanics to outlive non-Hispanic Whites. With data from vital statistics and the national census, we calculate lung cancer death rates in 2000 for four US subpopulations: foreign-born, native-born, Hispanic and non-Hispanic White. We then use three different methods-the Peto-Lopez method, the Preston-Glei-Wilmoth method and a novel method developed in this article-to generate three alternative estimates of smoking-related mortality for each of the four subpopulations, extrapolating from lung cancer death rates. We then measure the contribution of smoking-related mortality to disparities in all-cause mortality. Taking estimates from any of the three methods, we find that smoking explains >50% of the difference in life expectancy at 50 years between foreign- and native-born men, and >70% of the difference between foreign- and native-born women; smoking explains >75% of the difference in life expectancy at 50 years between US Hispanic and non-Hispanic White men, and close to 75% of the Hispanic advantage among women. Low smoking-related mortality was the main reason for immigrants' and Hispanics' longevity advantage in the USA in 2000.

Iterative raw measurements restoration method with penalized weighted least squares approach for low-dose CT

NASA Astrophysics Data System (ADS)

Takahashi, Hisashi; Goto, Taiga; Hirokawa, Koichi; Miyazaki, Osamu

2014-03-01

Statistical iterative reconstruction and post-log data restoration algorithms for CT noise reduction have been widely studied and these techniques have enabled us to reduce irradiation doses while maintaining image qualities. In low dose scanning, electronic noise becomes obvious and it results in some non-positive signals in raw measurements. The nonpositive signal should be converted to positive signal so that it can be log-transformed. Since conventional conversion methods do not consider local variance on the sinogram, they have difficulty of controlling the strength of the filtering. Thus, in this work, we propose a method to convert the non-positive signal to the positive signal by mainly controlling the local variance. The method is implemented in two separate steps. First, an iterative restoration algorithm based on penalized weighted least squares is used to mitigate the effect of electronic noise. The algorithm preserves the local mean and reduces the local variance induced by the electronic noise. Second, smoothed raw measurements by the iterative algorithm are converted to the positive signal according to a function which replaces the non-positive signal with its local mean. In phantom studies, we confirm that the proposed method properly preserves the local mean and reduce the variance induced by the electronic noise. Our technique results in dramatically reduced shading artifacts and can also successfully cooperate with the post-log data filter to reduce streak artifacts.

Iterative reconstruction methods in atmospheric tomography: FEWHA, Kaczmarz and Gradient-based algorithm

NASA Astrophysics Data System (ADS)

Ramlau, R.; Saxenhuber, D.; Yudytskiy, M.

2014-07-01

The problem of atmospheric tomography arises in ground-based telescope imaging with adaptive optics (AO), where one aims to compensate in real-time for the rapidly changing optical distortions in the atmosphere. Many of these systems depend on a sufficient reconstruction of the turbulence profiles in order to obtain a good correction. Due to steadily growing telescope sizes, there is a strong increase in the computational load for atmospheric reconstruction with current methods, first and foremost the MVM. In this paper we present and compare three novel iterative reconstruction methods. The first iterative approach is the Finite Element- Wavelet Hybrid Algorithm (FEWHA), which combines wavelet-based techniques and conjugate gradient schemes to efficiently and accurately tackle the problem of atmospheric reconstruction. The method is extremely fast, highly flexible and yields superior quality. Another novel iterative reconstruction algorithm is the three step approach which decouples the problem in the reconstruction of the incoming wavefronts, the reconstruction of the turbulent layers (atmospheric tomography) and the computation of the best mirror correction (fitting step). For the atmospheric tomography problem within the three step approach, the Kaczmarz algorithm and the Gradient-based method have been developed. We present a detailed comparison of our reconstructors both in terms of quality and speed performance in the context of a Multi-Object Adaptive Optics (MOAO) system for the E-ELT setting on OCTOPUS, the ESO end-to-end simulation tool.

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1996-01-01

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy.

PubMed

Zelyak, O; Fallone, B G; St-Aubin, J

2017-12-14

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy

NASA Astrophysics Data System (ADS)

Zelyak, O.; Fallone, B. G.; St-Aubin, J.

2018-01-01

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

Corrigendum to "Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy".

PubMed

Zelyak, Oleksandr; Fallone, B Gino; St-Aubin, Joel

2018-03-12

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation. © 2018 Institute of Physics and Engineering in Medicine.

Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

NASA Astrophysics Data System (ADS)

Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

2013-09-01

Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

ITER-FEAT operation

NASA Astrophysics Data System (ADS)

Shimomura, Y.; Aymar, R.; Chuyanov, V. A.; Huguet, M.; Matsumoto, H.; Mizoguchi, T.; Murakami, Y.; Polevoi, A. R.; Shimada, M.; ITER Joint Central Team; ITER Home Teams

2001-03-01

ITER is planned to be the first fusion experimental reactor in the world operating for research in physics and engineering. The first ten years of operation will be devoted primarily to physics issues at low neutron fluence and the following ten years of operation to engineering testing at higher fluence. ITER can accommodate various plasma configurations and plasma operation modes, such as inductive high Q modes, long pulse hybrid modes and non-inductive steady state modes, with large ranges of plasma current, density, beta and fusion power, and with various heating and current drive methods. This flexibility will provide an advantage for coping with uncertainties in the physics database, in studying burning plasmas, in introducing advanced features and in optimizing the plasma performance for the different programme objectives. Remote sites will be able to participate in the ITER experiment. This concept will provide an advantage not only in operating ITER for 24 hours a day but also in involving the worldwide fusion community and in promoting scientific competition among the ITER Parties.

A response to Yu et al. "A forward-backward fragment assembling algorithm for the identification of genomic amplification and deletion breakpoints using high-density single nucleotide polymorphism (SNP) array", BMC Bioinformatics 2007, 8: 145.

PubMed

Rueda, Oscar M; Diaz-Uriarte, Ramon

2007-10-16

Yu et al. (BMC Bioinformatics 2007,8: 145+) have recently compared the performance of several methods for the detection of genomic amplification and deletion breakpoints using data from high-density single nucleotide polymorphism arrays. One of the methods compared is our non-homogenous Hidden Markov Model approach. Our approach uses Markov Chain Monte Carlo for inference, but Yu et al. ran the sampler for a severely insufficient number of iterations for a Markov Chain Monte Carlo-based method. Moreover, they did not use the appropriate reference level for the non-altered state. We rerun the analysis in Yu et al. using appropriate settings for both the Markov Chain Monte Carlo iterations and the reference level. Additionally, to show how easy it is to obtain answers to additional specific questions, we have added a new analysis targeted specifically to the detection of breakpoints. The reanalysis shows that the performance of our method is comparable to that of the other methods analyzed. In addition, we can provide probabilities of a given spot being a breakpoint, something unique among the methods examined. Markov Chain Monte Carlo methods require using a sufficient number of iterations before they can be assumed to yield samples from the distribution of interest. Running our method with too small a number of iterations cannot be representative of its performance. Moreover, our analysis shows how our original approach can be easily adapted to answer specific additional questions (e.g., identify edges).

Testing the Perey effect

DOE PAGES

Titus, L. J.; Nunes, Filomena M.

2014-03-12

Here, the effects of non-local potentials have historically been approximately included by applying a correction factor to the solution of the corresponding equation for the local equivalent interaction. This is usually referred to as the Perey correction factor. In this work we investigate the validity of the Perey correction factor for single-channel bound and scattering states, as well as in transfer (p, d) cross sections. Method: We solve the scattering and bound state equations for non-local interactions of the Perey-Buck type, through an iterative method. Using the distorted wave Born approximation, we construct the T-matrix for (p,d) on 17O, 41Ca,more » 49Ca, 127Sn, 133Sn, and 209Pb at 20 and 50 MeV. As a result, we found that for bound states, the Perey corrected wave function resulting from the local equation agreed well with that from the non-local equation in the interior region, but discrepancies were found in the surface and peripheral regions. Overall, the Perey correction factor was adequate for scattering states, with the exception of a few partial waves corresponding to the grazing impact parameters. These differences proved to be important for transfer reactions. In conclusion, the Perey correction factor does offer an improvement over taking a direct local equivalent solution. However, if the desired accuracy is to be better than 10%, the exact solution of the non-local equation should be pursued.« less

Development and Evaluation of an Intuitive Operations Planning Process

DTIC Science & Technology

2006-03-01

designed to be iterative and also prescribes the way in which iterations should occur. On the other hand, participants’ perceived level of trust and...16 4. DESIGN AND METHOD OF THE EXPERIMENTAL EVALUATION OF THE INTUITIVE PLANNING PROCESS...20 4.1.3 Design

The second iteration of the Systems Prioritization Method: A systems prioritization and decision-aiding tool for the Waste Isolation Pilot Plant: Volume 2, Summary of technical input and model implementation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prindle, N.H.; Mendenhall, F.T.; Trauth, K.

1996-05-01

The Systems Prioritization Method (SPM) is a decision-aiding tool developed by Sandia National Laboratories (SNL). SPM provides an analytical basis for supporting programmatic decisions for the Waste Isolation Pilot Plant (WIPP) to meet selected portions of the applicable US EPA long-term performance regulations. The first iteration of SPM (SPM-1), the prototype for SPM< was completed in 1994. It served as a benchmark and a test bed for developing the tools needed for the second iteration of SPM (SPM-2). SPM-2, completed in 1995, is intended for programmatic decision making. This is Volume II of the three-volume final report of the secondmore » iteration of the SPM. It describes the technical input and model implementation for SPM-2, and presents the SPM-2 technical baseline and the activities, activity outcomes, outcome probabilities, and the input parameters for SPM-2 analysis.« less

Finite-beta equilibria for Wendelstein 7-X configurations using the Princeton Iterative Equilibrium Solver code

NASA Astrophysics Data System (ADS)

Arndt, S.; Merkel, P.; Monticello, D. A.; Reiman, A. H.

1999-04-01

Fixed- and free-boundary equilibria for Wendelstein 7-X (W7-X) [W. Lotz et al., Plasma Physics and Controlled Nuclear Fusion Research 1990 (Proc. 13th Int. Conf. Washington, DC, 1990), (International Atomic Energy Agency, Vienna, 1991), Vol. 2, p. 603] configurations are calculated using the Princeton Iterative Equilibrium Solver (PIES) [A. H. Reiman et al., Comput. Phys. Commun., 43, 157 (1986)] to deal with magnetic islands and stochastic regions. Usually, these W7-X configurations require a large number of iterations for PIES convergence. Here, two methods have been successfully tested in an attempt to decrease the number of iterations needed for convergence. First, periodic sequences of different blending parameters are used. Second, the initial guess is vastly improved by using results of the Variational Moments Equilibrium Code (VMEC) [S. P. Hirshmann et al., Phys. Fluids 26, 3553 (1983)]. Use of these two methods have allowed verification of the Hamada condition and tendency of "self-healing" of islands has been observed.

Fast solution of elliptic partial differential equations using linear combinations of plane waves.

PubMed

Pérez-Jordá, José M

2016-02-01

Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

Programmable Iterative Optical Image And Data Processing

NASA Technical Reports Server (NTRS)

Jackson, Deborah J.

1995-01-01

Proposed method of iterative optical image and data processing overcomes limitations imposed by loss of optical power after repeated passes through many optical elements - especially, beam splitters. Involves selective, timed combination of optical wavefront phase conjugation and amplification to regenerate images in real time to compensate for losses in optical iteration loops; timing such that amplification turned on to regenerate desired image, then turned off so as not to regenerate other, undesired images or spurious light propagating through loops from unwanted reflections.

Large Deviations and Quasipotential for Finite State Mean Field Interacting Particle Systems

DTIC Science & Technology

2014-05-01

The conclusion then follows by applying Lemma 4.4.2. 132 119 4.4.1 Iterative solver: The widest neighborhood structure We employ Gauss - Seidel ...nearest neighborhood structure described in Section 4.4.2. We use Gauss - Seidel iterative method for our numerical experiments. The Gauss - Seidel ...x ∈ Bh, M x ∈ Sh\\Bh, where M ∈ (V,∞) is a very large number, so that the iteration (4.5.1) converges quickly. For simplicity, we restrict our

The Battlefield Environment Division Modeling Framework (BMF). Part 1: Optimizing the Atmospheric Boundary Layer Environment Model for Cluster Computing

DTIC Science & Technology

2014-02-01

idle waiting for the wavefront to reach it. To overcome this, Reeve et al. (2001) 3 developed a scheme in analogy to the red-black Gauss - Seidel iterative ...understandable procedure calls. Parallelization of the SIMPLE iterative scheme with SIP used a red-black scheme similar to the red-black Gauss - Seidel ...scheme, the SIMPLE method, for pressure-velocity coupling. The result is a slowing convergence of the outer iterations . The red-black scheme excites a 2

[Comparison of different methods in dealing with HIV viral load data with diversified missing value mechanism on HIV positive MSM].

PubMed

Jiang, Z; Dou, Z; Song, W L; Xu, J; Wu, Z Y

2017-11-10

Objective: To compare results of different methods: in organizing HIV viral load (VL) data with missing values mechanism. Methods We used software SPSS 17.0 to simulate complete and missing data with different missing value mechanism from HIV viral loading data collected from MSM in 16 cities in China in 2013. Maximum Likelihood Methods Using the Expectation and Maximization Algorithm (EM), regressive method, mean imputation, delete method, and Markov Chain Monte Carlo (MCMC) were used to supplement missing data respectively. The results: of different methods were compared according to distribution characteristics, accuracy and precision. Results HIV VL data could not be transferred into a normal distribution. All the methods showed good results in iterating data which is Missing Completely at Random Mechanism (MCAR). For the other types of missing data, regressive and MCMC methods were used to keep the main characteristic of the original data. The means of iterating database with different methods were all close to the original one. The EM, regressive method, mean imputation, and delete method under-estimate VL while MCMC overestimates it. Conclusion: MCMC can be used as the main imputation method for HIV virus loading missing data. The iterated data can be used as a reference for mean HIV VL estimation among the investigated population.

Composition of Web Services Using Markov Decision Processes and Dynamic Programming

PubMed Central

Uc-Cetina, Víctor; Moo-Mena, Francisco; Hernandez-Ucan, Rafael

2015-01-01

We propose a Markov decision process model for solving the Web service composition (WSC) problem. Iterative policy evaluation, value iteration, and policy iteration algorithms are used to experimentally validate our approach, with artificial and real data. The experimental results show the reliability of the model and the methods employed, with policy iteration being the best one in terms of the minimum number of iterations needed to estimate an optimal policy, with the highest Quality of Service attributes. Our experimental work shows how the solution of a WSC problem involving a set of 100,000 individual Web services and where a valid composition requiring the selection of 1,000 services from the available set can be computed in the worst case in less than 200 seconds, using an Intel Core i5 computer with 6 GB RAM. Moreover, a real WSC problem involving only 7 individual Web services requires less than 0.08 seconds, using the same computational power. Finally, a comparison with two popular reinforcement learning algorithms, sarsa and Q-learning, shows that these algorithms require one or two orders of magnitude and more time than policy iteration, iterative policy evaluation, and value iteration to handle WSC problems of the same complexity. PMID:25874247

Equivalent charge source model based iterative maximum neighbor weight for sparse EEG source localization.

