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

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.

Use of Picard and Newton iteration for solving nonlinear ground water flow equations

USGS Publications Warehouse

Mehl, S.

2006-01-01

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.

Accuracy Improvement for Light-Emitting-Diode-Based Colorimeter by Iterative Algorithm

NASA Astrophysics Data System (ADS)

Yang, Pao-Keng

2011-09-01

We present a simple algorithm, combining an interpolating method with an iterative calculation, to enhance the resolution of spectral reflectance by removing the spectral broadening effect due to the finite bandwidth of the light-emitting diode (LED) from it. The proposed algorithm can be used to improve the accuracy of a reflective colorimeter using multicolor LEDs as probing light sources and is also applicable to the case when the probing LEDs have different bandwidths in different spectral ranges, to which the powerful deconvolution method cannot be applied.

Simple Common Plane contact detection algorithm for FE/FD methods

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

Vorobiev, O

2006-07-19

Common-plane (CP) algorithm is widely used in Discrete Element Method (DEM) to model contact forces between interacting particles or blocks. A new simple contact detection algorithm is proposed to model contacts in FE/FD methods which is similar to the CP algorithm. The CP is defined as a plane separating interacting faces of FE/FD mesh instead of blocks or particles in the original CP method. The method does not require iterations. It is very robust and easy to implement both in 2D and 3D case.

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.

Comments on the variational modified-hypernetted-chain theory for simple fluids

NASA Astrophysics Data System (ADS)

Rosenfeld, Yaakov

1986-02-01

The variational modified-hypernetted-chain (VMHNC) theory, based on the approximation of universality of the bridge functions, is reformulated. The new formulation includes recent calculations by Lado and by Lado, Foiles, and Ashcroft, as two stages in a systematic approach which is analyzed. A variational iterative procedure for solving the exact (diagrammatic) equations for the fluid structure which is formally identical to the VMHNC is described, featuring the theory of simple classical fluids as a one-iteration theory. An accurate method for calculating the pair structure for a given potential and for inverting structure factor data in order to obtain the potential and the thermodynamic functions, follows from our analysis.

A simple iterative independent component analysis algorithm for vibration source signal identification of complex structures

NASA Astrophysics Data System (ADS)

Lee, Dong-Sup; Cho, Dae-Seung; Kim, Kookhyun; Jeon, Jae-Jin; Jung, Woo-Jin; Kang, Myeng-Hwan; Kim, Jae-Ho

2015-01-01

Independent Component Analysis (ICA), one of the blind source separation methods, can be applied for extracting unknown source signals only from received signals. This is accomplished by finding statistical independence of signal mixtures and has been successfully applied to myriad fields such as medical science, image processing, and numerous others. Nevertheless, there are inherent problems that have been reported when using this technique: instability and invalid ordering of separated signals, particularly when using a conventional ICA technique in vibratory source signal identification of complex structures. In this study, a simple iterative algorithm of the conventional ICA has been proposed to mitigate these problems. The proposed method to extract more stable source signals having valid order includes an iterative and reordering process of extracted mixing matrix to reconstruct finally converged source signals, referring to the magnitudes of correlation coefficients between the intermediately separated signals and the signals measured on or nearby sources. In order to review the problems of the conventional ICA technique and to validate the proposed method, numerical analyses have been carried out for a virtual response model and a 30 m class submarine model. Moreover, in order to investigate applicability of the proposed method to real problem of complex structure, an experiment has been carried out for a scaled submarine mockup. The results show that the proposed method could resolve the inherent problems of a conventional ICA technique.

Improving performances of suboptimal greedy iterative biclustering heuristics via localization.

PubMed

Erten, Cesim; Sözdinler, Melih

2010-10-15

Biclustering gene expression data is the problem of extracting submatrices of genes and conditions exhibiting significant correlation across both the rows and the columns of a data matrix of expression values. Even the simplest versions of the problem are computationally hard. Most of the proposed solutions therefore employ greedy iterative heuristics that locally optimize a suitably assigned scoring function. We provide a fast and simple pre-processing algorithm called localization that reorders the rows and columns of the input data matrix in such a way as to group correlated entries in small local neighborhoods within the matrix. The proposed localization algorithm takes its roots from effective use of graph-theoretical methods applied to problems exhibiting a similar structure to that of biclustering. In order to evaluate the effectivenesss of the localization pre-processing algorithm, we focus on three representative greedy iterative heuristic methods. We show how the localization pre-processing can be incorporated into each representative algorithm to improve biclustering performance. Furthermore, we propose a simple biclustering algorithm, Random Extraction After Localization (REAL) that randomly extracts submatrices from the localization pre-processed data matrix, eliminates those with low similarity scores, and provides the rest as correlated structures representing biclusters. We compare the proposed localization pre-processing with another pre-processing alternative, non-negative matrix factorization. We show that our fast and simple localization procedure provides similar or even better results than the computationally heavy matrix factorization pre-processing with regards to H-value tests. We next demonstrate that the performances of the three representative greedy iterative heuristic methods improve with localization pre-processing when biological correlations in the form of functional enrichment and PPI verification constitute the main performance criteria. The fact that the random extraction method based on localization REAL performs better than the representative greedy heuristic methods under same criteria also confirms the effectiveness of the suggested pre-processing method. Supplementary material including code implementations in LEDA C++ library, experimental data, and the results are available at http://code.google.com/p/biclustering/ cesim@khas.edu.tr; melihsozdinler@boun.edu.tr Supplementary data are available at Bioinformatics online.

Spreadsheets in Science Teaching.

ERIC Educational Resources Information Center

Elliot, Chris

1988-01-01

Described is the use of a spreadsheet to model dynamic phenomena using numerical iterative methods. Uses the discharge of a capacitor, simple and damped harmonic motion, and the flow of heat along a bar as examples. (Author/CW)

The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Harada, Kyouji; Morimoto, Munenori; Sakakihara, Michio

2004-03-01

Several preconditioned iterative methods reported in the literature have been used for improving the convergence rate of the Gauss-Seidel method. In this article, on the basis of nonnegative matrix, comparisons between some splittings for such preconditioned matrices are derived. Simple numerical examples are also given.

Computationally efficient finite-difference modal method for the solution of Maxwell's equations.

PubMed

Semenikhin, Igor; Zanuccoli, Mauro

2013-12-01

In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method.

Simple Common Plane contact algorithm for explicit FE/FD methods

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

Vorobiev, O

2006-12-18

Common-plane (CP) algorithm is widely used in Discrete Element Method (DEM) to model contact forces between interacting particles or blocks. A new simple contact algorithm is proposed to model contacts in FE/FD methods which is similar to the CP algorithm. The CP is defined as a plane separating interacting faces of FE/FD mesh instead of blocks or particles used in the original CP method. The new method does not require iterations even for very stiff contacts. It is very robust and easy to implement both in 2D and 3D parallel codes.

Program for the solution of multipoint boundary value problems of quasilinear differential equations

NASA Technical Reports Server (NTRS)

1973-01-01

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

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.

Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations

NASA Astrophysics Data System (ADS)

Kao, Chiu Yen; Osher, Stanley; Qian, Jianliang

2004-05-01

We propose a simple, fast sweeping method based on the Lax-Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton-Jacobi equations in any number of spatial dimensions. By using the Lax-Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss-Seidel type nonlinear iterative method can be utilized. Furthermore, by incorporating a group-wise causality principle into the Gauss-Seidel iteration by following a finite group of characteristics, we have an easy-to-implement, sweeping-type, and fast convergent numerical method. However, unlike other methods based on the Godunov numerical Hamiltonian, some computational boundary conditions are needed in the implementation. We give a simple recipe which enforces a version of discrete min-max principle. Some convergence analysis is done for the one-dimensional eikonal equation. Extensive 2-D and 3-D numerical examples illustrate the efficiency and accuracy of the new approach. To our knowledge, this is the first fast numerical method based on discretizing the Hamilton-Jacobi equation directly without assuming convexity and/or homogeneity of the Hamiltonian.

Symmetry dependence of holograms for optical trapping

NASA Astrophysics Data System (ADS)

Curtis, Jennifer E.; Schmitz, Christian H. J.; Spatz, Joachim P.

2005-08-01

No iterative algorithm is necessary to calculate holograms for most holographic optical trapping patterns. Instead, holograms may be produced by a simple extension of the prisms-and-lenses method. This formulaic approach yields the same diffraction efficiency as iterative algorithms for any asymmetric or symmetric but nonperiodic pattern of points while requiring less calculation time. A slight spatial disordering of periodic patterns significantly reduces intensity variations between the different traps without extra calculation costs. Eliminating laborious hologram calculations should greatly facilitate interactive holographic trapping.