PubMed

Xu, Peng; Tian, Yin; Lei, Xu; Hu, Xiao; Yao, Dezhong

2008-12-01

How to localize the neural electric activities within brain effectively and precisely from the scalp electroencephalogram (EEG) recordings is a critical issue for current study in clinical neurology and cognitive neuroscience. In this paper, based on the charge source model and the iterative re-weighted strategy, proposed is a new maximum neighbor weight based iterative sparse source imaging method, termed as CMOSS (Charge source model based Maximum neighbOr weight Sparse Solution). Different from the weight used in focal underdetermined system solver (FOCUSS) where the weight for each point in the discrete solution space is independently updated in iterations, the new designed weight for each point in each iteration is determined by the source solution of the last iteration at both the point and its neighbors. Using such a new weight, the next iteration may have a bigger chance to rectify the local source location bias existed in the previous iteration solution. The simulation studies with comparison to FOCUSS and LORETA for various source configurations were conducted on a realistic 3-shell head model, and the results confirmed the validation of CMOSS for sparse EEG source localization. Finally, CMOSS was applied to localize sources elicited in a visual stimuli experiment, and the result was consistent with those source areas involved in visual processing reported in previous studies.

Fast generating Greenberger-Horne-Zeilinger state via iterative interaction pictures

NASA Astrophysics Data System (ADS)

Huang, Bi-Hua; Chen, Ye-Hong; Wu, Qi-Cheng; Song, Jie; Xia, Yan

2016-10-01

We delve a little deeper into the construction of shortcuts to adiabatic passage for three-level systems by iterative interaction picture (multiple Schrödinger dynamics). As an application example, we use the deduced iterative based shortcuts to rapidly generate the Greenberger-Horne-Zeilinger (GHZ) state in a three-atom system with the help of quantum Zeno dynamics. Numerical simulation shows the dynamics designed by the iterative picture method is physically feasible and the shortcut scheme performs much better than that using the conventional adiabatic passage techniques. Also, the influences of various decoherence processes are discussed by numerical simulation and the results prove that the scheme is fast and robust against decoherence and operational imperfection.

Simultaneous Localization and Mapping with Iterative Sparse Extended Information Filter for Autonomous Vehicles.

PubMed

He, Bo; Liu, Yang; Dong, Diya; Shen, Yue; Yan, Tianhong; Nian, Rui

2015-08-13

In this paper, a novel iterative sparse extended information filter (ISEIF) was proposed to solve the simultaneous localization and mapping problem (SLAM), which is very crucial for autonomous vehicles. The proposed algorithm solves the measurement update equations with iterative methods adaptively to reduce linearization errors. With the scalability advantage being kept, the consistency and accuracy of SEIF is improved. Simulations and practical experiments were carried out with both a land car benchmark and an autonomous underwater vehicle. Comparisons between iterative SEIF (ISEIF), standard EKF and SEIF are presented. All of the results convincingly show that ISEIF yields more consistent and accurate estimates compared to SEIF and preserves the scalability advantage over EKF, as well.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation

NASA Astrophysics Data System (ADS)

Costa, Carlos A. N.; Campos, Itamara S.; Costa, Jessé C.; Neto, Francisco A.; Schleicher, Jörg; Novais, Amélia

2013-08-01

Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality.

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

DOE PAGES

Shao, Meiyue; Aktulga, H.  Metin; Yang, Chao; ...

2017-09-14

In this paper, we describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. Themore » use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. Finally, we also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.« less

An Iterative Decambering Approach for Post-Stall Prediction of Wing Characteristics using known Section Data

NASA Technical Reports Server (NTRS)

Mukherjee, Rinku; Gopalarathnam, Ashok; Kim, Sung Wan

2003-01-01

An iterative decambering approach for the post stall prediction of wings using known section data as inputs is presented. The method can currently be used for incompressible .ow and can be extended to compressible subsonic .ow using Mach number correction schemes. A detailed discussion of past work on this topic is presented first. Next, an overview of the decambering approach is presented and is illustrated by applying the approach to the prediction of the two-dimensional C(sub l) and C(sub m) curves for an airfoil. The implementation of the approach for iterative decambering of wing sections is then discussed. A novel feature of the current e.ort is the use of a multidimensional Newton iteration for taking into consideration the coupling between the di.erent sections of the wing. The approach lends itself to implementation in a variety of finite-wing analysis methods such as lifting-line theory, discrete-vortex Weissinger's method, and vortex lattice codes. Results are presented for a rectangular wing for a from 0 to 25 deg. The results are compared for both increasing and decreasing directions of a, and they show that a hysteresis loop can be predicted for post-stall angles of attack.

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

PubMed

Coriani, Sonia; Høst, Stinne; Jansík, Branislav; Thøgersen, Lea; Olsen, Jeppe; Jørgensen, Poul; Reine, Simen; Pawłowski, Filip; Helgaker, Trygve; Sałek, Paweł

2007-04-21

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Blind motion image deblurring using nonconvex higher-order total variation model

NASA Astrophysics Data System (ADS)

Li, Weihong; Chen, Rui; Xu, Shangwen; Gong, Weiguo

2016-09-01

We propose a nonconvex higher-order total variation (TV) method for blind motion image deblurring. First, we introduce a nonconvex higher-order TV differential operator to define a new model of the blind motion image deblurring, which can effectively eliminate the staircase effect of the deblurred image; meanwhile, we employ an image sparse prior to improve the edge recovery quality. Second, to improve the accuracy of the estimated motion blur kernel, we use L1 norm and H1 norm as the blur kernel regularization term, considering the sparsity and smoothing of the motion blur kernel. Third, because it is difficult to solve the numerically computational complexity problem of the proposed model owing to the intrinsic nonconvexity, we propose a binary iterative strategy, which incorporates a reweighted minimization approximating scheme in the outer iteration, and a split Bregman algorithm in the inner iteration. And we also discuss the convergence of the proposed binary iterative strategy. Last, we conduct extensive experiments on both synthetic and real-world degraded images. The results demonstrate that the proposed method outperforms the previous representative methods in both quality of visual perception and quantitative measurement.

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shao, Meiyue; Aktulga, H.  Metin; Yang, Chao

In this paper, we describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. Themore » use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. Finally, we also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.« less

Improvements in surface singularity analysis and design methods. [applicable to airfoils

NASA Technical Reports Server (NTRS)

Bristow, D. R.

1979-01-01

The coupling of the combined source vortex distribution of Green's potential flow function with contemporary numerical techniques is shown to provide accurate, efficient, and stable solutions to subsonic inviscid analysis and design problems for multi-element airfoils. The analysis problem is solved by direct calculation of the surface singularity distribution required to satisfy the flow tangency boundary condition. The design or inverse problem is solved by an iteration process. In this process, the geometry and the associated pressure distribution are iterated until the pressure distribution most nearly corresponding to the prescribed design distribution is obtained. Typically, five iteration cycles are required for convergence. A description of the analysis and design method is presented, along with supporting examples.

Radiofrequency pulse design using nonlinear gradient magnetic fields.

PubMed

Kopanoglu, Emre; Constable, R Todd

2015-09-01

An iterative k-space trajectory and radiofrequency (RF) pulse design method is proposed for excitation using nonlinear gradient magnetic fields. The spatial encoding functions (SEFs) generated by nonlinear gradient fields are linearly dependent in Cartesian coordinates. Left uncorrected, this may lead to flip angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a matching pursuit algorithm, and the RF pulse is designed using a conjugate gradient algorithm. Three variants of the proposed approach are given: the full algorithm, a computationally cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. The method is compared with other iterative (matching pursuit and conjugate gradient) and noniterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity. An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. © 2014 Wiley Periodicals, Inc.

A Self-Adapting System for the Automated Detection of Inter-Ictal Epileptiform Discharges

PubMed Central

Lodder, Shaun S.; van Putten, Michel J. A. M.

2014-01-01

Purpose Scalp EEG remains the standard clinical procedure for the diagnosis of epilepsy. Manual detection of inter-ictal epileptiform discharges (IEDs) is slow and cumbersome, and few automated methods are used to assist in practice. This is mostly due to low sensitivities, high false positive rates, or a lack of trust in the automated method. In this study we aim to find a solution that will make computer assisted detection more efficient than conventional methods, while preserving the detection certainty of a manual search. Methods Our solution consists of two phases. First, a detection phase finds all events similar to epileptiform activity by using a large database of template waveforms. Individual template detections are combined to form “IED nominations”, each with a corresponding certainty value based on the reliability of their contributing templates. The second phase uses the ten nominations with highest certainty and presents them to the reviewer one by one for confirmation. Confirmations are used to update certainty values of the remaining nominations, and another iteration is performed where ten nominations with the highest certainty are presented. This continues until the reviewer is satisfied with what has been seen. Reviewer feedback is also used to update template accuracies globally and improve future detections. Key Findings Using the described method and fifteen evaluation EEGs (241 IEDs), one third of all inter-ictal events were shown after one iteration, half after two iterations, and 74%, 90%, and 95% after 5, 10 and 15 iterations respectively. Reviewing fifteen iterations for the 20–30 min recordings 1took approximately 5 min. Significance The proposed method shows a practical approach for combining automated detection with visual searching for inter-ictal epileptiform activity. Further evaluation is needed to verify its clinical feasibility and measure the added value it presents. PMID:24454813

An Iterative Method for Problems with Multiscale Conductivity

PubMed Central

Kim, Hyea Hyun; Minhas, Atul S.; Woo, Eung Je

2012-01-01

A model with its conductivity varying highly across a very thin layer will be considered. It is related to a stable phantom model, which is invented to generate a certain apparent conductivity inside a region surrounded by a thin cylinder with holes. The thin cylinder is an insulator and both inside and outside the thin cylinderare filled with the same saline. The injected current can enter only through the holes adopted to the thin cylinder. The model has a high contrast of conductivity discontinuity across the thin cylinder and the thickness of the layer and the size of holes are very small compared to the domain of the model problem. Numerical methods for such a model require a very fine mesh near the thin layer to resolve the conductivity discontinuity. In this work, an efficient numerical method for such a model problem is proposed by employing a uniform mesh, which need not resolve the conductivity discontinuity. The discrete problem is then solved by an iterative method, where the solution is improved by solving a simple discrete problem with a uniform conductivity. At each iteration, the right-hand side is updated by integrating the previous iterate over the thin cylinder. This process results in a certain smoothing effect on microscopic structures and our discrete model can provide a more practical tool for simulating the apparent conductivity. The convergence of the iterative method is analyzed regarding the contrast in the conductivity and the relative thickness of the layer. In numerical experiments, solutions of our method are compared to reference solutions obtained from COMSOL, where very fine meshes are used to resolve the conductivity discontinuity in the model. Errors of the voltage in L2 norm follow O(h) asymptotically and the current density matches quitewell those from the reference solution for a sufficiently small mesh size h. The experimental results present a promising feature of our approach for simulating the apparent conductivity related to changes in microscopic cellular structures. PMID:23304238

Solution of the symmetric eigenproblem AX=lambda BX by delayed division

NASA Technical Reports Server (NTRS)

Thurston, G. A.; Bains, N. J. C.

1986-01-01

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity.

A multi-frequency iterative imaging method for discontinuous inverse medium problem

NASA Astrophysics Data System (ADS)

Zhang, Lei; Feng, Lixin

2018-06-01

The inverse medium problem with discontinuous refractive index is a kind of challenging inverse problem. We employ the primal dual theory and fast solution of integral equations, and propose a new iterative imaging method. The selection criteria of regularization parameter is given by the method of generalized cross-validation. Based on multi-frequency measurements of the scattered field, a recursive linearization algorithm has been presented with respect to the frequency from low to high. We also discuss the initial guess selection strategy by semi-analytical approaches. Numerical experiments are presented to show the effectiveness of the proposed method.

A unified convergence theory of a numerical method, and applications to the replenishment policies.

PubMed

Mi, Xiang-jiang; Wang, Xing-hua

2004-01-01

In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But this approach requires calculation of the second derivative of the function. Avoiding this complex computation we use another iterative method presented by the second author. One of the goals of this paper is to present a unified convergence theory of this method. Then we give a numerical example to show the application of our theory.

Iterative algorithm for reconstructing rotationally asymmetric surface deviation with pixel-level spatial resolution

NASA Astrophysics Data System (ADS)

Quan, Haiyang; Wu, Fan; Hou, Xi

2015-10-01

New method for reconstructing rotationally asymmetric surface deviation with pixel-level spatial resolution is proposed. It is based on basic iterative scheme and accelerates the Gauss-Seidel method by introducing an acceleration parameter. This modified Successive Over-relaxation (SOR) is effective for solving the rotationally asymmetric components with pixel-level spatial resolution, without the usage of a fitting procedure. Compared to the Jacobi and Gauss-Seidel method, the modified SOR method with an optimal relaxation factor converges much faster and saves more computational costs and memory space without reducing accuracy. It has been proved by real experimental results.

AZTEC: A parallel iterative package for the solving linear systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S.

1996-12-31

We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.

Approximate Solution of Time-Fractional Advection-Dispersion Equation via Fractional Variational Iteration Method

PubMed Central

İbiş, Birol

2014-01-01

This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie's modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs. PMID:24578662

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

DTIC Science & Technology

2014-03-01

accuracy, with rapid convergence over each physical time step, typically less than five Newton iter - ations. 1 Contents 1 Introduction 3 2 Hyperbolic...however, we employ the Gauss - Seidel (GS) relaxation, which is also an O(N) method for the discretization arising from hyperbolic advection-diffusion system...advection-diffusion scheme. The linear dependency of the iterations on Table 1: Boundary layer problem ( Convergence criteria: Residuals < 10−8.) log10Re

Heat Transfer Effects on a Fully Premixed Methane Impinging Flame

DTIC Science & Technology

2014-10-30

Houzeaux et al., 2009). The GM- RES solver is also employed to solve for the enthalpy and species mass fractions. The Gauss - Seidel iterative method is...the system is therefore split to solve the mo- mentum and continuity equations independently. This is achieved by applying an iterative strategy...the momentum equation twice and the continuity equation once. The momentum equation is solved using the GMRES or BICGSTAB method (diagonal and Gauss

Method for beam hardening correction in quantitative computed X-ray tomography

NASA Technical Reports Server (NTRS)

Yan, Chye Hwang (Inventor); Whalen, Robert T. (Inventor); Napel, Sandy (Inventor)

2001-01-01

Each voxel is assumed to contain exactly two distinct materials, with the volume fraction of each material being iteratively calculated. According to the method, the spectrum of the X-ray beam must be known, and the attenuation spectra of the materials in the object must be known, and be monotonically decreasing with increasing X-ray photon energy. Then, a volume fraction is estimated for the voxel, and the spectrum is iteratively calculated.

Solving Differential Equations Using Modified Picard Iteration

ERIC Educational Resources Information Center

Robin, W. A.

2010-01-01

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

Iterative near-term ecological forecasting: Needs, opportunities, and challenges

USGS Publications Warehouse

Dietze, Michael C.; Fox, Andrew; Beck-Johnson, Lindsay; Betancourt, Julio L.; Hooten, Mevin B.; Jarnevich, Catherine S.; Keitt, Timothy H.; Kenney, Melissa A.; Laney, Christine M.; Larsen, Laurel G.; Loescher, Henry W.; Lunch, Claire K.; Pijanowski, Bryan; Randerson, James T.; Read, Emily; Tredennick, Andrew T.; Vargas, Rodrigo; Weathers, Kathleen C.; White, Ethan P.

2018-01-01

Two foundational questions about sustainability are “How are ecosystems and the services they provide going to change in the future?” and “How do human decisions affect these trajectories?” Answering these questions requires an ability to forecast ecological processes. Unfortunately, most ecological forecasts focus on centennial-scale climate responses, therefore neither meeting the needs of near-term (daily to decadal) environmental decision-making nor allowing comparison of specific, quantitative predictions to new observational data, one of the strongest tests of scientific theory. Near-term forecasts provide the opportunity to iteratively cycle between performing analyses and updating predictions in light of new evidence. This iterative process of gaining feedback, building experience, and correcting models and methods is critical for improving forecasts. Iterative, near-term forecasting will accelerate ecological research, make it more relevant to society, and inform sustainable decision-making under high uncertainty and adaptive management. Here, we identify the immediate scientific and societal needs, opportunities, and challenges for iterative near-term ecological forecasting. Over the past decade, data volume, variety, and accessibility have greatly increased, but challenges remain in interoperability, latency, and uncertainty quantification. Similarly, ecologists have made considerable advances in applying computational, informatic, and statistical methods, but opportunities exist for improving forecast-specific theory, methods, and cyberinfrastructure. Effective forecasting will also require changes in scientific training, culture, and institutions. The need to start forecasting is now; the time for making ecology more predictive is here, and learning by doing is the fastest route to drive the science forward.

Iterative near-term ecological forecasting: Needs, opportunities, and challenges.

PubMed

Dietze, Michael C; Fox, Andrew; Beck-Johnson, Lindsay M; Betancourt, Julio L; Hooten, Mevin B; Jarnevich, Catherine S; Keitt, Timothy H; Kenney, Melissa A; Laney, Christine M; Larsen, Laurel G; Loescher, Henry W; Lunch, Claire K; Pijanowski, Bryan C; Randerson, James T; Read, Emily K; Tredennick, Andrew T; Vargas, Rodrigo; Weathers, Kathleen C; White, Ethan P

2018-02-13

Two foundational questions about sustainability are "How are ecosystems and the services they provide going to change in the future?" and "How do human decisions affect these trajectories?" Answering these questions requires an ability to forecast ecological processes. Unfortunately, most ecological forecasts focus on centennial-scale climate responses, therefore neither meeting the needs of near-term (daily to decadal) environmental decision-making nor allowing comparison of specific, quantitative predictions to new observational data, one of the strongest tests of scientific theory. Near-term forecasts provide the opportunity to iteratively cycle between performing analyses and updating predictions in light of new evidence. This iterative process of gaining feedback, building experience, and correcting models and methods is critical for improving forecasts. Iterative, near-term forecasting will accelerate ecological research, make it more relevant to society, and inform sustainable decision-making under high uncertainty and adaptive management. Here, we identify the immediate scientific and societal needs, opportunities, and challenges for iterative near-term ecological forecasting. Over the past decade, data volume, variety, and accessibility have greatly increased, but challenges remain in interoperability, latency, and uncertainty quantification. Similarly, ecologists have made considerable advances in applying computational, informatic, and statistical methods, but opportunities exist for improving forecast-specific theory, methods, and cyberinfrastructure. Effective forecasting will also require changes in scientific training, culture, and institutions. The need to start forecasting is now; the time for making ecology more predictive is here, and learning by doing is the fastest route to drive the science forward.

ITER-relevant calibration technique for soft x-ray spectrometer.

PubMed

Rzadkiewicz, J; Książek, I; Zastrow, K-D; Coffey, I H; Jakubowska, K; Lawson, K D

2010-10-01

The ITER-oriented JET research program brings new requirements for the low-Z impurity monitoring, in particular for the Be—the future main wall component of JET and ITER. Monitoring based on Bragg spectroscopy requires an absolute sensitivity calibration, which is challenging for large tokamaks. This paper describes both “component-by-component” and “continua” calibration methods used for the Be IV channel (75.9 Å) of the Bragg rotor spectrometer deployed on JET. The calibration techniques presented here rely on multiorder reflectivity calculations and measurements of continuum radiation emitted from helium plasmas. These offer excellent conditions for the absolute photon flux calibration due to their low level of impurities. It was found that the component-by-component method gives results that are four times higher than those obtained by means of the continua method. A better understanding of this discrepancy requires further investigations.

A frequency dependent preconditioned wavelet method for atmospheric tomography

NASA Astrophysics Data System (ADS)

Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny

2013-12-01

Atmospheric tomography, i.e. the reconstruction of the turbulence in the atmosphere, is a main task for the adaptive optics systems of the next generation telescopes. For extremely large telescopes, such as the European Extremely Large Telescope, this problem becomes overly complex and an efficient algorithm is needed to reduce numerical costs. Recently, a conjugate gradient method based on wavelet parametrization of turbulence layers was introduced [5]. An iterative algorithm can only be numerically efficient when the number of iterations required for a sufficient reconstruction is low. A way to achieve this is to design an efficient preconditioner. In this paper we propose a new frequency-dependent preconditioner for the wavelet method. In the context of a multi conjugate adaptive optics (MCAO) system simulated on the official end-to-end simulation tool OCTOPUS of the European Southern Observatory we demonstrate robustness and speed of the preconditioned algorithm. We show that three iterations are sufficient for a good reconstruction.

On iterative processes in the Krylov-Sonneveld subspaces

NASA Astrophysics Data System (ADS)

Ilin, Valery P.

2016-10-01

The iterative Induced Dimension Reduction (IDR) methods are considered for solving large systems of linear algebraic equations (SLAEs) with nonsingular nonsymmetric matrices. These approaches are investigated by many authors and are charachterized sometimes as the alternative to the classical processes of Krylov type. The key moments of the IDR algorithms consist in the construction of the embedded Sonneveld subspaces, which have the decreasing dimensions and use the orthogonalization to some fixed subspace. Other independent approaches for research and optimization of the iterations are based on the augmented and modified Krylov subspaces by using the aggregation and deflation procedures with present various low rank approximations of the original matrices. The goal of this paper is to show, that IDR method in Sonneveld subspaces present an original interpretation of the modified algorithms in the Krylov subspaces. In particular, such description is given for the multi-preconditioned semi-conjugate direction methods which are actual for the parallel algebraic domain decomposition approaches.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Run-time parallelization and scheduling of loops

NASA Technical Reports Server (NTRS)

Saltz, Joel H.; Mirchandaney, Ravi; Crowley, Kay

1990-01-01

Run time methods are studied to automatically parallelize and schedule iterations of a do loop in certain cases, where compile-time information is inadequate. The methods presented involve execution time preprocessing of the loop. At compile-time, these methods set up the framework for performing a loop dependency analysis. At run time, wave fronts of concurrently executable loop iterations are identified. Using this wavefront information, loop iterations are reordered for increased parallelism. Symbolic transformation rules are used to produce: inspector procedures that perform execution time preprocessing and executors or transformed versions of source code loop structures. These transformed loop structures carry out the calculations planned in the inspector procedures. Performance results are presented from experiments conducted on the Encore Multimax. These results illustrate that run time reordering of loop indices can have a significant impact on performance. Furthermore, the overheads associated with this type of reordering are amortized when the loop is executed several times with the same dependency structure.

Numerical modeling of the radiative transfer in a turbid medium using the synthetic iteration.

PubMed

Budak, Vladimir P; Kaloshin, Gennady A; Shagalov, Oleg V; Zheltov, Victor S

2015-07-27

In this paper we propose the fast, but the accurate algorithm for numerical modeling of light fields in the turbid media slab. For the numerical solution of the radiative transfer equation (RTE) it is required its discretization based on the elimination of the solution anisotropic part and the replacement of the scattering integral by a finite sum. The solution regular part is determined numerically. A good choice of the method of the solution anisotropic part elimination determines the high convergence of the algorithm in the mean square metric. The method of synthetic iterations can be used to improve the convergence in the uniform metric. A significant increase in the solution accuracy with the use of synthetic iterations allows applying the two-stream approximation for the regular part determination. This approach permits to generalize the proposed method in the case of an arbitrary 3D geometry of the medium.

Comparing the basins of attraction for several methods in the circular Sitnikov problem with spheroid primaries

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.

2018-06-01

The circular Sitnikov problem, where the two primary bodies are prolate or oblate spheroids, is numerically investigated. In particular, the basins of convergence on the complex plane are revealed by using a large collection of numerical methods of several order. We consider four cases, regarding the value of the oblateness coefficient which determines the nature of the roots (attractors) of the system. For all cases we use the iterative schemes for performing a thorough and systematic classification of the nodes on the complex plane. The distribution of the iterations as well as the probability and their correlations with the corresponding basins of convergence are also discussed. Our numerical computations indicate that most of the iterative schemes provide relatively similar convergence structures on the complex plane. However, there are some numerical methods for which the corresponding basins of attraction are extremely complicated with highly fractal basin boundaries. Moreover, it is proved that the efficiency strongly varies between the numerical methods.

Solution of an eigenvalue problem for the Laplace operator on a spherical surface. M.S. Thesis - Maryland Univ.

NASA Technical Reports Server (NTRS)

Walden, H.

1974-01-01

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

Iterative method for in situ measurement of lens aberrations in lithographic tools using CTC-based quadratic aberration model.

PubMed

Liu, Shiyuan; Xu, Shuang; Wu, Xiaofei; Liu, Wei

2012-06-18

This paper proposes an iterative method for in situ lens aberration measurement in lithographic tools based on a quadratic aberration model (QAM) that is a natural extension of the linear model formed by taking into account interactions among individual Zernike coefficients. By introducing a generalized operator named cross triple correlation (CTC), the quadratic model can be calculated very quickly and accurately with the help of fast Fourier transform (FFT). The Zernike coefficients up to the 37th order or even higher are determined by solving an inverse problem through an iterative procedure from several through-focus aerial images of a specially designed mask pattern. The simulation work has validated the theoretical derivation and confirms that such a method is simple to implement and yields a superior quality of wavefront estimate, particularly for the case when the aberrations are relatively large. It is fully expected that this method will provide a useful practical means for the in-line monitoring of the imaging quality of lithographic tools.

Analysis and Design of ITER 1 MV Core Snubber

NASA Astrophysics Data System (ADS)

Wang, Haitian; Li, Ge

2012-11-01

The core snubber, as a passive protection device, can suppress arc current and absorb stored energy in stray capacitance during the electrical breakdown in accelerating electrodes of ITER NBI. In order to design the core snubber of ITER, the control parameters of the arc peak current have been firstly analyzed by the Fink-Baker-Owren (FBO) method, which are used for designing the DIIID 100 kV snubber. The B-H curve can be derived from the measured voltage and current waveforms, and the hysteresis loss of the core snubber can be derived using the revised parallelogram method. The core snubber can be a simplified representation as an equivalent parallel resistance and inductance, which has been neglected by the FBO method. A simulation code including the parallel equivalent resistance and inductance has been set up. The simulation and experiments result in dramatically large arc shorting currents due to the parallel inductance effect. The case shows that the core snubber utilizing the FBO method gives more compact design.

GWASinlps: Nonlocal prior based iterative SNP selection tool for genome-wide association studies.

PubMed

Sanyal, Nilotpal; Lo, Min-Tzu; Kauppi, Karolina; Djurovic, Srdjan; Andreassen, Ole A; Johnson, Valen E; Chen, Chi-Hua

2018-06-19

Multiple marker analysis of the genome-wide association study (GWAS) data has gained ample attention in recent years. However, because of the ultra high-dimensionality of GWAS data, such analysis is challenging. Frequently used penalized regression methods often lead to large number of false positives, whereas Bayesian methods are computationally very expensive. Motivated to ameliorate these issues simultaneously, we consider the novel approach of using nonlocal priors in an iterative variable selection framework. We develop a variable selection method, named, iterative nonlocal prior based selection for GWAS, or GWASinlps, that combines, in an iterative variable selection framework, the computational efficiency of the screen-and-select approach based on some association learning and the parsimonious uncertainty quantification provided by the use of nonlocal priors. The hallmark of our method is the introduction of 'structured screen-and-select' strategy, that considers hierarchical screening, which is not only based on response-predictor associations, but also based on response-response associations, and concatenates variable selection within that hierarchy. Extensive simulation studies with SNPs having realistic linkage disequilibrium structures demonstrate the advantages of our computationally efficient method compared to several frequentist and Bayesian variable selection methods, in terms of true positive rate, false discovery rate, mean squared error, and effect size estimation error. Further, we provide empirical power analysis useful for study design. Finally, a real GWAS data application was considered with human height as phenotype. An R-package for implementing the GWASinlps method is available at https://cran.r-project.org/web/packages/GWASinlps/index.html. Supplementary data are available at Bioinformatics online.

Estimation of brood and nest survival: Comparative methods in the presence of heterogeneity

USGS Publications Warehouse

Manly, Bryan F.J.; Schmutz, Joel A.

2001-01-01

The Mayfield method has been widely used for estimating survival of nests and young animals, especially when data are collected at irregular observation intervals. However, this method assumes survival is constant throughout the study period, which often ignores biologically relevant variation and may lead to biased survival estimates. We examined the bias and accuracy of 1 modification to the Mayfield method that allows for temporal variation in survival, and we developed and similarly tested 2 additional methods. One of these 2 new methods is simply an iterative extension of Klett and Johnson's method, which we refer to as the Iterative Mayfield method and bears similarity to Kaplan-Meier methods. The other method uses maximum likelihood techniques for estimation and is best applied to survival of animals in groups or families, rather than as independent individuals. We also examined how robust these estimators are to heterogeneity in the data, which can arise from such sources as dependent survival probabilities among siblings, inherent differences among families, and adoption. Testing of estimator performance with respect to bias, accuracy, and heterogeneity was done using simulations that mimicked a study of survival of emperor goose (Chen canagica) goslings. Assuming constant survival for inappropriately long periods of time or use of Klett and Johnson's methods resulted in large bias or poor accuracy (often >5% bias or root mean square error) compared to our Iterative Mayfield or maximum likelihood methods. Overall, estimator performance was slightly better with our Iterative Mayfield than our maximum likelihood method, but the maximum likelihood method provides a more rigorous framework for testing covariates and explicity models a heterogeneity factor. We demonstrated use of all estimators with data from emperor goose goslings. We advocate that future studies use the new methods outlined here rather than the traditional Mayfield method or its previous modifications.