A Machine Learning System for Analyzing Human Tactics in a Game

NASA Astrophysics Data System (ADS)

Ito, Hirotaka; Tanaka, Toshimitsu; Sugie, Noboru

In order to realize advanced man-machine interfaces, it is desired to develop a system that can infer the mental state of human users and then return appropriate responses. As the first step toward the above goal, we developed a system capable of inferring human tactics in a simple game played between the system and a human. We present a machine learning system that plays a color expectation game. The system infers the tactics of the opponent, and then decides the action based on the result. We employed a modified version of classifier system like XCS in order to design the system. In addition, three methods are proposed in order to accelerate the learning rate. They are a masking method, an iterative method, and tactics templates. The results of computer experiments confirmed that the proposed methods effectively accelerate the machine learning. The masking method and the iterative method are effective to a simple strategy that considers only a part of past information. However, study speed of these methods is not enough for the tactics that refers to a lot of past information. For the case, the tactics template was able to settle the study rapidly when the tactics is identified.

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.

A Coupling Strategy of FEM and BEM for the Solution of a 3D Industrial Crack Problem

NASA Astrophysics Data System (ADS)

Kouitat Njiwa, Richard; Taha Niane, Ngadia; Frey, Jeremy; Schwartz, Martin; Bristiel, Philippe

2015-03-01

Analyzing crack stability in an industrial context is challenging due to the geometry of the structure. The finite element method is effective for defect-free problems. The boundary element method is effective for problems in simple geometries with singularities. We present a strategy that takes advantage of both approaches. Within the iterative solution procedure, the FEM solves a defect-free problem over the structure while the BEM solves the crack problem over a fictitious domain with simple geometry. The effectiveness of the approach is demonstrated on some simple examples which allow comparison with literature results and on an industrial problem.

Iterative combining rules for the van der Waals potentials of mixed rare gas systems

NASA Astrophysics Data System (ADS)

Wei, L. M.; Li, P.; Tang, K. T.

2017-05-01

An iterative procedure is introduced to make the results of some simple combining rules compatible with the Tang-Toennies potential model. The method is used to calculate the well locations Re and the well depths De of the van der Waals potentials of the mixed rare gas systems from the corresponding values of the homo-nuclear dimers. When the ;sizes; of the two interacting atoms are very different, several rounds of iteration are required for the results to converge. The converged results can be substantially different from the starting values obtained from the combining rules. However, if the sizes of the interacting atoms are close, only one or even no iteration is necessary for the results to converge. In either case, the converged results are the accurate descriptions of the interaction potentials of the hetero-nuclear dimers.

A Fractal Excursion.

ERIC Educational Resources Information Center

Camp, Dane R.

1991-01-01

After introducing the two-dimensional Koch curve, which is generated by simple recursions on an equilateral triangle, the process is extended to three dimensions with simple recursions on a regular tetrahedron. Included, for both fractal sequences, are iterative formulae, illustrations of the first several iterations, and a sample PASCAL program.…

Application of the Homotopy Perturbation Method to the Nonlinear Pendulum

ERIC Educational Resources Information Center

Belendez, A.; Hernandez, A.; Belendez, T.; Marquez, A.

2007-01-01

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as…

Techniques for Accelerating Iterative Methods for the Solution of Mathematical Problems

DTIC Science & Technology

1989-07-01

m, we can find a solu ion to the problem by using generalized inverses. Hence, ;= Ih.i = GAi = G - where G is of the form (18). A simple choice for V...have understood why I was not available for many of their activities and not home many of the nights. Their love is forever. I have saved the best for...Xk) Extrapolation applied to terms xP through Xk F Operator on x G Iteration function Ik Identity matrix of rank k Solution of the problem or the limit

P-Tether-Mediated, Iterative SN2'-Cuprate Alkylation Strategy to Skipped Polyol Stereotetrads: Utility of an Oxidative "Function Switch" with Phosphite-Borane Tethers.

PubMed

Markley, Jana L; Hanson, Paul R

2017-05-19

The development of a P-tether-mediated, iterative S N 2'-cuprate alkylation protocol for the formation of 1,3-skipped polyol stereotetrads is reported. This two-directional synthetic strategy builds molecular complexity from simple, readily prepared C 2 -symmetric dienediols and unites the chemistry of both temporary phosphite-borane tethers and temporary phosphate tethers-through an oxidative "function switch" of the P-tether itself-to generate intermediates that were previously inaccessible via either method alone.

New perspectives in face correlation: discrimination enhancement in face recognition based on iterative algorithm

NASA Astrophysics Data System (ADS)

Wang, Q.; Alfalou, A.; Brosseau, C.

2016-04-01

Here, we report a brief review on the recent developments of correlation algorithms. Several implementation schemes and specific applications proposed in recent years are also given to illustrate powerful applications of these methods. Following a discussion and comparison of the implementation of these schemes, we believe that all-numerical implementation is the most practical choice for application of the correlation method because the advantages of optical processing cannot compensate the technical and/or financial cost needed for an optical implementation platform. We also present a simple iterative algorithm to optimize the training images of composite correlation filters. By making use of three or four iterations, the peak-to-correlation energy (PCE) value of correlation plane can be significantly enhanced. A simulation test using the Pointing Head Pose Image Database (PHPID) illustrates the effectiveness of this statement. Our method can be applied in many composite filters based on linear composition of training images as an optimization means.

Fast sweeping method for the factored eikonal equation

NASA Astrophysics Data System (ADS)

Fomel, Sergey; Luo, Songting; Zhao, Hongkai

2009-09-01

We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

Function Invariant and Parameter Scale-Free Transformation Methods

ERIC Educational Resources Information Center

Bentler, P. M.; Wingard, Joseph A.

1977-01-01

A scale-invariant simple structure function of previously studied function components for principal component analysis and factor analysis is defined. First and second partial derivatives are obtained, and Newton-Raphson iterations are utilized. The resulting solutions are locally optimal and subjectively pleasing. (Author/JKS)

On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

NASA Astrophysics Data System (ADS)

Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei

2018-06-01

In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.

Two-level Schwartz methods for nonconforming finite elements and discontinuous coefficients

NASA Technical Reports Server (NTRS)

Sarkis, Marcus

1993-01-01

Two-level domain decomposition methods are developed for a simple nonconforming approximation of second order elliptic problems. A bound is established for the condition number of these iterative methods, which grows only logarithmically with the number of degrees of freedom in each subregion. This bound holds for two and three dimensions and is independent of jumps in the value of the coefficients.

Constructing LDPC Codes from Loop-Free Encoding Modules

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Dolinar, Samuel; Jones, Christopher; Thorpe, Jeremy; Andrews, Kenneth

2009-01-01

A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to channel capacity limits can be achieved for the codes of the type in question having low maximum variable node degrees. The decoding thresholds in these examples are lower than those of the best-known unstructured irregular LDPC codes constrained to have the same maximum node degrees. Furthermore, the present method enables the construction of codes of any desired rate with thresholds that stay uniformly close to their respective channel capacity thresholds.

Comparison of iterative inverse coarse-graining methods

NASA Astrophysics Data System (ADS)

Rosenberger, David; Hanke, Martin; van der Vegt, Nico F. A.

2016-10-01

Deriving potentials for coarse-grained Molecular Dynamics (MD) simulations is frequently done by solving an inverse problem. Methods like Iterative Boltzmann Inversion (IBI) or Inverse Monte Carlo (IMC) have been widely used to solve this problem. The solution obtained by application of these methods guarantees a match in the radial distribution function (RDF) between the underlying fine-grained system and the derived coarse-grained system. However, these methods often fail in reproducing thermodynamic properties. To overcome this deficiency, additional thermodynamic constraints such as pressure or Kirkwood-Buff integrals (KBI) may be added to these methods. In this communication we test the ability of these methods to converge to a known solution of the inverse problem. With this goal in mind we have studied a binary mixture of two simple Lennard-Jones (LJ) fluids, in which no actual coarse-graining is performed. We further discuss whether full convergence is actually needed to achieve thermodynamic representability.

Deblurring in digital tomosynthesis by iterative self-layer subtraction

NASA Astrophysics Data System (ADS)

Youn, Hanbean; Kim, Jee Young; Jang, SunYoung; Cho, Min Kook; Cho, Seungryong; Kim, Ho Kyung

2010-04-01

Recent developments in large-area flat-panel detectors have made tomosynthesis technology revisited in multiplanar xray imaging. However, the typical shift-and-add (SAA) or backprojection reconstruction method is notably claimed by a lack of sharpness in the reconstructed images because of blur artifact which is the superposition of objects which are out of planes. In this study, we have devised an intuitive simple method to reduce the blur artifact based on an iterative approach. This method repeats a forward and backward projection procedure to determine the blur artifact affecting on the plane-of-interest (POI), and then subtracts it from the POI. The proposed method does not include any Fourierdomain operations hence excluding the Fourier-domain-originated artifacts. We describe the concept of the self-layer subtractive tomosynthesis and demonstrate its performance with numerical simulation and experiments. Comparative analysis with the conventional methods, such as the SAA and filtered backprojection methods, is addressed.