Characterisation of structure-borne sound source using reception plate method.

PubMed

Putra, A; Saari, N F; Bakri, H; Ramlan, R; Dan, R M

2013-01-01

A laboratory-based experiment procedure of reception plate method for structure-borne sound source characterisation is reported in this paper. The method uses the assumption that the input power from the source installed on the plate is equal to the power dissipated by the plate. In this experiment, rectangular plates having high and low mobility relative to that of the source were used as the reception plates and a small electric fan motor was acting as the structure-borne source. The data representing the source characteristics, namely, the free velocity and the source mobility, were obtained and compared with those from direct measurement. Assumptions and constraints employing this method are discussed.

Iterative Image Reconstruction for PROPELLER-MRI using the NonUniform Fast Fourier Transform

PubMed Central

Tamhane, Ashish A.; Anastasio, Mark A.; Gui, Minzhi; Arfanakis, Konstantinos

2013-01-01

Purpose To investigate an iterative image reconstruction algorithm using the non-uniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping parallEL Lines with Enhanced Reconstruction) MRI. Materials and Methods Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it to that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated. Results It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased SNR, reduced artifacts, for similar spatial resolution, compared to gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach. Conclusion An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter the new reconstruction technique may provide PROPELLER images with improved image quality compared to conventional gridding. PMID:20578028

An iterated Laplacian based semi-supervised dimensionality reduction for classification of breast cancer on ultrasound images.

PubMed

Liu, Xiao; Shi, Jun; Zhou, Shichong; Lu, Minhua

2014-01-01

The dimensionality reduction is an important step in ultrasound image based computer-aided diagnosis (CAD) for breast cancer. A newly proposed l2,1 regularized correntropy algorithm for robust feature selection (CRFS) has achieved good performance for noise corrupted data. Therefore, it has the potential to reduce the dimensions of ultrasound image features. However, in clinical practice, the collection of labeled instances is usually expensive and time costing, while it is relatively easy to acquire the unlabeled or undetermined instances. Therefore, the semi-supervised learning is very suitable for clinical CAD. The iterated Laplacian regularization (Iter-LR) is a new regularization method, which has been proved to outperform the traditional graph Laplacian regularization in semi-supervised classification and ranking. In this study, to augment the classification accuracy of the breast ultrasound CAD based on texture feature, we propose an Iter-LR-based semi-supervised CRFS (Iter-LR-CRFS) algorithm, and then apply it to reduce the feature dimensions of ultrasound images for breast CAD. We compared the Iter-LR-CRFS with LR-CRFS, original supervised CRFS, and principal component analysis. The experimental results indicate that the proposed Iter-LR-CRFS significantly outperforms all other algorithms.

Source apportionment for fine particulate matter in a Chinese city using an improved gas-constrained method and comparison with multiple receptor models.

PubMed

Shi, Guoliang; Liu, Jiayuan; Wang, Haiting; Tian, Yingze; Wen, Jie; Shi, Xurong; Feng, Yinchang; Ivey, Cesunica E; Russell, Armistead G

2018-02-01

PM 2.5 is one of the most studied atmospheric pollutants due to its adverse impacts on human health and welfare and the environment. An improved model (the chemical mass balance gas constraint-Iteration: CMBGC-Iteration) is proposed and applied to identify source categories and estimate source contributions of PM 2.5. The CMBGC-Iteration model uses the ratio of gases to PM as constraints and considers the uncertainties of source profiles and receptor datasets, which is crucial information for source apportionment. To apply this model, samples of PM 2.5 were collected at Tianjin, a megacity in northern China. The ambient PM 2.5 dataset, source information, and gas-to-particle ratios (such as SO 2 /PM 2.5 , CO/PM 2.5 , and NOx/PM 2.5 ratios) were introduced into the CMBGC-Iteration to identify the potential sources and their contributions. Six source categories were identified by this model and the order based on their contributions to PM 2.5 was as follows: secondary sources (30%), crustal dust (25%), vehicle exhaust (16%), coal combustion (13%), SOC (7.6%), and cement dust (0.40%). In addition, the same dataset was also calculated by other receptor models (CMB, CMB-Iteration, CMB-GC, PMF, WALSPMF, and NCAPCA), and the results obtained were compared. Ensemble-average source impacts were calculated based on the seven source apportionment results: contributions of secondary sources (28%), crustal dust (20%), coal combustion (18%), vehicle exhaust (17%), SOC (11%), and cement dust (1.3%). The similar results of CMBGC-Iteration and ensemble method indicated that CMBGC-Iteration can produce relatively appropriate results. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Block Preconditioned Conjugate Gradient-type Iterative Solver for Linear Systems in Thermal Reservoir Simulation

NASA Astrophysics Data System (ADS)

Betté, Srinivas; Diaz, Julio C.; Jines, William R.; Steihaug, Trond

1986-11-01

A preconditioned residual-norm-reducing iterative solver is described. Based on a truncated form of the generalized-conjugate-gradient method for nonsymmetric systems of linear equations, the iterative scheme is very effective for linear systems generated in reservoir simulation of thermal oil recovery processes. As a consequence of employing an adaptive implicit finite-difference scheme to solve the model equations, the number of variables per cell-block varies dynamically over the grid. The data structure allows for 5- and 9-point operators in the areal model, 5-point in the cross-sectional model, and 7- and 11-point operators in the three-dimensional model. Block-diagonal-scaling of the linear system, done prior to iteration, is found to have a significant effect on the rate of convergence. Block-incomplete-LU-decomposition (BILU) and block-symmetric-Gauss-Seidel (BSGS) methods, which result in no fill-in, are used as preconditioning procedures. A full factorization is done on the well terms, and the cells are ordered in a manner which minimizes the fill-in in the well-column due to this factorization. The convergence criterion for the linear (inner) iteration is linked to that of the nonlinear (Newton) iteration, thereby enhancing the efficiency of the computation. The algorithm, with both BILU and BSGS preconditioners, is evaluated in the context of a variety of thermal simulation problems. The solver is robust and can be used with little or no user intervention.

Analysis of Eigenvalue and Eigenfunction of Klein Gordon Equation Using Asymptotic Iteration Method for Separable Non-central Cylindrical Potential

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Lilis Elviyanti, Isnaini

2018-04-01

Analysis of relativistic energy and wave function for zero spin particles using Klein Gordon equation was influenced by separable noncentral cylindrical potential was solved by asymptotic iteration method (AIM). By using cylindrical coordinates, the Klein Gordon equation for the case of symmetry spin was reduced to three one-dimensional Schrodinger like equations that were solvable using variable separation method. The relativistic energy was calculated numerically with Matlab software, and the general unnormalized wave function was expressed in hypergeometric terms.

Restoration of multichannel microwave radiometric images

NASA Technical Reports Server (NTRS)

Chin, R. T.; Yeh, C. L.; Olson, W. S.

1983-01-01

A constrained iterative image restoration method is applied to multichannel diffraction-limited imagery. This method is based on the Gerchberg-Papoulis algorithm utilizing incomplete information and partial constraints. The procedure is described using the orthogonal projection operators which project onto two prescribed subspaces iteratively. Some of its properties and limitations are also presented. The selection of appropriate constraints was emphasized in a practical application. Multichannel microwave images, each having different spatial resolution, were restored to a common highest resolution to demonstrate the effectiveness of the method. Both noise-free and noisy images were used in this investigation.

Iterative algorithms for computing the feedback Nash equilibrium point for positive systems

NASA Astrophysics Data System (ADS)

Ivanov, I.; Imsland, Lars; Bogdanova, B.

2017-03-01

The paper studies N-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilising solution of a set of generalised algebraic Riccati equations. The latter is related to the Nash equilibrium point of the considered game model. Moreover, we derive the sufficient conditions for convergence of the proposed methods. Finally, we discuss two numerical examples so as to illustrate the performance of both of the algorithms.

Iterative Magnetometer Calibration

NASA Technical Reports Server (NTRS)

Sedlak, Joseph

2006-01-01

This paper presents an iterative method for three-axis magnetometer (TAM) calibration that makes use of three existing utilities recently incorporated into the attitude ground support system used at NASA's Goddard Space Flight Center. The method combines attitude-independent and attitude-dependent calibration algorithms with a new spinning spacecraft Kalman filter to solve for biases, scale factors, nonorthogonal corrections to the alignment, and the orthogonal sensor alignment. The method is particularly well-suited to spin-stabilized spacecraft, but may also be useful for three-axis stabilized missions given sufficient data to provide observability.

Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cinal, M.; Holas, A.

2011-06-15

The reported algorithm determines the exact exchange potential v{sub x} in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v{sub x} and the latter for increments of ES and OS due to subsequent changes of v{sub x}. Thus, the need for solution of the differential equations for OSs, used by Kuemmel and Perdew [Phys. Rev. Lett. 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms ofmore » ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v{sub x} so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10{sup -6} after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10{sup -4} hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of v{sub x} iteration, while the accuracy limit of 10{sup -6} to 10{sup -7} hartree is reached after 20 density iterations.« less

Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

NASA Astrophysics Data System (ADS)

Cinal, M.; Holas, A.

2011-06-01

The reported algorithm determines the exact exchange potential vx in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to vx and the latter for increments of ES and OS due to subsequent changes of vx. Thus, the need for solution of the differential equations for OSs, used by Kümmel and Perdew [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.90.043004 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms of ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact vx so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10-6 after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10-4 hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of vx iteration, while the accuracy limit of 10-6 to 10-7 hartree is reached after 20 density iterations.

Multishot cartesian turbo spin-echo diffusion imaging using iterative POCSMUSE Reconstruction.

PubMed

Zhang, Zhe; Zhang, Bing; Li, Ming; Liang, Xue; Chen, Xiaodong; Liu, Renyuan; Zhang, Xin; Guo, Hua

2017-07-01

To report a diffusion imaging technique insensitive to off-resonance artifacts and motion-induced ghost artifacts using multishot Cartesian turbo spin-echo (TSE) acquisition and iterative POCS-based reconstruction of multiplexed sensitivity encoded magnetic resonance imaging (MRI) (POCSMUSE) for phase correction. Phase insensitive diffusion preparation was used to deal with the violation of the Carr-Purcell-Meiboom-Gill (CPMG) conditions of TSE diffusion-weighted imaging (DWI), followed by a multishot Cartesian TSE readout for data acquisition. An iterative diffusion phase correction method, iterative POCSMUSE, was developed and implemented to eliminate the ghost artifacts in multishot TSE DWI. The in vivo human brain diffusion images (from one healthy volunteer and 10 patients) using multishot Cartesian TSE were acquired at 3T and reconstructed using iterative POCSMUSE, and compared with single-shot and multishot echo-planar imaging (EPI) results. These images were evaluated by two radiologists using visual scores (considering both image quality and distortion levels) from 1 to 5. The proposed iterative POCSMUSE reconstruction was able to correct the ghost artifacts in multishot DWI. The ghost-to-signal ratio of TSE DWI using iterative POCSMUSE (0.0174 ± 0.0024) was significantly (P < 0.0005) smaller than using POCSMUSE (0.0253 ± 0.0040). The image scores of multishot TSE DWI were significantly higher than single-shot (P = 0.004 and 0.006 from two reviewers) and multishot (P = 0.008 and 0.004 from two reviewers) EPI-based methods. The proposed multishot Cartesian TSE DWI using iterative POCSMUSE reconstruction can provide high-quality diffusion images insensitive to motion-induced ghost artifacts and off-resonance related artifacts such as chemical shifts and susceptibility-induced image distortions. 1 Technical Efficacy: Stage 1 J. MAGN. RESON. IMAGING 2017;46:167-174. © 2016 International Society for Magnetic Resonance in Medicine.

Solution of the within-group multidimensional discrete ordinates transport equations on massively parallel architectures

NASA Astrophysics Data System (ADS)

Zerr, Robert Joseph

2011-12-01

The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of thousands of processors. The PGS method does outperform SI DSA for the periodic heterogeneous layers (PHL) configuration problems. Although this demonstrates a relative strength/weakness between the two methods, the practicality of these problems is much less, further limiting instances where it would be beneficial to select ITMM over SI DSA. The results strongly indicate a need for a robust, stable, and efficient acceleration method (or preconditioner for PGMRES). The spatial multigrid (SMG) method is currently incomplete in that it does not work for all cases considered and does not effectively improve the convergence rate for all values of scattering ratio c or cell dimension h. Nevertheless, it does display the desired trend for highly scattering, optically thin problems. That is, it tends to lower the rate of growth of number of iterations with increasing number of processes, P, while not increasing the number of additional operations per iteration to the extent that the total execution time of the rapidly converging accelerated iterations exceeds that of the slower unaccelerated iterations. A predictive parallel performance model has been developed for the PBJ method. Timing tests were performed such that trend lines could be fitted to the data for the different components and used to estimate the execution times. Applied to the weak scaling results, the model notably underestimates construction time, but combined with a slight overestimation in iterative solution time, the model predicts total execution time very well for large P. It also does a decent job with the strong scaling results, closely predicting the construction time and time per iteration, especially as P increases. Although not shown to be competitive up to 1,024 processing elements with the current state of the art, the parallelized ITMM exhibits promising scaling trends. Ultimately, compared to the KBA method, the parallelized ITMM may be found to be a very attractive option for transport calculations spatially decomposed over several tens of thousands of processes. Acceleration/preconditioning of the parallelized ITMM once developed will improve the convergence rate and improve its competitiveness. (Abstract shortened by UMI.)

Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations.

PubMed

Banerjee, Amartya S; Lin, Lin; Suryanarayana, Phanish; Yang, Chao; Pask, John E

2018-06-12

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).

Vectorized and multitasked solution of the few-group neutron diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zee, S.K.; Turinsky, P.J.; Shayer, Z.

1989-03-01

A numerical algorithm with parallelism was used to solve the two-group, multidimensional neutron diffusion equations on computers characterized by shared memory, vector pipeline, and multi-CPU architecture features. Specifically, solutions were obtained on the Cray X/MP-48, the IBM-3090 with vector facilities, and the FPS-164. The material-centered mesh finite difference method approximation and outer-inner iteration method were employed. Parallelism was introduced in the inner iterations using the cyclic line successive overrelaxation iterative method and solving in parallel across lines. The outer iterations were completed using the Chebyshev semi-iterative method that allows parallelism to be introduced in both space and energy groups. Formore » the three-dimensional model, power, soluble boron, and transient fission product feedbacks were included. Concentrating on the pressurized water reactor (PWR), the thermal-hydraulic calculation of moderator density assumed single-phase flow and a closed flow channel, allowing parallelism to be introduced in the solution across the radial plane. Using a pinwise detail, quarter-core model of a typical PWR in cycle 1, for the two-dimensional model without feedback the measured million floating point operations per second (MFLOPS)/vector speedups were 83/11.7. 18/2.2, and 2.4/5.6 on the Cray, IBM, and FPS without multitasking, respectively. Lower performance was observed with a coarser mesh, i.e., shorter vector length, due to vector pipeline start-up. For an 18 x 18 x 30 (x-y-z) three-dimensional model with feedback of the same core, MFLOPS/vector speedups of --61/6.7 and an execution time of 0.8 CPU seconds on the Cray without multitasking were measured. Finally, using two CPUs and the vector pipelines of the Cray, a multitasking efficiency of 81% was noted for the three-dimensional model.« less

Accelerated iterative beam angle selection in IMRT.