Solving Rational Expectations Models Using Excel

ERIC Educational Resources Information Center

Strulik, Holger

2004-01-01

Simple problems of discrete-time optimal control can be solved using a standard spreadsheet software. The employed-solution method of backward iteration is intuitively understandable, does not require any programming skills, and is easy to implement so that it is suitable for classroom exercises with rational-expectations models. The author…

Adaptive Discrete Hypergraph Matching.

PubMed

Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao

2018-02-01

This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.

An interative solution of an integral equation for radiative transfer by using variational technique

NASA Technical Reports Server (NTRS)

Yoshikawa, K. K.

1973-01-01

An effective iterative technique is introduced to solve a nonlinear integral equation frequently associated with radiative transfer problems. The problem is formulated in such a way that each step of an iterative sequence requires the solution of a linear integral equation. The advantage of a previously introduced variational technique which utilizes a stepwise constant trial function is exploited to cope with the nonlinear problem. The method is simple and straightforward. Rapid convergence is obtained by employing a linear interpolation of the iterative solutions. Using absorption coefficients of the Milne-Eddington type, which are applicable to some planetary atmospheric radiation problems. Solutions are found in terms of temperature and radiative flux. These solutions are presented numerically and show excellent agreement with other numerical solutions.

Simulating transient dynamics of the time-dependent time fractional Fokker-Planck systems

NASA Astrophysics Data System (ADS)

Kang, Yan-Mei

2016-09-01

For a physically realistic type of time-dependent time fractional Fokker-Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker-Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed.

Computing eigenfunctions and eigenvalues of boundary-value problems with the orthogonal spectral renormalization method

NASA Astrophysics Data System (ADS)

Cartarius, Holger; Musslimani, Ziad H.; Schwarz, Lukas; Wunner, Günter

2018-03-01

The spectral renormalization method was introduced in 2005 as an effective way to compute ground states of nonlinear Schrödinger and Gross-Pitaevskii type equations. In this paper, we introduce an orthogonal spectral renormalization (OSR) method to compute ground and excited states (and their respective eigenvalues) of linear and nonlinear eigenvalue problems. The implementation of the algorithm follows four simple steps: (i) reformulate the underlying eigenvalue problem as a fixed-point equation, (ii) introduce a renormalization factor that controls the convergence properties of the iteration, (iii) perform a Gram-Schmidt orthogonalization process in order to prevent the iteration from converging to an unwanted mode, and (iv) compute the solution sought using a fixed-point iteration. The advantages of the OSR scheme over other known methods (such as Newton's and self-consistency) are (i) it allows the flexibility to choose large varieties of initial guesses without diverging, (ii) it is easy to implement especially at higher dimensions, and (iii) it can easily handle problems with complex and random potentials. The OSR method is implemented on benchmark Hermitian linear and nonlinear eigenvalue problems as well as linear and nonlinear non-Hermitian PT -symmetric models.

A new method for computation of eigenvector derivatives with distinct and repeated eigenvalues in structural dynamic analysis

NASA Astrophysics Data System (ADS)

Li, Zhengguang; Lai, Siu-Kai; Wu, Baisheng

2018-07-01

Determining eigenvector derivatives is a challenging task due to the singularity of the coefficient matrices of the governing equations, especially for those structural dynamic systems with repeated eigenvalues. An effective strategy is proposed to construct a non-singular coefficient matrix, which can be directly used to obtain the eigenvector derivatives with distinct and repeated eigenvalues. This approach also has an advantage that only requires eigenvalues and eigenvectors of interest, without solving the particular solutions of eigenvector derivatives. The Symmetric Quasi-Minimal Residual (SQMR) method is then adopted to solve the governing equations, only the existing factored (shifted) stiffness matrix from an iterative eigensolution such as the subspace iteration method or the Lanczos algorithm is utilized. The present method can deal with both cases of simple and repeated eigenvalues in a unified manner. Three numerical examples are given to illustrate the accuracy and validity of the proposed algorithm. Highly accurate approximations to the eigenvector derivatives are obtained within a few iteration steps, making a significant reduction of the computational effort. This method can be incorporated into a coupled eigensolver/derivative software module. In particular, it is applicable for finite element models with large sparse matrices.

Code Samples Used for Complexity and Control

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

The following sections are included: * MathematicaⓇ Code * Generic Chaotic Simulator * Vector Differential Operators * NLS Explorer * 2C++ Code * C++ Lambda Functions for Real Calculus * Accelerometer Data Processor * Simple Predictor-Corrector Integrator * Solving the BVP with the Shooting Method * Linear Hyperbolic PDE Solver * Linear Elliptic PDE Solver * Method of Lines for a Set of the NLS Equations * C# Code * Iterative Equation Solver * Simulated Annealing: A Function Minimum * Simple Nonlinear Dynamics * Nonlinear Pendulum Simulator * Lagrangian Dynamics Simulator * Complex-Valued Crowd Attractor Dynamics * Freeform Fortran Code * Lorenz Attractor Simulator * Complex Lorenz Attractor * Simple SGE Soliton * Complex Signal Presentation * Gaussian Wave Packet * Hermitian Matrices * Euclidean L2-Norm * Vector/Matrix Operations * Plain C-Code: Levenberg-Marquardt Optimizer * Free Basic Code: 2D Crowd Dynamics with 3000 Agents

Comparison of the convolution quadrature method and enhanced inverse FFT with application in elastodynamic boundary element method

NASA Astrophysics Data System (ADS)

Schanz, Martin; Ye, Wenjing; Xiao, Jinyou

2016-04-01

Transient problems can often be solved with transformation methods, where the inverse transformation is usually performed numerically. Here, the discrete Fourier transform in combination with the exponential window method is compared with the convolution quadrature method formulated as inverse transformation. Both are inverse Laplace transforms, which are formally identical but use different complex frequencies. A numerical study is performed, first with simple convolution integrals and, second, with a boundary element method (BEM) for elastodynamics. Essentially, when combined with the BEM, the discrete Fourier transform needs less frequency calculations, but finer mesh compared to the convolution quadrature method to obtain the same level of accuracy. If further fast methods like the fast multipole method are used to accelerate the boundary element method the convolution quadrature method is better, because the iterative solver needs much less iterations to converge. This is caused by the larger real part of the complex frequencies necessary for the calculation, which improves the conditions of system matrix.

Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference

NASA Astrophysics Data System (ADS)

Shen, Cheng; Guo, Cheng; Tan, Jiubin; Liu, Shutian; Liu, Zhengjun

2018-06-01

Multi-image iterative phase retrieval methods have been successfully applied in plenty of research fields due to their simple but efficient implementation. However, there is a mismatch between the measurement of the first long imaging distance and the sequential interval. In this paper, an amplitude-phase retrieval algorithm with reference is put forward without additional measurements or priori knowledge. It gets rid of measuring the first imaging distance. With a designed update formula, it significantly raises the convergence speed and the reconstruction fidelity, especially in phase retrieval. Its superiority over the original amplitude-phase retrieval (APR) method is validated by numerical analysis and experiments. Furthermore, it provides a conceptual design of a compact holographic image sensor, which can achieve numerical refocusing easily.

Multi-atlas segmentation enables robust multi-contrast MRI spleen segmentation for splenomegaly

NASA Astrophysics Data System (ADS)

Huo, Yuankai; Liu, Jiaqi; Xu, Zhoubing; Harrigan, Robert L.; Assad, Albert; Abramson, Richard G.; Landman, Bennett A.

2017-02-01

Non-invasive spleen volume estimation is essential in detecting splenomegaly. Magnetic resonance imaging (MRI) has been used to facilitate splenomegaly diagnosis in vivo. However, achieving accurate spleen volume estimation from MR images is challenging given the great inter-subject variance of human abdomens and wide variety of clinical images/modalities. Multi-atlas segmentation has been shown to be a promising approach to handle heterogeneous data and difficult anatomical scenarios. In this paper, we propose to use multi-atlas segmentation frameworks for MRI spleen segmentation for splenomegaly. To the best of our knowledge, this is the first work that integrates multi-atlas segmentation for splenomegaly as seen on MRI. To address the particular concerns of spleen MRI, automated and novel semi-automated atlas selection approaches are introduced. The automated approach interactively selects a subset of atlases using selective and iterative method for performance level estimation (SIMPLE) approach. To further control the outliers, semi-automated craniocaudal length based SIMPLE atlas selection (L-SIMPLE) is proposed to introduce a spatial prior in a fashion to guide the iterative atlas selection. A dataset from a clinical trial containing 55 MRI volumes (28 T1 weighted and 27 T2 weighted) was used to evaluate different methods. Both automated and semi-automated methods achieved median DSC > 0.9. The outliers were alleviated by the L-SIMPLE (≍1 min manual efforts per scan), which achieved 0.9713 Pearson correlation compared with the manual segmentation. The results demonstrated that the multi-atlas segmentation is able to achieve accurate spleen segmentation from the multi-contrast splenomegaly MRI scans.

Multi-atlas Segmentation Enables Robust Multi-contrast MRI Spleen Segmentation for Splenomegaly.

PubMed

Huo, Yuankai; Liu, Jiaqi; Xu, Zhoubing; Harrigan, Robert L; Assad, Albert; Abramson, Richard G; Landman, Bennett A

2017-02-11

Non-invasive spleen volume estimation is essential in detecting splenomegaly. Magnetic resonance imaging (MRI) has been used to facilitate splenomegaly diagnosis in vivo. However, achieving accurate spleen volume estimation from MR images is challenging given the great inter-subject variance of human abdomens and wide variety of clinical images/modalities. Multi-atlas segmentation has been shown to be a promising approach to handle heterogeneous data and difficult anatomical scenarios. In this paper, we propose to use multi-atlas segmentation frameworks for MRI spleen segmentation for splenomegaly. To the best of our knowledge, this is the first work that integrates multi-atlas segmentation for splenomegaly as seen on MRI. To address the particular concerns of spleen MRI, automated and novel semi-automated atlas selection approaches are introduced. The automated approach interactively selects a subset of atlases using selective and iterative method for performance level estimation (SIMPLE) approach. To further control the outliers, semi-automated craniocaudal length based SIMPLE atlas selection (L-SIMPLE) is proposed to introduce a spatial prior in a fashion to guide the iterative atlas selection. A dataset from a clinical trial containing 55 MRI volumes (28 T1 weighted and 27 T2 weighted) was used to evaluate different methods. Both automated and semi-automated methods achieved median DSC > 0.9. The outliers were alleviated by the L-SIMPLE (≈1 min manual efforts per scan), which achieved 0.9713 Pearson correlation compared with the manual segmentation. The results demonstrated that the multi-atlas segmentation is able to achieve accurate spleen segmentation from the multi-contrast splenomegaly MRI scans.

DETECTORS AND EXPERIMENTAL METHODS: Heuristic approach for peak regions estimation in gamma-ray spectra measured by a NaI detector

NASA Astrophysics Data System (ADS)

Zhu, Meng-Hua; Liu, Liang-Gang; You, Zhong; Xu, Ao-Ao

2009-03-01

In this paper, a heuristic approach based on Slavic's peak searching method has been employed to estimate the width of peak regions for background removing. Synthetic and experimental data are used to test this method. With the estimated peak regions using the proposed method in the whole spectrum, we find it is simple and effective enough to be used together with the Statistics-sensitive Nonlinear Iterative Peak-Clipping method.

Hidden Connections between Regression Models of Strain-Gage Balance Calibration Data

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert

2013-01-01

Hidden connections between regression models of wind tunnel strain-gage balance calibration data are investigated. These connections become visible whenever balance calibration data is supplied in its design format and both the Iterative and Non-Iterative Method are used to process the data. First, it is shown how the regression coefficients of the fitted balance loads of a force balance can be approximated by using the corresponding regression coefficients of the fitted strain-gage outputs. Then, data from the manual calibration of the Ames MK40 six-component force balance is chosen to illustrate how estimates of the regression coefficients of the fitted balance loads can be obtained from the regression coefficients of the fitted strain-gage outputs. The study illustrates that load predictions obtained by applying the Iterative or the Non-Iterative Method originate from two related regression solutions of the balance calibration data as long as balance loads are given in the design format of the balance, gage outputs behave highly linear, strict statistical quality metrics are used to assess regression models of the data, and regression model term combinations of the fitted loads and gage outputs can be obtained by a simple variable exchange.

Inverse imaging of the breast with a material classification technique.

PubMed

Manry, C W; Broschat, S L

1998-03-01

In recent publications [Chew et al., IEEE Trans. Blomed. Eng. BME-9, 218-225 (1990); Borup et al., Ultrason. Imaging 14, 69-85 (1992)] the inverse imaging problem has been solved by means of a two-step iterative method. In this paper, a third step is introduced for ultrasound imaging of the breast. In this step, which is based on statistical pattern recognition, classification of tissue types and a priori knowledge of the anatomy of the breast are integrated into the iterative method. Use of this material classification technique results in more rapid convergence to the inverse solution--approximately 40% fewer iterations are required--as well as greater accuracy. In addition, tumors are detected early in the reconstruction process. Results for reconstructions of a simple two-dimensional model of the human breast are presented. These reconstructions are extremely accurate when system noise and variations in tissue parameters are not too great. However, for the algorithm used, degradation of the reconstructions and divergence from the correct solution occur when system noise and variations in parameters exceed threshold values. Even in this case, however, tumors are still identified within a few iterations.

Non-iterative distance constraints enforcement for cloth drapes simulation

NASA Astrophysics Data System (ADS)

Hidajat, R. L. L. G.; Wibowo, Arifin, Z.; Suyitno

2016-03-01

A cloth simulation represents the behavior of cloth objects such as flag, tablecloth, or even garments has application in clothing animation for games and virtual shops. Elastically deformable models have widely used to provide realistic and efficient simulation, however problem of overstretching is encountered. We introduce a new cloth simulation algorithm that replaces iterative distance constraint enforcement steps with non-iterative ones for preventing over stretching in a spring-mass system for cloth modeling. Our method is based on a simple position correction procedure applied at one end of a spring. In our experiments, we developed a rectangle cloth model which is initially at a horizontal position with one point is fixed, and it is allowed to drape by its own weight. Our simulation is able to achieve a plausible cloth drapes as in reality. This paper aims to demonstrate the reliability of our approach to overcome overstretches while decreasing the computational cost of the constraint enforcement process due to an iterative procedure that is eliminated.

Speckle reduction in optical coherence tomography using two-step iteration method (Conference Presentation)

NASA Astrophysics Data System (ADS)

Wang, Xianghong; Liu, Xinyu; Wang, Nanshuo; Yu, Xiaojun; Bo, En; Chen, Si; Liu, Linbo

2017-02-01

Optical coherence tomography (OCT) provides high resolution and cross-sectional images of biological tissue and is widely used for diagnosis of ocular diseases. However, OCT images suffer from speckle noise, which typically considered as multiplicative noise in nature, reducing the image resolution and contrast. In this study, we propose a two-step iteration (TSI) method to suppress those noises. We first utilize augmented Lagrange method to recover a low-rank OCT image and remove additive Gaussian noise, and then employ the simple and efficient split Bregman method to solve the Total-Variation Denoising model. We validated such proposed method using images of swine, rabbit and human retina. Results demonstrate that our TSI method outperforms the other popular methods in achieving higher peak signal-to-noise ratio (PSNR) and structure similarity (SSIM) while preserving important structural details, such as tiny capillaries and thin layers in retinal OCT images. In addition, the results of our TSI method show clearer boundaries and maintains high image contrast, which facilitates better image interpretations and analyses.

Bounded-Angle Iterative Decoding of LDPC Codes

NASA Technical Reports Server (NTRS)

Dolinar, Samuel; Andrews, Kenneth; Pollara, Fabrizio; Divsalar, Dariush

2009-01-01

Bounded-angle iterative decoding is a modified version of conventional iterative decoding, conceived as a means of reducing undetected-error rates for short low-density parity-check (LDPC) codes. For a given code, bounded-angle iterative decoding can be implemented by means of a simple modification of the decoder algorithm, without redesigning the code. Bounded-angle iterative decoding is based on a representation of received words and code words as vectors in an n-dimensional Euclidean space (where n is an integer).

Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange.

PubMed

Kümmel, Stephan; Perdew, John P

2003-01-31

For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential V(xcsigma)(r) must be obtained as the solution of the optimized effective potential (OEP) integral equation. This is very demanding and has limited the use of orbital functionals. We demonstrate that instead the OEP can be obtained iteratively by solving the partial differential equations for the orbital shifts that exactify the Krieger-Li-Iafrate approximation. Unoccupied orbitals do not need to be calculated. Accuracy and efficiency of the method are shown for atoms and clusters using the exact-exchange energy. Counterintuitive asymptotic limits of the exact OEP are presented.

Not so Complex: Iteration in the Complex Plane

ERIC Educational Resources Information Center

O'Dell, Robin S.

2014-01-01

The simple process of iteration can produce complex and beautiful figures. In this article, Robin O'Dell presents a set of tasks requiring students to use the geometric interpretation of complex number multiplication to construct linear iteration rules. When the outputs are plotted in the complex plane, the graphs trace pleasing designs…

Sensitivity calculations for iteratively solved problems

NASA Technical Reports Server (NTRS)

Haftka, R. T.