PubMed

Bangert, Mark; Unkelbach, Jan

2016-03-01

Iterative methods for beam angle selection (BAS) for intensity-modulated radiation therapy (IMRT) planning sequentially construct a beneficial ensemble of beam directions. In a naïve implementation, the nth beam is selected by adding beam orientations one-by-one from a discrete set of candidates to an existing ensemble of (n - 1) beams. The best beam orientation is identified in a time consuming process by solving the fluence map optimization (FMO) problem for every candidate beam and selecting the beam that yields the largest improvement to the objective function value. This paper evaluates two alternative methods to accelerate iterative BAS based on surrogates for the FMO objective function value. We suggest to select candidate beams not based on the FMO objective function value after convergence but (1) based on the objective function value after five FMO iterations of a gradient based algorithm and (2) based on a projected gradient of the FMO problem in the first iteration. The performance of the objective function surrogates is evaluated based on the resulting objective function values and dose statistics in a treatment planning study comprising three intracranial, three pancreas, and three prostate cases. Furthermore, iterative BAS is evaluated for an application in which a small number of noncoplanar beams complement a set of coplanar beam orientations. This scenario is of practical interest as noncoplanar setups may require additional attention of the treatment personnel for every couch rotation. Iterative BAS relying on objective function surrogates yields similar results compared to naïve BAS with regard to the objective function values and dose statistics. At the same time, early stopping of the FMO and using the projected gradient during the first iteration enable reductions in computation time by approximately one to two orders of magnitude. With regard to the clinical delivery of noncoplanar IMRT treatments, we could show that optimized beam ensembles using only a few noncoplanar beam orientations often approach the plan quality of fully noncoplanar ensembles. We conclude that iterative BAS in combination with objective function surrogates can be a viable option to implement automated BAS at clinically acceptable computation times.

An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications

NASA Astrophysics Data System (ADS)

Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.

2009-12-01

A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss-Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

NASA Astrophysics Data System (ADS)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

SU-F-I-49: Vendor-Independent, Model-Based Iterative Reconstruction On a Rotating Grid with Coordinate-Descent Optimization for CT Imaging Investigations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Young, S; Hoffman, J; McNitt-Gray, M

Purpose: Iterative reconstruction methods show promise for improving image quality and lowering the dose in helical CT. We aim to develop a novel model-based reconstruction method that offers potential for dose reduction with reasonable computation speed and storage requirements for vendor-independent reconstruction from clinical data on a normal desktop computer. Methods: In 2012, Xu proposed reconstructing on rotating slices to exploit helical symmetry and reduce the storage requirements for the CT system matrix. Inspired by this concept, we have developed a novel reconstruction method incorporating the stored-system-matrix approach together with iterative coordinate-descent (ICD) optimization. A penalized-least-squares objective function with amore » quadratic penalty term is solved analytically voxel-by-voxel, sequentially iterating along the axial direction first, followed by the transaxial direction. 8 in-plane (transaxial) neighbors are used for the ICD algorithm. The forward problem is modeled via a unique approach that combines the principle of Joseph’s method with trilinear B-spline interpolation to enable accurate reconstruction with low storage requirements. Iterations are accelerated with multi-CPU OpenMP libraries. For preliminary evaluations, we reconstructed (1) a simulated 3D ellipse phantom and (2) an ACR accreditation phantom dataset exported from a clinical scanner (Definition AS, Siemens Healthcare). Image quality was evaluated in the resolution module. Results: Image quality was excellent for the ellipse phantom. For the ACR phantom, image quality was comparable to clinical reconstructions and reconstructions using open-source FreeCT-wFBP software. Also, we did not observe any deleterious impact associated with the utilization of rotating slices. The system matrix storage requirement was only 4.5GB, and reconstruction time was 50 seconds per iteration. Conclusion: Our reconstruction method shows potential for furthering research in low-dose helical CT, in particular as part of our ongoing development of an acquisition/reconstruction pipeline for generating images under a wide range of conditions. Our algorithm will be made available open-source as “FreeCT-ICD”. NIH U01 CA181156; Disclosures (McNitt-Gray): Institutional research agreement, Siemens Healthcare; Past recipient, research grant support, Siemens Healthcare; Consultant, Toshiba America Medical Systems; Consultant, Samsung Electronics.« less

LETTER TO THE EDITOR: Iteratively-coupled propagating exterior complex scaling method for electron hydrogen collisions

NASA Astrophysics Data System (ADS)

Bartlett, Philip L.; Stelbovics, Andris T.; Bray, Igor

2004-02-01

A newly-derived iterative coupling procedure for the propagating exterior complex scaling (PECS) method is used to efficiently calculate the electron-impact wavefunctions for atomic hydrogen. An overview of this method is given along with methods for extracting scattering cross sections. Differential scattering cross sections at 30 eV are presented for the electron-impact excitation to the n = 1, 2, 3 and 4 final states, for both PECS and convergent close coupling (CCC), which are in excellent agreement with each other and with experiment. PECS results are presented at 27.2 eV and 30 eV for symmetric and asymmetric energy-sharing triple differential cross sections, which are in excellent agreement with CCC and exterior complex scaling calculations, and with experimental data. At these intermediate energies, the efficiency of the PECS method with iterative coupling has allowed highly accurate partial-wave solutions of the full Schrödinger equation, for L les 50 and a large number of coupled angular momentum states, to be obtained with minimal computing resources.

Domain decomposition methods for the parallel computation of reacting flows

NASA Technical Reports Server (NTRS)

Keyes, David E.

1988-01-01

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm

NASA Astrophysics Data System (ADS)

Zhang, B.; Sang, Jun; Alam, Mohammad S.

2013-03-01

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.

Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction

PubMed Central

Nikazad, T; Davidi, R; Herman, G. T.

2013-01-01

We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least squares solution. Perturbation resilience is utilized to approximate the minimum of a convex functional subject to the equations. A main contribution, as compared to previously published approaches to achieving similar aims, is a more than an order of magnitude speed-up, as demonstrated by applying the methods to problems of image reconstruction from projections. In addition, the accelerated algorithms are illustrated to be better, in a strict sense provided by the method of statistical hypothesis testing, than their unaccelerated versions for the task of detecting small tumors in the brain from X-ray CT projection data. PMID:23440911

Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction.

PubMed

Nikazad, T; Davidi, R; Herman, G T

2012-03-01

We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least squares solution. Perturbation resilience is utilized to approximate the minimum of a convex functional subject to the equations. A main contribution, as compared to previously published approaches to achieving similar aims, is a more than an order of magnitude speed-up, as demonstrated by applying the methods to problems of image reconstruction from projections. In addition, the accelerated algorithms are illustrated to be better, in a strict sense provided by the method of statistical hypothesis testing, than their unaccelerated versions for the task of detecting small tumors in the brain from X-ray CT projection data.

Varying-energy CT imaging method based on EM-TV

NASA Astrophysics Data System (ADS)

Chen, Ping; Han, Yan

2016-11-01

For complicated structural components with wide x-ray attenuation ranges, conventional fixed-energy computed tomography (CT) imaging cannot obtain all the structural information. This limitation results in a shortage of CT information because the effective thickness of the components along the direction of x-ray penetration exceeds the limit of the dynamic range of the x-ray imaging system. To address this problem, a varying-energy x-ray CT imaging method is proposed. In this new method, the tube voltage is adjusted several times with the fixed lesser interval. Next, the fusion of grey consistency and logarithm demodulation are applied to obtain full and lower noise projection with a high dynamic range (HDR). In addition, for the noise suppression problem of the analytical method, EM-TV (expectation maximization-total Jvariation) iteration reconstruction is used. In the process of iteration, the reconstruction result obtained at one x-ray energy is used as the initial condition of the next iteration. An accompanying experiment demonstrates that this EM-TV reconstruction can also extend the dynamic range of x-ray imaging systems and provide a higher reconstruction quality relative to the fusion reconstruction method.

Improved sensitivity of computed tomography towards iodine and gold nanoparticle contrast agents via iterative reconstruction methods

PubMed Central

Bernstein, Ally Leigh; Dhanantwari, Amar; Jurcova, Martina; Cheheltani, Rabee; Naha, Pratap Chandra; Ivanc, Thomas; Shefer, Efrat; Cormode, David Peter

2016-01-01

Computed tomography is a widely used medical imaging technique that has high spatial and temporal resolution. Its weakness is its low sensitivity towards contrast media. Iterative reconstruction techniques (ITER) have recently become available, which provide reduced image noise compared with traditional filtered back-projection methods (FBP), which may allow the sensitivity of CT to be improved, however this effect has not been studied in detail. We scanned phantoms containing either an iodine contrast agent or gold nanoparticles. We used a range of tube voltages and currents. We performed reconstruction with FBP, ITER and a novel, iterative, modal-based reconstruction (IMR) algorithm. We found that noise decreased in an algorithm dependent manner (FBP > ITER > IMR) for every scan and that no differences were observed in attenuation rates of the agents. The contrast to noise ratio (CNR) of iodine was highest at 80 kV, whilst the CNR for gold was highest at 140 kV. The CNR of IMR images was almost tenfold higher than that of FBP images. Similar trends were found in dual energy images formed using these algorithms. In conclusion, IMR-based reconstruction techniques will allow contrast agents to be detected with greater sensitivity, and may allow lower contrast agent doses to be used. PMID:27185492

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

NASA Astrophysics Data System (ADS)

Litaker, Eric T.

1994-12-01

The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

An iterative sinogram gap-filling method with object- and scanner-dedicated discrete cosine transform (DCT)-domain filters for high resolution PET scanners.

PubMed

Kim, Kwangdon; Lee, Kisung; Lee, Hakjae; Joo, Sungkwan; Kang, Jungwon

2018-01-01

We aimed to develop a gap-filling algorithm, in particular the filter mask design method of the algorithm, which optimizes the filter to the imaging object by an adaptive and iterative process, rather than by manual means. Two numerical phantoms (Shepp-Logan and Jaszczak) were used for sinogram generation. The algorithm works iteratively, not only on the gap-filling iteration but also on the mask generation, to identify the object-dedicated low frequency area in the DCT-domain that is to be preserved. We redefine the low frequency preserving region of the filter mask at every gap-filling iteration, and the region verges on the property of the original image in the DCT domain. The previous DCT2 mask for each phantom case had been manually well optimized, and the results show little difference from the reference image and sinogram. We observed little or no difference between the results of the manually optimized DCT2 algorithm and those of the proposed algorithm. The proposed algorithm works well for various types of scanning object and shows results that compare to those of the manually optimized DCT2 algorithm without perfect or full information of the imaging object.

Two-Level Hierarchical FEM Method for Modeling Passive Microwave Devices

NASA Astrophysics Data System (ADS)

Polstyanko, Sergey V.; Lee, Jin-Fa

1998-03-01

In recent years multigrid methods have been proven to be very efficient for solving large systems of linear equations resulting from the discretization of positive definite differential equations by either the finite difference method or theh-version of the finite element method. In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which arise from thep-version of the finite element analysis applied to indefinite problems. A two-levelV-cycle algorithm has been implemented and studied with a Gauss-Seidel iterative scheme used as a smoother. The convergence of the method has been investigated, and numerical results for a number of numerical examples are presented.

On Born approximation in black hole scattering

NASA Astrophysics Data System (ADS)

Batic, D.; Kelkar, N. G.; Nowakowski, M.

2011-12-01

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordström and Reissner-Nordström-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.

A diffusion-based truncated projection artifact reduction method for iterative digital breast tomosynthesis reconstruction

PubMed Central

Lu, Yao; Chan, Heang-Ping; Wei, Jun; Hadjiiski, Lubomir M

2014-01-01

Digital breast tomosynthesis (DBT) has strong promise to improve sensitivity for detecting breast cancer. DBT reconstruction estimates the breast tissue attenuation using projection views (PVs) acquired in a limited angular range. Because of the limited field of view (FOV) of the detector, the PVs may not completely cover the breast in the x-ray source motion direction at large projection angles. The voxels in the imaged volume cannot be updated when they are outside the FOV, thus causing a discontinuity in intensity across the FOV boundaries in the reconstructed slices, which we refer to as the truncated projection artifact (TPA). Most existing TPA reduction methods were developed for the filtered backprojection method in the context of computed tomography. In this study, we developed a new diffusion-based method to reduce TPAs during DBT reconstruction using the simultaneous algebraic reconstruction technique (SART). Our TPA reduction method compensates for the discontinuity in background intensity outside the FOV of the current PV after each PV updating in SART. The difference in voxel values across the FOV boundary is smoothly diffused to the region beyond the FOV of the current PV. Diffusion-based background intensity estimation is performed iteratively to avoid structured artifacts. The method is applicable to TPA in both the forward and backward directions of the PVs and for any number of iterations during reconstruction. The effectiveness of the new method was evaluated by comparing the visual quality of the reconstructed slices and the measured discontinuities across the TPA with and without artifact correction at various iterations. The results demonstrated that the diffusion-based intensity compensation method reduced the TPA while preserving the detailed tissue structures. The visibility of breast lesions obscured by the TPA was improved after artifact reduction. PMID:23318346

GPU-accelerated iterative reconstruction from Compton scattered data using a matched pair of conic projector and backprojector.

PubMed

Nguyen, Van-Giang; Lee, Soo-Jin

2016-07-01

Iterative reconstruction from Compton scattered data is known to be computationally more challenging than that from conventional line-projection based emission data in that the gamma rays that undergo Compton scattering are modeled as conic projections rather than line projections. In conventional tomographic reconstruction, to parallelize the projection and backprojection operations using the graphics processing unit (GPU), approximated methods that use an unmatched pair of ray-tracing forward projector and voxel-driven backprojector have been widely used. In this work, we propose a new GPU-accelerated method for Compton camera reconstruction which is more accurate by using exactly matched pair of projector and backprojector. To calculate conic forward projection, we first sample the cone surface into conic rays and accumulate the intersecting chord lengths of the conic rays passing through voxels using a fast ray-tracing method (RTM). For conic backprojection, to obtain the true adjoint of the conic forward projection, while retaining the computational efficiency of the GPU, we use a voxel-driven RTM which is essentially the same as the standard RTM used for the conic forward projector. Our simulation results show that, while the new method is about 3 times slower than the approximated method, it is still about 16 times faster than the CPU-based method without any loss of accuracy. The net conclusion is that our proposed method is guaranteed to retain the reconstruction accuracy regardless of the number of iterations by providing a perfectly matched projector-backprojector pair, which makes iterative reconstruction methods for Compton imaging faster and more accurate. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Self-consistent field for fragmented quantum mechanical model of large molecular systems.

PubMed

Jin, Yingdi; Su, Neil Qiang; Xu, Xin; Hu, Hao

2016-01-30

Fragment-based linear scaling quantum chemistry methods are a promising tool for the accurate simulation of chemical and biomolecular systems. Because of the coupled inter-fragment electrostatic interactions, a dual-layer iterative scheme is often employed to compute the fragment electronic structure and the total energy. In the dual-layer scheme, the self-consistent field (SCF) of the electronic structure of a fragment must be solved first, then followed by the updating of the inter-fragment electrostatic interactions. The two steps are sequentially carried out and repeated; as such a significant total number of fragment SCF iterations is required to converge the total energy and becomes the computational bottleneck in many fragment quantum chemistry methods. To reduce the number of fragment SCF iterations and speed up the convergence of the total energy, we develop here a new SCF scheme in which the inter-fragment interactions can be updated concurrently without converging the fragment electronic structure. By constructing the global, block-wise Fock matrix and density matrix, we prove that the commutation between the two global matrices guarantees the commutation of the corresponding matrices in each fragment. Therefore, many highly efficient numerical techniques such as the direct inversion of the iterative subspace method can be employed to converge simultaneously the electronic structure of all fragments, reducing significantly the computational cost. Numerical examples for water clusters of different sizes suggest that the method shall be very useful in improving the scalability of fragment quantum chemistry methods. © 2015 Wiley Periodicals, Inc.

Implicit methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Yoon, S.; Kwak, D.

1990-01-01

Numerical solutions of the Navier-Stokes equations using explicit schemes can be obtained at the expense of efficiency. Conventional implicit methods which often achieve fast convergence rates suffer high cost per iteration. A new implicit scheme based on lower-upper factorization and symmetric Gauss-Seidel relaxation offers very low cost per iteration as well as fast convergence. High efficiency is achieved by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

A new least-squares transport equation compatible with voids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, J. B.; Morel, J. E.

2013-07-01

We define a new least-squares transport equation that is applicable in voids, can be solved using source iteration with diffusion-synthetic acceleration, and requires only the solution of an independent set of second-order self-adjoint equations for each direction during each source iteration. We derive the equation, discretize it using the S{sub n} method in conjunction with a linear-continuous finite-element method in space, and computationally demonstrate various of its properties. (authors)

Iterative nonlinear joint transform correlation for the detection of objects in cluttered scenes

NASA Astrophysics Data System (ADS)

Haist, Tobias; Tiziani, Hans J.

1999-03-01

An iterative correlation technique with digital image processing in the feedback loop for the detection of small objects in cluttered scenes is proposed. A scanning aperture is combined with the method in order to improve the immunity against noise and clutter. Multiple reference objects or different views of one object are processed in parallel. We demonstrate the method by detecting a noisy and distorted face in a crowd with a nonlinear joint transform correlator.

Recent advances in Lanczos-based iterative methods for nonsymmetric linear systems

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Golub, Gene H.; Nachtigal, Noel M.

1992-01-01

In recent years, there has been a true revival of the nonsymmetric Lanczos method. On the one hand, the possible breakdowns in the classical algorithm are now better understood, and so-called look-ahead variants of the Lanczos process have been developed, which remedy this problem. On the other hand, various new Lanczos-based iterative schemes for solving nonsymmetric linear systems have been proposed. This paper gives a survey of some of these recent developments.

Internet-based biosurveillance methods for vector-borne diseases: Are they novel public health tools or just novelties?

PubMed

Pollett, Simon; Althouse, Benjamin M; Forshey, Brett; Rutherford, George W; Jarman, Richard G

2017-11-01

Internet-based surveillance methods for vector-borne diseases (VBDs) using "big data" sources such as Google, Twitter, and internet newswire scraping have recently been developed, yet reviews on such "digital disease detection" methods have focused on respiratory pathogens, particularly in high-income regions. Here, we present a narrative review of the literature that has examined the performance of internet-based biosurveillance for diseases caused by vector-borne viruses, parasites, and other pathogens, including Zika, dengue, other arthropod-borne viruses, malaria, leishmaniasis, and Lyme disease across a range of settings, including low- and middle-income countries. The fundamental features, advantages, and drawbacks of each internet big data source are presented for those with varying familiarity of "digital epidemiology." We conclude with some of the challenges and future directions in using internet-based biosurveillance for the surveillance and control of VBD.

Internet-based biosurveillance methods for vector-borne diseases: Are they novel public health tools or just novelties?

PubMed Central

Pollett, Simon; Althouse, Benjamin M.; Forshey, Brett; Rutherford, George W.; Jarman, Richard G.

2017-01-01

Internet-based surveillance methods for vector-borne diseases (VBDs) using “big data” sources such as Google, Twitter, and internet newswire scraping have recently been developed, yet reviews on such “digital disease detection” methods have focused on respiratory pathogens, particularly in high-income regions. Here, we present a narrative review of the literature that has examined the performance of internet-based biosurveillance for diseases caused by vector-borne viruses, parasites, and other pathogens, including Zika, dengue, other arthropod-borne viruses, malaria, leishmaniasis, and Lyme disease across a range of settings, including low- and middle-income countries. The fundamental features, advantages, and drawbacks of each internet big data source are presented for those with varying familiarity of “digital epidemiology.” We conclude with some of the challenges and future directions in using internet-based biosurveillance for the surveillance and control of VBD. PMID:29190281

Simultaneous Localization and Mapping with Iterative Sparse Extended Information Filter for Autonomous Vehicles

PubMed Central

He, Bo; Liu, Yang; Dong, Diya; Shen, Yue; Yan, Tianhong; Nian, Rui

2015-01-01

In this paper, a novel iterative sparse extended information filter (ISEIF) was proposed to solve the simultaneous localization and mapping problem (SLAM), which is very crucial for autonomous vehicles. The proposed algorithm solves the measurement update equations with iterative methods adaptively to reduce linearization errors. With the scalability advantage being kept, the consistency and accuracy of SEIF is improved. Simulations and practical experiments were carried out with both a land car benchmark and an autonomous underwater vehicle. Comparisons between iterative SEIF (ISEIF), standard EKF and SEIF are presented. All of the results convincingly show that ISEIF yields more consistent and accurate estimates compared to SEIF and preserves the scalability advantage over EKF, as well. PMID:26287194

An Assessment of Iterative Reconstruction Methods for Sparse Ultrasound Imaging

PubMed Central

Valente, Solivan A.; Zibetti, Marcelo V. W.; Pipa, Daniel R.; Maia, Joaquim M.; Schneider, Fabio K.

2017-01-01

Ultrasonic image reconstruction using inverse problems has recently appeared as an alternative to enhance ultrasound imaging over beamforming methods. This approach depends on the accuracy of the acquisition model used to represent transducers, reflectivity, and medium physics. Iterative methods, well known in general sparse signal reconstruction, are also suited for imaging. In this paper, a discrete acquisition model is assessed by solving a linear system of equations by an ℓ1-regularized least-squares minimization, where the solution sparsity may be adjusted as desired. The paper surveys 11 variants of four well-known algorithms for sparse reconstruction, and assesses their optimization parameters with the goal of finding the best approach for iterative ultrasound imaging. The strategy for the model evaluation consists of using two distinct datasets. We first generate data from a synthetic phantom that mimics real targets inside a professional ultrasound phantom device. This dataset is contaminated with Gaussian noise with an estimated SNR, and all methods are assessed by their resulting images and performances. The model and methods are then assessed with real data collected by a research ultrasound platform when scanning the same phantom device, and results are compared with beamforming. A distinct real dataset is finally used to further validate the proposed modeling. Although high computational effort is required by iterative methods, results show that the discrete model may lead to images closer to ground-truth than traditional beamforming. However, computing capabilities of current platforms need to evolve before frame rates currently delivered by ultrasound equipments are achievable. PMID:28282862

An iterative method for airway segmentation using multiscale leakage detection

NASA Astrophysics Data System (ADS)

Nadeem, Syed Ahmed; Jin, Dakai; Hoffman, Eric A.; Saha, Punam K.

2017-02-01

There are growing applications of quantitative computed tomography for assessment of pulmonary diseases by characterizing lung parenchyma as well as the bronchial tree. Many large multi-center studies incorporating lung imaging as a study component are interested in phenotypes relating airway branching patterns, wall-thickness, and other morphological measures. To our knowledge, there are no fully automated airway tree segmentation methods, free of the need for user review. Even when there are failures in a small fraction of segmentation results, the airway tree masks must be manually reviewed for all results which is laborious considering that several thousands of image data sets are evaluated in large studies. In this paper, we present a CT-based novel airway tree segmentation algorithm using iterative multi-scale leakage detection, freezing, and active seed detection. The method is fully automated requiring no manual inputs or post-segmentation editing. It uses simple intensity based connectivity and a new leakage detection algorithm to iteratively grow an airway tree starting from an initial seed inside the trachea. It begins with a conservative threshold and then, iteratively shifts toward generous values. The method was applied on chest CT scans of ten non-smoking subjects at total lung capacity and ten at functional residual capacity. Airway segmentation results were compared to an expert's manually edited segmentations. Branch level accuracy of the new segmentation method was examined along five standardized segmental airway paths (RB1, RB4, RB10, LB1, LB10) and two generations beyond these branches. The method successfully detected all branches up to two generations beyond these segmental bronchi with no visual leakages.

Outlier detection for particle image velocimetry data using a locally estimated noise variance

NASA Astrophysics Data System (ADS)

Lee, Yong; Yang, Hua; Yin, ZhouPing

2017-03-01

This work describes an adaptive spatial variable threshold outlier detection algorithm for raw gridded particle image velocimetry data using a locally estimated noise variance. This method is an iterative procedure, and each iteration is composed of a reference vector field reconstruction step and an outlier detection step. We construct the reference vector field using a weighted adaptive smoothing method (Garcia 2010 Comput. Stat. Data Anal. 54 1167-78), and the weights are determined in the outlier detection step using a modified outlier detector (Ma et al 2014 IEEE Trans. Image Process. 23 1706-21). A hard decision on the final weights of the iteration can produce outlier labels of the field. The technical contribution is that the spatial variable threshold motivation is embedded in the modified outlier detector with a locally estimated noise variance in an iterative framework for the first time. It turns out that a spatial variable threshold is preferable to a single spatial constant threshold in complicated flows such as vortex flows or turbulent flows. Synthetic cellular vortical flows with simulated scattered or clustered outliers are adopted to evaluate the performance of our proposed method in comparison with popular validation approaches. This method also turns out to be beneficial in a real PIV measurement of turbulent flow. The experimental results demonstrated that the proposed method yields the competitive performance in terms of outlier under-detection count and over-detection count. In addition, the outlier detection method is computational efficient and adaptive, requires no user-defined parameters, and corresponding implementations are also provided in supplementary materials.

A fast reconstruction algorithm for fluorescence optical diffusion tomography based on preiteration.

PubMed

Song, Xiaolei; Xiong, Xiaoyun; Bai, Jing

2007-01-01

Fluorescence optical diffusion tomography in the near-infrared (NIR) bandwidth is considered to be one of the most promising ways for noninvasive molecular-based imaging. Many reconstructive approaches to it utilize iterative methods for data inversion. However, they are time-consuming and they are far from meeting the real-time imaging demands. In this work, a fast preiteration algorithm based on the generalized inverse matrix is proposed. This method needs only one step of matrix-vector multiplication online, by pushing the iteration process to be executed offline. In the preiteration process, the second-order iterative format is employed to exponentially accelerate the convergence. Simulations based on an analytical diffusion model show that the distribution of fluorescent yield can be well estimated by this algorithm and the reconstructed speed is remarkably increased.

Analytic approximation for random muffin-tin alloys

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mills, R.; Gray, L.J.; Kaplan, T.

1983-03-15

The methods introduced in a previous paper under the name of ''traveling-cluster approximation'' (TCA) are applied, in a multiple-scattering approach, to the case of a random muffin-tin substitutional alloy. This permits the iterative part of a self-consistent calculation to be carried out entirely in terms of on-the-energy-shell scattering amplitudes. Off-shell components of the mean resolvent, needed for the calculation of spectral functions, are obtained by standard methods involving single-site scattering wave functions. The single-site TCA is just the usual coherent-potential approximation, expressed in a form particularly suited for iteration. A fixed-point theorem is proved for the general t-matrix TCA, ensuringmore » convergence upon iteration to a unique self-consistent solution with the physically essential Herglotz properties.« less

Noniterative Multireference Coupled Cluster Methods on Heterogeneous CPU-GPU Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhaskaran-Nair, Kiran; Ma, Wenjing; Krishnamoorthy, Sriram

2013-04-09

A novel parallel algorithm for non-iterative multireference coupled cluster (MRCC) theories, which merges recently introduced reference-level parallelism (RLP) [K. Bhaskaran-Nair, J.Brabec, E. Aprà, H.J.J. van Dam, J. Pittner, K. Kowalski, J. Chem. Phys. 137, 094112 (2012)] with the possibility of accelerating numerical calculations using graphics processing unit (GPU) is presented. We discuss the performance of this algorithm on the example of the MRCCSD(T) method (iterative singles and doubles and perturbative triples), where the corrections due to triples are added to the diagonal elements of the MRCCSD (iterative singles and doubles) effective Hamiltonian matrix. The performance of the combined RLP/GPU algorithmmore » is illustrated on the example of the Brillouin-Wigner (BW) and Mukherjee (Mk) state-specific MRCCSD(T) formulations.« less

Real-Time Nonlocal Means-Based Despeckling.

PubMed

Breivik, Lars Hofsoy; Snare, Sten Roar; Steen, Erik Normann; Solberg, Anne H Schistad

2017-06-01

In this paper, we propose a multiscale nonlocal means-based despeckling method for medical ultrasound. The multiscale approach leads to large computational savings and improves despeckling results over single-scale iterative approaches. We present two variants of the method. The first, denoted multiscale nonlocal means (MNLM), yields uniform robust filtering of speckle both in structured and homogeneous regions. The second, denoted unnormalized MNLM (UMNLM), is more conservative in regions of structure assuring minimal disruption of salient image details. Due to the popularity of anisotropic diffusion-based methods in the despeckling literature, we review the connection between anisotropic diffusion and iterative variants of NLM. These iterative variants in turn relate to our multiscale variant. As part of our evaluation, we conduct a simulation study making use of ground truth phantoms generated from clinical B-mode ultrasound images. We evaluate our method against a set of popular methods from the despeckling literature on both fine and coarse speckle noise. In terms of computational efficiency, our method outperforms the other considered methods. Quantitatively on simulations and on a tissue-mimicking phantom, our method is found to be competitive with the state-of-the-art. On clinical B-mode images, our method is found to effectively smooth speckle while preserving low-contrast and highly localized salient image detail.