1985-01-01

The calculation of sensitivity derivatives of solutions of iteratively solved systems of algebraic equations is investigated. A modified finite difference procedure is presented which improves the accuracy of the calculated derivatives. The procedure is demonstrated for a simple algebraic example as well as an element-by-element preconditioned conjugate gradient iterative solution technique applied to truss examples.

Choosing order of operations to accelerate strip structure analysis in parameter range

NASA Astrophysics Data System (ADS)

Kuksenko, S. P.; Akhunov, R. R.; Gazizov, T. R.

2018-05-01

The paper considers the issue of using iteration methods in solving the sequence of linear algebraic systems obtained in quasistatic analysis of strip structures with the method of moments. Using the analysis of 4 strip structures, the authors have proved that additional acceleration (up to 2.21 times) of the iterative process can be obtained during the process of solving linear systems repeatedly by means of choosing a proper order of operations and a preconditioner. The obtained results can be used to accelerate the process of computer-aided design of various strip structures. The choice of the order of operations to accelerate the process is quite simple, universal and could be used not only for strip structure analysis but also for a wide range of computational problems.

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.

A biological phantom for evaluation of CT image reconstruction algorithms

NASA Astrophysics Data System (ADS)

Cammin, J.; Fung, G. S. K.; Fishman, E. K.; Siewerdsen, J. H.; Stayman, J. W.; Taguchi, K.

2014-03-01

In recent years, iterative algorithms have become popular in diagnostic CT imaging to reduce noise or radiation dose to the patient. The non-linear nature of these algorithms leads to non-linearities in the imaging chain. However, the methods to assess the performance of CT imaging systems were developed assuming the linear process of filtered backprojection (FBP). Those methods may not be suitable any longer when applied to non-linear systems. In order to evaluate the imaging performance, a phantom is typically scanned and the image quality is measured using various indices. For reasons of practicality, cost, and durability, those phantoms often consist of simple water containers with uniform cylinder inserts. However, these phantoms do not represent the rich structure and patterns of real tissue accurately. As a result, the measured image quality or detectability performance for lesions may not reflect the performance on clinical images. The discrepancy between estimated and real performance may be even larger for iterative methods which sometimes produce "plastic-like", patchy images with homogeneous patterns. Consequently, more realistic phantoms should be used to assess the performance of iterative algorithms. We designed and constructed a biological phantom consisting of porcine organs and tissue that models a human abdomen, including liver lesions. We scanned the phantom on a clinical CT scanner and compared basic image quality indices between filtered backprojection and an iterative reconstruction algorithm.

A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations

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

Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu

2016-07-15

Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished bymore » allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.« less

A Heuristic Fast Method to Solve the Nonlinear Schroedinger Equation in Fiber Bragg Gratings with Arbitrary Shape Input Pulse

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

Emami, F.; Hatami, M.; Keshavarz, A. R.

2009-08-13

Using a combination of Runge-Kutta and Jacobi iterative method, we could solve the nonlinear Schroedinger equation describing the pulse propagation in FBGs. By decomposing the electric field to forward and backward components in fiber Bragg grating and utilizing the Fourier series analysis technique, the boundary value problem of a set of coupled equations governing the pulse propagation in FBG changes to an initial condition coupled equations which can be solved by simple Runge-Kutta method.

Image based method for aberration measurement of lithographic tools

NASA Astrophysics Data System (ADS)

Xu, Shuang; Tao, Bo; Guo, Yongxing; Li, Gongfa

2018-01-01

Information of lens aberration of lithographic tools is important as it directly affects the intensity distribution in the image plane. Zernike polynomials are commonly used for a mathematical description of lens aberrations. Due to the advantage of lower cost and easier implementation of tools, image based measurement techniques have been widely used. Lithographic tools are typically partially coherent systems that can be described by a bilinear model, which entails time consuming calculations and does not lend a simple and intuitive relationship between lens aberrations and the resulted images. Previous methods for retrieving lens aberrations in such partially coherent systems involve through-focus image measurements and time-consuming iterative algorithms. In this work, we propose a method for aberration measurement in lithographic tools, which only requires measuring two images of intensity distribution. Two linear formulations are derived in matrix forms that directly relate the measured images to the unknown Zernike coefficients. Consequently, an efficient non-iterative solution is obtained.

Note: A simple image processing based fiducial auto-alignment method for sample registration.

PubMed

Robertson, Wesley D; Porto, Lucas R; Ip, Candice J X; Nantel, Megan K T; Tellkamp, Friedjof; Lu, Yinfei; Miller, R J Dwayne

2015-08-01

A simple method for the location and auto-alignment of sample fiducials for sample registration using widely available MATLAB/LabVIEW software is demonstrated. The method is robust, easily implemented, and applicable to a wide variety of experiment types for improved reproducibility and increased setup speed. The software uses image processing to locate and measure the diameter and center point of circular fiducials for distance self-calibration and iterative alignment and can be used with most imaging systems. The method is demonstrated to be fast and reliable in locating and aligning sample fiducials, provided here by a nanofabricated array, with accuracy within the optical resolution of the imaging system. The software was further demonstrated to register, load, and sample the dynamically wetted array.

Iterative Stable Alignment and Clustering of 2D Transmission Electron Microscope Images

PubMed Central

Yang, Zhengfan; Fang, Jia; Chittuluru, Johnathan; Asturias, Francisco J.; Penczek, Pawel A.

2012-01-01

SUMMARY Identification of homogeneous subsets of images in a macromolecular electron microscopy (EM) image data set is a critical step in single-particle analysis. The task is handled by iterative algorithms, whose performance is compromised by the compounded limitations of image alignment and K-means clustering. Here we describe an approach, iterative stable alignment and clustering (ISAC) that, relying on a new clustering method and on the concepts of stability and reproducibility, can extract validated, homogeneous subsets of images. ISAC requires only a small number of simple parameters and, with minimal human intervention, can eliminate bias from two-dimensional image clustering and maximize the quality of group averages that can be used for ab initio three-dimensional structural determination and analysis of macromolecular conformational variability. Repeated testing of the stability and reproducibility of a solution within ISAC eliminates heterogeneous or incorrect classes and introduces critical validation to the process of EM image clustering. PMID:22325773

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

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

D'Elia, M.; Edwards, H. C.; Hu, J.

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

DOE PAGES

D'Elia, M.; Edwards, H. C.; Hu, J.; ...

2018-01-18

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

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

Gradient optimization and nonlinear control

NASA Technical Reports Server (NTRS)

Hasdorff, L.

1976-01-01

The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.

ITER structural design criteria and their extension to advanced reactor blankets*1

NASA Astrophysics Data System (ADS)

Majumdar, S.; Kalinin, G.

2000-12-01

Applications of the recent ITER structural design criteria (ISDC) are illustrated by two components. First, the low-temperature-design rules are applied to copper alloys that are particularly prone to irradiation embrittlement at relatively low fluences at certain temperatures. Allowable stresses are derived and the impact of the embrittlement on allowable surface heat flux of a simple first-wall/limiter design is demonstrated. Next, the high-temperature-design rules of ISDC are applied to evaporation of lithium and vapor extraction (EVOLVE), a blanket design concept currently being investigated under the US Advanced Power Extraction (APEX) program. A single tungsten first-wall tube is considered for thermal and stress analyses by finite-element method.

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.

An efficient transport solver for tokamak plasmas

DOE PAGES

Park, Jin Myung; Murakami, Masanori; St. John, H. E.; ...

2017-01-03

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

Rapid, simple and inexpensive production of custom 3D printed equipment for large-volume fluorescence microscopy

PubMed Central

Tyson, Adam L.; Hilton, Stephen T.; Andreae, Laura C.

2015-01-01

The cost of 3D printing has reduced dramatically over the last few years and is now within reach of many scientific laboratories. This work presents an example of how 3D printing can be applied to the development of custom laboratory equipment that is specifically adapted for use with the novel brain tissue clearing technique, CLARITY. A simple, freely available online software tool was used, along with consumer-grade equipment, to produce a brain slicing chamber and a combined antibody staining and imaging chamber. Using standard 3D printers we were able to produce research-grade parts in an iterative manner at a fraction of the cost of commercial equipment. 3D printing provides a reproducible, flexible, simple and cost-effective method for researchers to produce the equipment needed to quickly adopt new methods. PMID:25797056

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

A reduced complexity highly power/bandwidth efficient coded FQPSK system with iterative decoding

NASA Technical Reports Server (NTRS)

Simon, M. K.; Divsalar, D.

2001-01-01

Based on a representation of FQPSK as a trellis-coded modulation, this paper investigates the potential improvement in power efficiency obtained from the application of simple outer codes to form a concatenated coding arrangement with iterative decoding.

Fast and accurate computation of system matrix for area integral model-based algebraic reconstruction technique

NASA Astrophysics Data System (ADS)

Zhang, Shunli; Zhang, Dinghua; Gong, Hao; Ghasemalizadeh, Omid; Wang, Ge; Cao, Guohua

2014-11-01

Iterative algorithms, such as the algebraic reconstruction technique (ART), are popular for image reconstruction. For iterative reconstruction, the area integral model (AIM) is more accurate for better reconstruction quality than the line integral model (LIM). However, the computation of the system matrix for AIM is more complex and time-consuming than that for LIM. Here, we propose a fast and accurate method to compute the system matrix for AIM. First, we calculate the intersection of each boundary line of a narrow fan-beam with pixels in a recursive and efficient manner. Then, by grouping the beam-pixel intersection area into six types according to the slopes of the two boundary lines, we analytically compute the intersection area of the narrow fan-beam with the pixels in a simple algebraic fashion. Overall, experimental results show that our method is about three times faster than the Siddon algorithm and about two times faster than the distance-driven model (DDM) in computation of the system matrix. The reconstruction speed of our AIM-based ART is also faster than the LIM-based ART that uses the Siddon algorithm and DDM-based ART, for one iteration. The fast reconstruction speed of our method was accomplished without compromising the image quality.

Applying the scientific method to small catchment studies: Areview of the Panola Mountain experience

USGS Publications Warehouse

Hooper, R.P.

2001-01-01

A hallmark of the scientific method is its iterative application to a problem to increase and refine the understanding of the underlying processes controlling it. A successful iterative application of the scientific method to catchment science (including the fields of hillslope hydrology and biogeochemistry) has been hindered by two factors. First, the scale at which controlled experiments can be performed is much smaller than the scale of the phenomenon of interest. Second, computer simulation models generally have not been used as hypothesis-testing tools as rigorously as they might have been. Model evaluation often has gone only so far as evaluation of goodness of fit, rather than a full structural analysis, which is more useful when treating the model as a hypothesis. An iterative application of a simple mixing model to the Panola Mountain Research Watershed is reviewed to illustrate the increase in understanding gained by this approach and to discern general principles that may be applicable to other studies. The lessons learned include the need for an explicitly stated conceptual model of the catchment, the definition of objective measures of its applicability, and a clear linkage between the scale of observations and the scale of predictions. Published in 2001 by John Wiley & Sons. Ltd.

Similarity solution of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Lockington, D. A.; Parlange, J.-Y.; Parlange, M. B.; Selker, J.

Similarity transforms of the Boussinesq equation in a semi-infinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial differential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15-36] use a hodograph method to derive an integral equation formulation of the new differential equation which they solve by numerical iteration. In the present paper, the convergence of their scheme is improved such that numerical iteration can be avoided for all practical purposes. However, a simpler analytical approach is also presented which is based on Shampine's transformation of the boundary value problem to an initial value problem. This analytical approximation is remarkably simple and yet more accurate than the analytical hodograph approximations.

Nonlinear analysis of composite thin-walled helicopter blades

NASA Astrophysics Data System (ADS)

Kalfon, J. P.; Rand, O.

Nonlinear theoretical modeling of laminated thin-walled composite helicopter rotor blades is presented. The derivation is based on nonlinear geometry with a detailed treatment of the body loads in the axial direction which are induced by the rotation. While the in-plane warping is neglected, a three-dimensional generic out-of-plane warping distribution is included. The formulation may also handle varying thicknesses and mass distribution along the cross-sectional walls. The problem is solved by successive iterations in which a system of equations is constructed and solved for each cross-section. In this method, the differential equations in the spanwise directions are formulated and solved using a finite-differences scheme which allows simple adaptation of the spanwise discretization mesh during iterations.

Designing stellarator coils by a modified Newton method using FOCUS

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

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

Designing stellarator coils by a modified Newton method using FOCUS

NASA Astrophysics Data System (ADS)

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao; Wan, Yuanxi

2018-06-01

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

Designing stellarator coils by a modified Newton method using FOCUS

DOE PAGES

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao; ...

2018-03-22

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

Convergence of quasiparticle self-consistent GW calculations of transition metal monoxides

NASA Astrophysics Data System (ADS)

Das, Suvadip; Coulter, John E.; Manousakis, Efstratios

2015-03-01

We have investigated the electronic structure of the transition metal monoxides MnO, CoO, and NiO in their undistorted rock-salt structure within a fully iterated quasiparticle self-consistent GW (QPscGW) scheme. We have studied the convergence of the QPscGW method, i.e., how the quasiparticle energy eigenvalues and wavefunctions converge as a function of the QPscGW iterations, and compared the converged outputs obtained from different starting wavefunctions. We found that the convergence is slow and that a one-shot G0W0 calculation does not significantly improve the initial eigenvalues and states. In some cases the ``path'' to convergence may go through energy band reordering which cannot be captured by the simple initial unperturbed Hamiltonian. When a fully iterated solution is reached, the converged density of states, band-gaps and magnetic moments of these oxides are found to be only weakly dependent on the choice of the starting wavefunctions and in reasonable agreement with the experiment. National High Magnetic Field Laboratory.

Deconvolution of interferometric data using interior point iterative algorithms

NASA Astrophysics Data System (ADS)

Theys, C.; Lantéri, H.; Aime, C.

2016-09-01

We address the problem of deconvolution of astronomical images that could be obtained with future large interferometers in space. The presentation is made in two complementary parts. The first part gives an introduction to the image deconvolution with linear and nonlinear algorithms. The emphasis is made on nonlinear iterative algorithms that verify the constraints of non-negativity and constant flux. The Richardson-Lucy algorithm appears there as a special case for photon counting conditions. More generally, the algorithm published recently by Lanteri et al. (2015) is based on scale invariant divergences without assumption on the statistic model of the data. The two proposed algorithms are interior-point algorithms, the latter being more efficient in terms of speed of calculation. These algorithms are applied to the deconvolution of simulated images corresponding to an interferometric system of 16 diluted telescopes in space. Two non-redundant configurations, one disposed around a circle and the other on an hexagonal lattice, are compared for their effectiveness on a simple astronomical object. The comparison is made in the direct and Fourier spaces. Raw "dirty" images have many artifacts due to replicas of the original object. Linear methods cannot remove these replicas while iterative methods clearly show their efficacy in these examples.

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

Unsupervised change detection of multispectral images based on spatial constraint chi-squared transform and Markov random field model

NASA Astrophysics Data System (ADS)

Shi, Aiye; Wang, Chao; Shen, Shaohong; Huang, Fengchen; Ma, Zhenli

2016-10-01

Chi-squared transform (CST), as a statistical method, can describe the difference degree between vectors. The CST-based methods operate directly on information stored in the difference image and are simple and effective methods for detecting changes in remotely sensed images that have been registered and aligned. However, the technique does not take spatial information into consideration, which leads to much noise in the result of change detection. An improved unsupervised change detection method is proposed based on spatial constraint CST (SCCST) in combination with a Markov random field (MRF) model. First, the mean and variance matrix of the difference image of bitemporal images are estimated by an iterative trimming method. In each iteration, spatial information is injected to reduce scattered changed points (also known as "salt and pepper" noise). To determine the key parameter confidence level in the SCCST method, a pseudotraining dataset is constructed to estimate the optimal value. Then, the result of SCCST, as an initial solution of change detection, is further improved by the MRF model. The experiments on simulated and real multitemporal and multispectral images indicate that the proposed method performs well in comprehensive indices compared with other methods.

[Target volume segmentation of PET images by an iterative method based on threshold value].

PubMed

Castro, P; Huerga, C; Glaría, L A; Plaza, R; Rodado, S; Marín, M D; Mañas, A; Serrada, A; Núñez, L

2014-01-01

An automatic segmentation method is presented for PET images based on an iterative approximation by threshold value that includes the influence of both lesion size and background present during the acquisition. Optimal threshold values that represent a correct segmentation of volumes were determined based on a PET phantom study that contained different sizes spheres and different known radiation environments. These optimal values were normalized to background and adjusted by regression techniques to a two-variable function: lesion volume and signal-to-background ratio (SBR). This adjustment function was used to build an iterative segmentation method and then, based in this mention, a procedure of automatic delineation was proposed. This procedure was validated on phantom images and its viability was confirmed by retrospectively applying it on two oncology patients. The resulting adjustment function obtained had a linear dependence with the SBR and was inversely proportional and negative with the volume. During the validation of the proposed method, it was found that the volume deviations respect to its real value and CT volume were below 10% and 9%, respectively, except for lesions with a volume below 0.6 ml. The automatic segmentation method proposed can be applied in clinical practice to tumor radiotherapy treatment planning in a simple and reliable way with a precision close to the resolution of PET images. Copyright © 2013 Elsevier España, S.L.U. and SEMNIM. All rights reserved.