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Qiaofeng; Sawatzky, Alex; Anastasio, Mark A., E-mail: anastasio@wustl.edu

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that ismore » solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.« less

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

PubMed Central

Xu, Qiaofeng; Yang, Deshan; Tan, Jun; Sawatzky, Alex; Anastasio, Mark A.

2016-01-01

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets. PMID:27036582

Iterative methods for dose reduction and image enhancement in tomography

DOEpatents

Miao, Jianwei; Fahimian, Benjamin Pooya

2012-09-18

A system and method for creating a three dimensional cross sectional image of an object by the reconstruction of its projections that have been iteratively refined through modification in object space and Fourier space is disclosed. The invention provides systems and methods for use with any tomographic imaging system that reconstructs an object from its projections. In one embodiment, the invention presents a method to eliminate interpolations present in conventional tomography. The method has been experimentally shown to provide higher resolution and improved image quality parameters over existing approaches. A primary benefit of the method is radiation dose reduction since the invention can produce an image of a desired quality with a fewer number projections than seen with conventional methods.

Screening for Dysregulation among Toddlers Born Very Low Birth Weight

ERIC Educational Resources Information Center

Erickson, Sarah J.; MacLean, Peggy; Duvall, Susanne Woolsey; Lowe, Jean R.

2013-01-01

Background: Children born very low birth weight (VLBW) are at increased risk for regulatory difficulties. However, identifying toddlers at risk has been impeded by a lack of screening measures appropriate for this population. Methods: We studied the nature of dysregulation in toddlers born VLBW (N = 32) using the Infant-Toddler Social and…

Principal components and iterative regression analysis of geophysical series: Application to Sunspot number (1750 2004)

NASA Astrophysics Data System (ADS)

Nordemann, D. J. R.; Rigozo, N. R.; de Souza Echer, M. P.; Echer, E.

2008-11-01

We present here an implementation of a least squares iterative regression method applied to the sine functions embedded in the principal components extracted from geophysical time series. This method seems to represent a useful improvement for the non-stationary time series periodicity quantitative analysis. The principal components determination followed by the least squares iterative regression method was implemented in an algorithm written in the Scilab (2006) language. The main result of the method is to obtain the set of sine functions embedded in the series analyzed in decreasing order of significance, from the most important ones, likely to represent the physical processes involved in the generation of the series, to the less important ones that represent noise components. Taking into account the need of a deeper knowledge of the Sun's past history and its implication to global climate change, the method was applied to the Sunspot Number series (1750-2004). With the threshold and parameter values used here, the application of the method leads to a total of 441 explicit sine functions, among which 65 were considered as being significant and were used for a reconstruction that gave a normalized mean squared error of 0.146.

An Iterative Method for Restoring Noisy Blurred Images.

DTIC Science & Technology

1984-01-01

the gafa Is oomputed sing a linear WM Introduced in (2). The Iterative toeigme opimuai neem is updted at sub- hwver , do have ahvatagen when - , -d...condition lot me- that oil Aa) can be written an genes is never satisfied, thus reblurring is always necessary. nore generally, convergence is k1k asrdfo vr

Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry

NASA Technical Reports Server (NTRS)

Nelson, Andrea; Aftosmis, Michael J.; Nemec, Marian; Pulliam, Thomas H.

2004-01-01

Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the number of design variables is increased.

LiDAR-IMU Time Delay Calibration Based on Iterative Closest Point and Iterated Sigma Point Kalman Filter.

PubMed

Liu, Wanli

2017-03-08

The time delay calibration between Light Detection and Ranging (LiDAR) and Inertial Measurement Units (IMUs) is an essential prerequisite for its applications. However, the correspondences between LiDAR and IMU measurements are usually unknown, and thus cannot be computed directly for the time delay calibration. In order to solve the problem of LiDAR-IMU time delay calibration, this paper presents a fusion method based on iterative closest point (ICP) and iterated sigma point Kalman filter (ISPKF), which combines the advantages of ICP and ISPKF. The ICP algorithm can precisely determine the unknown transformation between LiDAR-IMU; and the ISPKF algorithm can optimally estimate the time delay calibration parameters. First of all, the coordinate transformation from the LiDAR frame to the IMU frame is realized. Second, the measurement model and time delay error model of LiDAR and IMU are established. Third, the methodology of the ICP and ISPKF procedure is presented for LiDAR-IMU time delay calibration. Experimental results are presented that validate the proposed method and demonstrate the time delay error can be accurately calibrated.

Reliable recovery of the optical properties of multi-layer turbid media by iteratively using a layered diffusion model at multiple source-detector separations

PubMed Central

Liao, Yu-Kai; Tseng, Sheng-Hao

2014-01-01

Accurately determining the optical properties of multi-layer turbid media using a layered diffusion model is often a difficult task and could be an ill-posed problem. In this study, an iterative algorithm was proposed for solving such problems. This algorithm employed a layered diffusion model to calculate the optical properties of a layered sample at several source-detector separations (SDSs). The optical properties determined at various SDSs were mutually referenced to complete one round of iteration and the optical properties were gradually revised in further iterations until a set of stable optical properties was obtained. We evaluated the performance of the proposed method using frequency domain Monte Carlo simulations and found that the method could robustly recover the layered sample properties with various layer thickness and optical property settings. It is expected that this algorithm can work with photon transport models in frequency and time domain for various applications, such as determination of subcutaneous fat or muscle optical properties and monitoring the hemodynamics of muscle. PMID:24688828

Implementation of the pyramid wavefront sensor as a direct phase detector for large amplitude aberrations

NASA Astrophysics Data System (ADS)

Kupke, Renate; Gavel, Don; Johnson, Jess; Reinig, Marc

2008-07-01

We investigate the non-modulating pyramid wave-front sensor's (P-WFS) implementation in the context of Lick Observatory's Villages visible light AO system on the Nickel 1-meter telescope. A complete adaptive optics correction, using a non-modulated P-WFS in slope sensing mode as a boot-strap to a regime in which the P-WFS can act as a direct phase sensor is explored. An iterative approach to reconstructing the wave-front phase, given the pyramid wave-front sensor's non-linear signal, is developed. Using Monte Carlo simulations, the iterative reconstruction method's photon noise propagation behavior is compared to both the pyramid sensor used in slope-sensing mode, and the traditional Shack Hartmann sensor's theoretical performance limits. We determine that bootstrapping using the P-WFS as a slope sensor does not offer enough correction to bring the phase residuals into a regime in which the iterative algorithm can provide much improvement in phase measurement. It is found that both the iterative phase reconstructor and the slope reconstruction methods offer an advantage in noise propagation over Shack Hartmann sensors.

Quantitative evaluation of ASiR image quality: an adaptive statistical iterative reconstruction technique

NASA Astrophysics Data System (ADS)

Van de Casteele, Elke; Parizel, Paul; Sijbers, Jan

2012-03-01

Adaptive statistical iterative reconstruction (ASiR) is a new reconstruction algorithm used in the field of medical X-ray imaging. This new reconstruction method combines the idealized system representation, as we know it from the standard Filtered Back Projection (FBP) algorithm, and the strength of iterative reconstruction by including a noise model in the reconstruction scheme. It studies how noise propagates through the reconstruction steps, feeds this model back into the loop and iteratively reduces noise in the reconstructed image without affecting spatial resolution. In this paper the effect of ASiR on the contrast to noise ratio is studied using the low contrast module of the Catphan phantom. The experiments were done on a GE LightSpeed VCT system at different voltages and currents. The results show reduced noise and increased contrast for the ASiR reconstructions compared to the standard FBP method. For the same contrast to noise ratio the images from ASiR can be obtained using 60% less current, leading to a reduction in dose of the same amount.

Metal-induced streak artifact reduction using iterative reconstruction algorithms in x-ray computed tomography image of the dentoalveolar region.

PubMed

Dong, Jian; Hayakawa, Yoshihiko; Kannenberg, Sven; Kober, Cornelia

2013-02-01

The objective of this study was to reduce metal-induced streak artifact on oral and maxillofacial x-ray computed tomography (CT) images by developing the fast statistical image reconstruction system using iterative reconstruction algorithms. Adjacent CT images often depict similar anatomical structures in thin slices. So, first, images were reconstructed using the same projection data of an artifact-free image. Second, images were processed by the successive iterative restoration method where projection data were generated from reconstructed image in sequence. Besides the maximum likelihood-expectation maximization algorithm, the ordered subset-expectation maximization algorithm (OS-EM) was examined. Also, small region of interest (ROI) setting and reverse processing were applied for improving performance. Both algorithms reduced artifacts instead of slightly decreasing gray levels. The OS-EM and small ROI reduced the processing duration without apparent detriments. Sequential and reverse processing did not show apparent effects. Two alternatives in iterative reconstruction methods were effective for artifact reduction. The OS-EM algorithm and small ROI setting improved the performance. Copyright © 2012 Elsevier Inc. All rights reserved.

Richardson-Lucy/maximum likelihood image restoration algorithm for fluorescence microscopy: further testing.

PubMed

Holmes, T J; Liu, Y H

1989-11-15

A maximum likelihood based iterative algorithm adapted from nuclear medicine imaging for noncoherent optical imaging was presented in a previous publication with some initial computer-simulation testing. This algorithm is identical in form to that previously derived in a different way by W. H. Richardson "Bayesian-Based Iterative Method of Image Restoration," J. Opt. Soc. Am. 62, 55-59 (1972) and L. B. Lucy "An Iterative Technique for the Rectification of Observed Distributions," Astron. J. 79, 745-765 (1974). Foreseen applications include superresolution and 3-D fluorescence microscopy. This paper presents further simulation testing of this algorithm and a preliminary experiment with a defocused camera. The simulations show quantified resolution improvement as a function of iteration number, and they show qualitatively the trend in limitations on restored resolution when noise is present in the data. Also shown are results of a simulation in restoring missing-cone information for 3-D imaging. Conclusions are in support of the feasibility of using these methods with real systems, while computational cost and timing estimates indicate that it should be realistic to implement these methods. Itis suggested in the Appendix that future extensions to the maximum likelihood based derivation of this algorithm will address some of the limitations that are experienced with the nonextended form of the algorithm presented here.

Microwave imaging by three-dimensional Born linearization of electromagnetic scattering

NASA Astrophysics Data System (ADS)

Caorsi, S.; Gragnani, G. L.; Pastorino, M.

1990-11-01

An approach to microwave imaging is proposed that uses a three-dimensional vectorial form of the Born approximation to linearize the equation of electromagnetic scattering. The inverse scattering problem is numerically solved for three-dimensional geometries by means of the moment method. A pseudoinversion algorithm is adopted to overcome ill conditioning. Results show that the method is well suited for qualitative imaging purposes, while its capability for exactly reconstructing the complex dielectric permittivity is affected by the limitations inherent in the Born approximation and in ill conditioning.

Variations in male-female infant ratios among births to Canadian- and Indian-born mothers, 1990-2011: a population-based register study

PubMed Central

Urquia, Marcelo L.; Ray, Joel G.; Wanigaratne, Susitha; Moineddin, Rahim; O'Campo, Patricia J.

2016-01-01

Background: We assessed variations in the male-female infant ratios among births to Canadian-born and Indian-born mothers according to year of birth, province and country of birth of each parent. Methods: In this population-based register study, we analyzed birth certificates of 5 853 970 singleton live births to Canadian-born and 177 990 singleton live births to Indian-born mothers giving birth in Canada from 1990 to 2011. Male-female ratios were stratified by live birth order and plotted by year of birth. Logistic regression was used to assess whether ratios varied between Canadian provinces and according to the birthplace of each parent. The deficit in the number of girls was estimated using bootstrap methods. Results: Among Canadian-born mothers, male-female ratios were about 1.05, with negligible fluctuations by birth order, year and province. Among Indian-born mothers, the overall male-female ratio at the third birth was 1.38 (95% confidence interval [CI] 1.34-1.41) and was 1.66 (95% CI 1.56-1.76) at the fourth or higher-order births. There was little variability in the ratios between provinces. Couples involving at least 1 Indian-born parent had higher than expected male-female ratios at the second and higher-order births, particularly when the father was Indian-born. The deficit in the expected number of girls among Indian immigrants to Canada in the study period was estimated to be 4472 (95% CI 3211-5921). Interpretation: Fewer than expected girls at the third and higher-order births have been born to Indian immigrants across Canada since 1990. This trend was also seen among couples of mixed nativity, including those involving a Canadian-born mother and an Indian-born father. Fathers should be considered when investigating sex ratios at birth. PMID:27398354

Iterative repair for scheduling and rescheduling

NASA Technical Reports Server (NTRS)

Zweben, Monte; Davis, Eugene; Deale, Michael

1991-01-01

An iterative repair search method is described called constraint based simulated annealing. Simulated annealing is a hill climbing search technique capable of escaping local minima. The utility of the constraint based framework is shown by comparing search performance with and without the constraint framework on a suite of randomly generated problems. Results are also shown of applying the technique to the NASA Space Shuttle ground processing problem. These experiments show that the search methods scales to complex, real world problems and reflects interesting anytime behavior.

Radiative transfer in molecular lines

NASA Astrophysics Data System (ADS)

Asensio Ramos, A.; Trujillo Bueno, J.; Cernicharo, J.

2001-07-01

The highly convergent iterative methods developed by Trujillo Bueno and Fabiani Bendicho (1995) for radiative transfer (RT) applications are generalized to spherical symmetry with velocity fields. These RT methods are based on Jacobi, Gauss-Seidel (GS), and SOR iteration and they form the basis of a new NLTE multilevel transfer code for atomic and molecular lines. The benchmark tests carried out so far are presented and discussed. The main aim is to develop a number of powerful RT tools for the theoretical interpretation of molecular spectra.

Absolutely and uniformly convergent iterative approach to inverse scattering with an infinite radius of convergence

DOEpatents

Kouri, Donald J [Houston, TX; Vijay, Amrendra [Houston, TX; Zhang, Haiyan [Houston, TX; Zhang, Jingfeng [Houston, TX; Hoffman, David K [Ames, IA

2007-05-01

A method and system for solving the inverse acoustic scattering problem using an iterative approach with consideration of half-off-shell transition matrix elements (near-field) information, where the Volterra inverse series correctly predicts the first two moments of the interaction, while the Fredholm inverse series is correct only for the first moment and that the Volterra approach provides a method for exactly obtaining interactions which can be written as a sum of delta functions.

Translation position determination in ptychographic coherent diffraction imaging.

PubMed

Zhang, Fucai; Peterson, Isaac; Vila-Comamala, Joan; Diaz, Ana; Berenguer, Felisa; Bean, Richard; Chen, Bo; Menzel, Andreas; Robinson, Ian K; Rodenburg, John M

2013-06-03

Accurate knowledge of translation positions is essential in ptychography to achieve a good image quality and the diffraction limited resolution. We propose a method to retrieve and correct position errors during the image reconstruction iterations. Sub-pixel position accuracy after refinement is shown to be achievable within several tens of iterations. Simulation and experimental results for both optical and X-ray wavelengths are given. The method improves both the quality of the retrieved object image and relaxes the position accuracy requirement while acquiring the diffraction patterns.

WavePacket: A Matlab package for numerical quantum dynamics.II: Open quantum systems, optimal control, and model reduction

NASA Astrophysics Data System (ADS)

Schmidt, Burkhard; Hartmann, Carsten

2018-07-01

WavePacket is an open-source program package for numeric simulations in quantum dynamics. It can solve time-independent or time-dependent linear Schrödinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows, e.g., to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semi-classical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. Being highly versatile and offering visualization of quantum dynamics 'on the fly', WavePacket is well suited for teaching or research projects in atomic, molecular and optical physics as well as in physical or theoretical chemistry. Building on the previous Part I [Comp. Phys. Comm. 213, 223-234 (2017)] which dealt with closed quantum systems and discrete variable representations, the present Part II focuses on the dynamics of open quantum systems, with Lindblad operators modeling dissipation and dephasing. This part also describes the WavePacket function for optimal control of quantum dynamics, building on rapid monotonically convergent iteration methods. Furthermore, two different approaches to dimension reduction implemented in WavePacket are documented here. In the first one, a balancing transformation based on the concepts of controllability and observability Gramians is used to identify states that are neither well controllable nor well observable. Those states are either truncated or averaged out. In the other approach, the H2-error for a given reduced dimensionality is minimized by H2 optimal model reduction techniques, utilizing a bilinear iterative rational Krylov algorithm. The present work describes the MATLAB version of WavePacket 5.3.0 which is hosted and further developed at the Sourceforge platform, where also extensive Wiki-documentation as well as numerous worked-out demonstration examples with animated graphics can be found.

Pediatric faculty and residents’ perspectives on In-Training Evaluation Reports (ITERs)

PubMed Central

Patel, Rikin; Drover, Anne; Chafe, Roger

2015-01-01

Background In-training evaluation reports (ITERs) are used by over 90% of postgraduate medical training programs in Canada for resident assessment. Our study examined the perspectives of faculty and residents in one pediatric program as a means to improve the ITER as an evaluation tool. Method Two separate focus groups were conducted, one with eight pediatric residents and one with nine clinical faculty within the pediatrics program of Memorial University’s Faculty of Medicine to discuss their perceptions of, and suggestions for improving, the use of ITERs. Results Residents and faculty shared many similar suggestions for improving the ITER as an evaluation tool. Both the faculty and residents emphasized the importance of written feedback, contextualizing the evaluation and timely follow-up. The biggest challenge appears to be the discrepancy in the quality of feedback sought by the residents and the faculty members’ ability to do so in a time effective manner. Others concerns related to the need for better engagement in setting rotation objectives and more direct observation by the faculty member completing the ITER. Conclusions The ITER is a useful tool in resident evaluations, but a number of issues relating to its actual use could improve the quality of feedback which residents receive. PMID:27004076

Derivative free Davidon-Fletcher-Powell (DFP) for solving symmetric systems of nonlinear equations

NASA Astrophysics Data System (ADS)

Mamat, M.; Dauda, M. K.; Mohamed, M. A. bin; Waziri, M. Y.; Mohamad, F. S.; Abdullah, H.

2018-03-01

Research from the work of engineers, economist, modelling, industry, computing, and scientist are mostly nonlinear equations in nature. Numerical solution to such systems is widely applied in those areas of mathematics. Over the years, there has been significant theoretical study to develop methods for solving such systems, despite these efforts, unfortunately the methods developed do have deficiency. In a contribution to solve systems of the form F(x) = 0, x ∈ Rn , a derivative free method via the classical Davidon-Fletcher-Powell (DFP) update is presented. This is achieved by simply approximating the inverse Hessian matrix with {Q}k+1-1 to θkI. The modified method satisfied the descent condition and possess local superlinear convergence properties. Interestingly, without computing any derivative, the proposed method never fail to converge throughout the numerical experiments. The output is based on number of iterations and CPU time, different initial starting points were used on a solve 40 benchmark test problems. With the aid of the squared norm merit function and derivative-free line search technique, the approach yield a method of solving symmetric systems of nonlinear equations that is capable of significantly reducing the CPU time and number of iteration, as compared to its counterparts. A comparison between the proposed method and classical DFP update were made and found that the proposed methodis the top performer and outperformed the existing method in almost all the cases. In terms of number of iterations, out of the 40 problems solved, the proposed method solved 38 successfully, (95%) while classical DFP solved 2 problems (i.e. 05%). In terms of CPU time, the proposed method solved 29 out of the 40 problems given, (i.e.72.5%) successfully whereas classical DFP solves 11 (27.5%). The method is valid in terms of derivation, reliable in terms of number of iterations and accurate in terms of CPU time. Thus, suitable and achived the objective.

Performance issues for iterative solvers in device simulation

NASA Technical Reports Server (NTRS)

Fan, Qing; Forsyth, P. A.; Mcmacken, J. R. F.; Tang, Wei-Pai

1994-01-01

Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods still suffer from reliability problems. The linear systems which appear in numerical simulation of semiconductor devices are notoriously ill-conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix solver on a variety of problems.

On the Convergence of an Implicitly Restarted Arnoldi Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehoucq, Richard B.

We show that Sorensen's [35] implicitly restarted Arnoldi method (including its block extension) is simultaneous iteration with an implicit projection step to accelerate convergence to the invariant subspace of interest. By using the geometric convergence theory for simultaneous iteration due to Watkins and Elsner [43], we prove that an implicitly restarted Arnoldi method can achieve a super-linear rate of convergence to the dominant invariant subspace of a matrix. Moreover, we show how an IRAM computes a nested sequence of approximations for the partial Schur decomposition associated with the dominant invariant subspace of a matrix.

Augmenting the one-shot framework by additional constraints

DOE PAGES

Bosse, Torsten

2016-05-12

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. Finally, a retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner.

Augmenting the one-shot framework by additional constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bosse, Torsten

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. Finally, a retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner.

Fast and secure encryption-decryption method based on chaotic dynamics

DOEpatents

Protopopescu, Vladimir A.; Santoro, Robert T.; Tolliver, Johnny S.

1995-01-01

A method and system for the secure encryption of information. The method comprises the steps of dividing a message of length L into its character components; generating m chaotic iterates from m independent chaotic maps; producing an "initial" value based upon the m chaotic iterates; transforming the "initial" value to create a pseudo-random integer; repeating the steps of generating, producing and transforming until a pseudo-random integer sequence of length L is created; and encrypting the message as ciphertext based upon the pseudo random integer sequence. A system for accomplishing the invention is also provided.

Fast multilevel radiative transfer

NASA Astrophysics Data System (ADS)

Paletou, Frédéric; Léger, Ludovick

2007-01-01

The vast majority of recent advances in the field of numerical radiative transfer relies on approximate operator methods better known in astrophysics as Accelerated Lambda-Iteration (ALI). A superior class of iterative schemes, in term of rates of convergence, such as Gauss-Seidel and Successive Overrelaxation methods were therefore quite naturally introduced in the field of radiative transfer by Trujillo Bueno & Fabiani Bendicho (1995); it was thoroughly described for the non-LTE two-level atom case. We describe hereafter in details how such methods can be generalized when dealing with non-LTE unpolarised radiation transfer with multilevel atomic models, in monodimensional geometry.

Non-oscillatory and non-diffusive solution of convection problems by the iteratively reweighted least-squares finite element method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1993-01-01

A comparative description is presented for the least-squares FEM (LSFEM) for 2D steady-state pure convection problems. In addition to exhibiting better control of the streamline derivative than the streamline upwinding Petrov-Galerkin method, numerical convergence rates are obtained which show the LSFEM to be virtually optimal. The LSFEM is used as a framework for an iteratively reweighted LSFEM yielding nonoscillatory and nondiffusive solutions for problems with contact discontinuities; this method is shown to convect contact discontinuities without error when using triangular and bilinear elements.

Simultaneous imaging/reflectivity measurements to assess diagnostic mirror cleaning.

PubMed

Skinner, C H; Gentile, C A; Doerner, R

2012-10-01

Practical methods to clean ITER's diagnostic mirrors and restore reflectivity will be critical to ITER's plasma operations. We describe a technique to assess the efficacy of mirror cleaning techniques and detect any damage to the mirror surface. The method combines microscopic imaging and reflectivity measurements in the red, green, and blue spectral regions and at selected wavelengths. The method has been applied to laser cleaning of single crystal molybdenum mirrors coated with either carbon or beryllium films 150-420 nm thick. It is suitable for hazardous materials such as beryllium as the mirrors remain sealed in a vacuum chamber.

Immigration, citizenship, and the mental health of adolescents

PubMed Central

Fenelon, Andrew; Boudreaux, Michel

2018-01-01

Purpose To examine the reported mental health outcomes of adolescent foreign-born non-citizens and adolescent foreign-born U.S. citizens compared to adolescent U.S.-born citizens. Methods Using the Strengths and Difficulties Questionnaire in the National Health Interview Survey, we compared mental health status of U.S.-born adolescent citizens to foreign-born citizens and non-citizens in the years 2010–2015, and examined how differences in emotional difficulty changed based on time spent in the U.S. Results Results suggest that non-citizen adolescents experience better mental health outcomes than U.S.-born citizens. However, the mental health status of foreign-born citizens is indistinguishable from that of the U.S.-born, after accounting for basic socio-demographic characteristics. The prevalence of emotional difficulty experienced by immigrant adolescents increased with a family’s duration in the U.S. Conclusion Our findings are consistent with a broader health advantage for the foreign-born, but we present new evidence that the mental health advantage of foreign-born adolescents exists only for non-citizens. PMID:29723297

Among overweight middle-aged men, first-borns have lower insulin sensitivity than second-borns

PubMed Central

Albert, Benjamin B.; de Bock, Martin; Derraik, José G. B.; Brennan, Christine M.; Biggs, Janene B.; Hofman, Paul L.; Cutfield, Wayne S.

2014-01-01

We aimed to assess whether birth order affects metabolism and body composition in overweight middle-aged men. We studied 50 men aged 45.6 ± 5.5 years, who were overweight (BMI 27.5 ± 1.7 kg/m2) but otherwise healthy in Auckland, New Zealand. These included 26 first-borns and 24 second-borns. Insulin sensitivity was assessed by the Matsuda method from an oral glucose tolerance test. Other assessments included DXA-derived body composition, lipid profiles, 24-hour ambulatory blood pressure, and carotid intima-media thickness. First-born men were 6.9 kg heavier (p = 0.013) and had greater BMI (29.1 vs 27.5 kg/m2; p = 0.004) than second-borns. Insulin sensitivity in first-born men was 33% lower than in second-borns (4.38 vs 6.51; p = 0.014), despite adjustment for fat mass. There were no significant differences in ambulatory blood pressure, lipid profile or carotid intima-media thickness between first- and second-borns. Thus, first-born adults may be at a greater risk of metabolic and cardiovascular diseases. PMID:24503677

Novel aspects of plasma control in ITER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humphreys, D.; Jackson, G.; Walker, M.

2015-02-15

ITER plasma control design solutions and performance requirements are strongly driven by its nuclear mission, aggressive commissioning constraints, and limited number of operational discharges. In addition, high plasma energy content, heat fluxes, neutron fluxes, and very long pulse operation place novel demands on control performance in many areas ranging from plasma boundary and divertor regulation to plasma kinetics and stability control. Both commissioning and experimental operations schedules provide limited time for tuning of control algorithms relative to operating devices. Although many aspects of the control solutions required by ITER have been well-demonstrated in present devices and even designed satisfactorily formore » ITER application, many elements unique to ITER including various crucial integration issues are presently under development. We describe selected novel aspects of plasma control in ITER, identifying unique parts of the control problem and highlighting some key areas of research remaining. Novel control areas described include control physics understanding (e.g., current profile regulation, tearing mode (TM) suppression), control mathematics (e.g., algorithmic and simulation approaches to high confidence robust performance), and integration solutions (e.g., methods for management of highly subscribed control resources). We identify unique aspects of the ITER TM suppression scheme, which will pulse gyrotrons to drive current within a magnetic island, and turn the drive off following suppression in order to minimize use of auxiliary power and maximize fusion gain. The potential role of active current profile control and approaches to design in ITER are discussed. Issues and approaches to fault handling algorithms are described, along with novel aspects of actuator sharing in ITER.« less

Novel aspects of plasma control in ITER

DOE PAGES

Humphreys, David; Ambrosino, G.; de Vries, Peter; ...

2015-02-12

ITER plasma control design solutions and performance requirements are strongly driven by its nuclear mission, aggressive commissioning constraints, and limited number of operational discharges. In addition, high plasma energy content, heat fluxes, neutron fluxes, and very long pulse operation place novel demands on control performance in many areas ranging from plasma boundary and divertor regulation to plasma kinetics and stability control. Both commissioning and experimental operations schedules provide limited time for tuning of control algorithms relative to operating devices. Although many aspects of the control solutions required by ITER have been well-demonstrated in present devices and even designed satisfactorily formore » ITER application, many elements unique to ITER including various crucial integration issues are presently under development. We describe selected novel aspects of plasma control in ITER, identifying unique parts of the control problem and highlighting some key areas of research remaining. Novel control areas described include control physics understanding (e.g. current profile regulation, tearing mode suppression (TM)), control mathematics (e.g. algorithmic and simulation approaches to high confidence robust performance), and integration solutions (e.g. methods for management of highly-subscribed control resources). We identify unique aspects of the ITER TM suppression scheme, which will pulse gyrotrons to drive current within a magnetic island, and turn the drive off following suppression in order to minimize use of auxiliary power and maximize fusion gain. The potential role of active current profile control and approaches to design in ITER are discussed. Finally, issues and approaches to fault handling algorithms are described, along with novel aspects of actuator sharing in ITER.« less

Local motion-compensated method for high-quality 3D coronary artery reconstruction

PubMed Central

Liu, Bo; Bai, Xiangzhi; Zhou, Fugen

2016-01-01

The 3D reconstruction of coronary artery from X-ray angiograms rotationally acquired on C-arm has great clinical value. While cardiac-gated reconstruction has shown promising results, it suffers from the problem of residual motion. This work proposed a new local motion-compensated reconstruction method to handle this issue. An initial image was firstly reconstructed using a regularized iterative reconstruction method. Then a 3D/2D registration method was proposed to estimate the residual vessel motion. Finally, the residual motion was compensated in the final reconstruction using the extended iterative reconstruction method. Through quantitative evaluation, it was found that high-quality 3D reconstruction could be obtained and the result was comparable to state-of-the-art method. PMID:28018741