A three phase optimization method for precopy based VM live migration.

PubMed

Sharma, Sangeeta; Chawla, Meenu

2016-01-01

Virtual machine live migration is a method of moving virtual machine across hosts within a virtualized datacenter. It provides significant benefits for administrator to manage datacenter efficiently. It reduces service interruption by transferring the virtual machine without stopping at source. Transfer of large number of virtual machine memory pages results in long migration time as well as downtime, which also affects the overall system performance. This situation becomes unbearable when migration takes place over slower network or a long distance migration within a cloud. In this paper, precopy based virtual machine live migration method is thoroughly analyzed to trace out the issues responsible for its performance drops. In order to address these issues, this paper proposes three phase optimization (TPO) method. It works in three phases as follows: (i) reduce the transfer of memory pages in first phase, (ii) reduce the transfer of duplicate pages by classifying frequently and non-frequently updated pages, and (iii) reduce the data sent in last iteration of migration by applying the simple RLE compression technique. As a result, each phase significantly reduces total pages transferred, total migration time and downtime respectively. The proposed TPO method is evaluated using different representative workloads on a Xen virtualized environment. Experimental results show that TPO method reduces total pages transferred by 71 %, total migration time by 70 %, downtime by 3 % for higher workload, and it does not impose significant overhead as compared to traditional precopy method. Comparison of TPO method with other methods is also done for supporting and showing its effectiveness. TPO method and precopy methods are also tested at different number of iterations. The TPO method gives better performance even with less number of iterations.

Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

NASA Astrophysics Data System (ADS)

Moatssime, H. Al; Esselaoui, D.; Hakim, A.; Raghay, S.

2001-08-01

This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss-Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright

Engineering Design Theory: Applying the Success of the Modern World to Campaign Creation

DTIC Science & Technology

2009-05-21

and school of thought) to the simple methods of design.6 This progression is analogous to Peter Senge’s levels of learning disciplines.7 Senge...iterative learning and adaptive action that develops and employs critical and creative thinking , enabling leaders to apply the necessary logic to...overcome mental rigidity and develop group insight, the Army must learn to utilize group learning and thinking , through a fluid and creative open process

A hybrid multigroup neutron-pattern model

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

Pogosbekyan, L.R.; Lysov, D.A.

In this paper, we use the general approach to construct a multigroup hybrid model for the neutron pattern. The equations are given together with a reasonably economic and simple iterative method of solving them. The algorithm can be used to calculate the pattern and the functionals as well as to correct the constants from the experimental data and to adapt the support over the constants to the engineering programs by reference to precision ones.

Slant correction for handwritten English documents

NASA Astrophysics Data System (ADS)

Shridhar, Malayappan; Kimura, Fumitaka; Ding, Yimei; Miller, John W. V.

2004-12-01

Optical character recognition of machine-printed documents is an effective means for extracting textural material. While the level of effectiveness for handwritten documents is much poorer, progress is being made in more constrained applications such as personal checks and postal addresses. In these applications a series of steps is performed for recognition beginning with removal of skew and slant. Slant is a characteristic unique to the writer and varies from writer to writer in which characters are tilted some amount from vertical. The second attribute is the skew that arises from the inability of the writer to write on a horizontal line. Several methods have been proposed and discussed for average slant estimation and correction in the earlier papers. However, analysis of many handwritten documents reveals that slant is a local property and slant varies even within a word. The use of an average slant for the entire word often results in overestimation or underestimation of the local slant. This paper describes three methods for local slant estimation, namely the simple iterative method, high-speed iterative method, and the 8-directional chain code method. The experimental results show that the proposed methods can estimate and correct local slant more effectively than the average slant correction.

Interpretation of magnetotelluric resistivity and phase soundings over horizontal layers

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

Patella, D.

1976-02-01

The present paper deals with a new inverse method for quantitatively interpreting magnetotelluric apparent resistivity and phase-lag sounding curves over horizontally stratified earth sections. The recurrent character of the general formula relating the wave impedance of an (n-l)-layered medium to that of an n-layered medium suggests the use of the method of reduction to a lower boundary plane, as originally termed by Koefoed in the case of dc resistivity soundings. The layering parameters are so directly derived by a simple iterative procedure. The method is applicable for any number of layers but only when both apparent resistivity and phase-lag soundingmore » curves are jointly available. Moreover no sophisticated algorithm is required: a simple desk electronic calculator together with a sheet of two-layer apparent resistivity and phase-lag master curves are sufficient to reproduce earth sections which, in the range of equivalence, are all consistent with field data.« less

Active Learning with a Human in The Loop

DTIC Science & Technology

2012-11-01

handwrit - ten digits (LeCun et al. [1998]). In the red curve the model is built iteratively: at each iteration the twenty examples with the lowest...continuum. The most we can say about MUC annotation is that it’s simple enough that other tasks are likely to impose a heavier load on the user for

Error Control Coding Techniques for Space and Satellite Communications

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.; Takeshita, Oscar Y.; Cabral, Hermano A.; He, Jiali; White, Gregory S.

1997-01-01

Turbo coding using iterative SOVA decoding and M-ary differentially coherent or non-coherent modulation can provide an effective coding modulation solution: (1) Energy efficient with relatively simple SOVA decoding and small packet lengths, depending on BEP required; (2) Low number of decoding iterations required; and (3) Robustness in fading with channel interleaving.

Convergence of quasiparticle self-consistent G W calculations of transition-metal monoxides

NASA Astrophysics Data System (ADS)

Das, Suvadip; Coulter, John E.; Manousakis, Efstratios

2015-03-01

Finding an accurate ab initio approach for calculating the electronic properties of transition-metal oxides has been a problem for several decades. In this paper, we investigate the electronic structure of the transition-metal monoxides MnO, CoO, and NiO in their undistorted rocksalt structure within a fully iterated quasiparticle self-consistent G W (QPsc G W ) scheme. We study the convergence of the QPsc G W method, i.e., how the quasiparticle energy eigenvalues and wave functions converge as a function of the QPsc G W iterations, and we compare the converged outputs obtained from different starting wave functions. We find that the convergence is slow and that a one-shot G0W0 calculation does not significantly improve the initial eigenvalues and states. It is important to notice that in some cases the "path" to convergence may go through energy band reordering which cannot be captured by the simple initial unperturbed Hamiltonian. When we reach a fully iterated solution, the converged density of states, band gaps, and magnetic moments of these oxides are found to be only weakly dependent on the choice of the starting wave functions and in reasonably good agreement with the experiment. Finally, this approach provides a clear picture of the interplay between the various orbitals near the Fermi level of these simple transition-metal monoxides. The results of these accurate ab initio calculations can provide input for models aiming at describing the low-energy physics in these materials.

Iterative inversion of deformation vector fields with feedback control.

PubMed

Dubey, Abhishek; Iliopoulos, Alexandros-Stavros; Sun, Xiaobai; Yin, Fang-Fang; Ren, Lei

2018-05-14

Often, the inverse deformation vector field (DVF) is needed together with the corresponding forward DVF in four-dimesional (4D) reconstruction and dose calculation, adaptive radiation therapy, and simultaneous deformable registration. This study aims at improving both accuracy and efficiency of iterative algorithms for DVF inversion, and advancing our understanding of divergence and latency conditions. We introduce a framework of fixed-point iteration algorithms with active feedback control for DVF inversion. Based on rigorous convergence analysis, we design control mechanisms for modulating the inverse consistency (IC) residual of the current iterate, to be used as feedback into the next iterate. The control is designed adaptively to the input DVF with the objective to enlarge the convergence area and expedite convergence. Three particular settings of feedback control are introduced: constant value over the domain throughout the iteration; alternating values between iteration steps; and spatially variant values. We also introduce three spectral measures of the displacement Jacobian for characterizing a DVF. These measures reveal the critical role of what we term the nontranslational displacement component (NTDC) of the DVF. We carry out inversion experiments with an analytical DVF pair, and with DVFs associated with thoracic CT images of six patients at end of expiration and end of inspiration. The NTDC-adaptive iterations are shown to attain a larger convergence region at a faster pace compared to previous nonadaptive DVF inversion iteration algorithms. By our numerical experiments, alternating control yields smaller IC residuals and inversion errors than constant control. Spatially variant control renders smaller residuals and errors by at least an order of magnitude, compared to other schemes, in no more than 10 steps. Inversion results also show remarkable quantitative agreement with analysis-based predictions. Our analysis captures properties of DVF data associated with clinical CT images, and provides new understanding of iterative DVF inversion algorithms with a simple residual feedback control. Adaptive control is necessary and highly effective in the presence of nonsmall NTDCs. The adaptive iterations or the spectral measures, or both, may potentially be incorporated into deformable image registration methods. © 2018 American Association of Physicists in Medicine.

Eighteen-month-olds' memory for short movies of simple stories.

PubMed

Kingo, Osman S; Krøjgaard, Peter

2015-04-01

This study investigated twenty four 18-month-olds' memory for dynamic visual stimuli. During the first visit participants saw one of two brief movies (30 seconds) with a simple storyline displayed in four iterations. After 2 weeks, memory was tested in the visual paired comparison paradigm in which the familiar and the novel movie were contrasted simultaneously and displayed in two iterations for a total of 60 seconds. Eye-tracking revealed that participants fixated the familiar movie significantly more than the novel movie, thus indicating memory for the familiar movie. Furthermore, time-dependent analysis of the data revealed that individual differences in the looking-patterns for the first and second iteration of the movies were related to individual differences in productive vocabulary. We suggest that infants' vocabulary may be indicative of their ability to understand and remember the storyline of the movies, thereby affecting their subsequent memory. © 2015 Scandinavian Psychological Associations and John Wiley & Sons Ltd.

Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

NASA Technical Reports Server (NTRS)

Ulbrich, N.; Volden, T.

2017-01-01

A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.

Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression.

PubMed

Meng, Yilin; Roux, Benoît

2015-08-11

The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost.

Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression

PubMed Central

2015-01-01

The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost. PMID:26574437

HITEMP Material and Structural Optimization Technology Transfer

NASA Technical Reports Server (NTRS)

Collier, Craig S.; Arnold, Steve (Technical Monitor)

2001-01-01

The feasibility of adding viscoelasticity and the Generalized Method of Cells (GMC) for micromechanical viscoelastic behavior into the commercial HyperSizer structural analysis and optimization code was investigated. The viscoelasticity methodology was developed in four steps. First, a simplified algorithm was devised to test the iterative time stepping method for simple one-dimensional multiple ply structures. Second, GMC code was made into a callable subroutine and incorporated into the one-dimensional code to test the accuracy and usability of the code. Third, the viscoelastic time-stepping and iterative scheme was incorporated into HyperSizer for homogeneous, isotropic viscoelastic materials. Finally, the GMC was included in a version of HyperSizer. MS Windows executable files implementing each of these steps is delivered with this report, as well as source code. The findings of this research are that both viscoelasticity and GMC are feasible and valuable additions to HyperSizer and that the door is open for more advanced nonlinear capability, such as viscoplasticity.

A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

PubMed

Benhammouda, Brahim

2016-01-01

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

Acceleration of the direct reconstruction of linear parametric images using nested algorithms.

PubMed

Wang, Guobao; Qi, Jinyi

2010-03-07

Parametric imaging using dynamic positron emission tomography (PET) provides important information for biological research and clinical diagnosis. Indirect and direct methods have been developed for reconstructing linear parametric images from dynamic PET data. Indirect methods are relatively simple and easy to implement because the image reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from raw PET data and are statistically more efficient. However, the convergence rate of direct algorithms can be slow due to the coupling between the reconstruction and kinetic modeling. Here we present two fast gradient-type algorithms for direct reconstruction of linear parametric images. The new algorithms decouple the reconstruction and linear parametric modeling at each iteration by employing the principle of optimization transfer. Convergence speed is accelerated by running more sub-iterations of linear parametric estimation because the computation cost of the linear parametric modeling is much less than that of the image reconstruction. Computer simulation studies demonstrated that the new algorithms converge much faster than the traditional expectation maximization (EM) and the preconditioned conjugate gradient algorithms for dynamic PET.

On some variational acceleration techniques and related methods for local refinement

NASA Astrophysics Data System (ADS)

Teigland, Rune

1998-10-01

This paper shows that the well-known variational acceleration method described by Wachspress (E. Wachspress, Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics, Prentice-Hall, Englewood Cliffs, NJ, 1966) and later generalized to multilevels (known as the additive correction multigrid method (B.R Huthchinson and G.D. Raithby, Numer. Heat Transf., 9, 511-537 (1986))) is similar to the FAC method of McCormick and Thomas (S.F McCormick and J.W. Thomas, Math. Comput., 46, 439-456 (1986)) and related multilevel methods. The performance of the method is demonstrated for some simple model problems using local refinement and suggestions for improving the performance of the method are given.

Coherent diffraction imaging by moving a lens.

PubMed

Shen, Cheng; Tan, Jiubin; Wei, Ce; Liu, Zhengjun

2016-07-25

A moveable lens is used for determining amplitude and phase on the object plane. The extended fractional Fourier transform is introduced to address the single lens imaging. We put forward a fast algorithm for the transform by convolution. Combined with parallel iterative phase retrieval algorithm, it is applied to reconstruct the complex amplitude of the object. Compared with inline holography, the implementation of our method is simple and easy. Without the oversampling operation, the computational load is less. Also the proposed method has a superiority of accuracy over the direct focusing measurement for the imaging of small size objects.

Application of viscous-inviscid interaction methods to transonic turbulent flows

NASA Technical Reports Server (NTRS)

Lee, D.; Pletcher, R. H.

1986-01-01

Two different viscous-inviscid interaction schemes were developed for the analysis of steady, turbulent, transonic, separated flows over axisymmetric bodies. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity approach. In the semi-inverse interaction scheme, the viscous and inviscid equations are solved in an explicitly separate manner and the displacement thickness distribution is iteratively updated by a simple coupling algorithm. In the simultaneous interaction method, local solutions of viscous and inviscid equations are treated simultaneously, and the displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure. The inviscid flow region is described by a direct finite-difference solution of a velocity potential equation in conservative form. The potential equation is solved on a numerically generated mesh by an approximate factorization (AF2) scheme in the semi-inverse interaction method and by a successive line overrelaxation (SLOR) scheme in the simultaneous interaction method. The boundary-layer equations are used for the viscous flow region. The continuity and momentum equations are solved inversely in a coupled manner using a fully implicit finite-difference scheme.

Architectural Specialization for Inter-Iteration Loop Dependence Patterns

DTIC Science & Technology

2015-10-01

Architectural Specialization for Inter-Iteration Loop Dependence Patterns Christopher Batten Computer Systems Laboratory School of Electrical and...Trends in Computer Architecture Transistors (Thousands) Frequency (MHz) Typical Power (W) MIPS R2K Intel P4 DEC Alpha 21264 Data collected by M...T as ks p er Jo ule ) Simple Processor Design Power Constraint High-Performance Architectures Embedded Architectures Design Performance

Fast Fourier transform-based solution of 2D and 3D magnetization problems in type-II superconductivity

NASA Astrophysics Data System (ADS)

Prigozhin, Leonid; Sokolovsky, Vladimir

2018-05-01

We consider the fast Fourier transform (FFT) based numerical method for thin film magnetization problems (Vestgården and Johansen 2012 Supercond. Sci. Technol. 25 104001), compare it with the finite element methods, and evaluate its accuracy. Proposed modifications of this method implementation ensure stable convergence of iterations and enhance its efficiency. A new method, also based on the FFT, is developed for 3D bulk magnetization problems. This method is based on a magnetic field formulation, different from the popular h-formulation of eddy current problems typically employed with the edge finite elements. The method is simple, easy to implement, and can be used with a general current–voltage relation; its efficiency is illustrated by numerical simulations.

Nontraditional method for determining unperturbed orbits of unknown space objects using incomplete optical observational data

NASA Astrophysics Data System (ADS)

Perov, N. I.

1985-02-01

A physical-geometrical method for computing the orbits of earth satellites on the basis of an inadequate number of angular observations (N3) was developed. Specifically, a new method has been developed for calculating the elements of Keplerian orbits of unidentified artificial satellites using two angular observations (alpha sub k, S sub k, k = 1). The first section gives procedures for determining the topocentric distance to AES on the basis of one optical observation. This is followed by description of a very simple method for determining unperturbed orbits using two satellite position vectors and a time interval which is applicable even in the case of antiparallel AED position vectors, a method designated the R sub 2 iterations method.

Forecasting Air Force Logistics Command Second Destination Transportation: An Application of Multiple Regression Analysis and Neural Networks

DTIC Science & Technology

1990-09-01

without the help from the DSXR staff. William Lyons, Charles Ramsey , and Martin Meeks went above and beyond to help complete this research. Special...develop a valid forecasting model that is significantly more accurate than the one presently used by DSXR and suggested the development and testing of a...method, Strom tested DSXR’s iterative linear regression forecasting technique by examining P1 in the simple regression equation to determine whether

The Derivation of Simple Poles in a Transfer Function from Real Frequency Information. Part 3. Object Classification and Identification,

DTIC Science & Technology

1977-01-10

This report is the third in a series of three that evaluate a technique (frequency-domain Prony) for obtaining the poles of a transfer function. The...main objective was to assess the feasibility of classifying or identifying ship-like targets by using pole sets derived from frequency-domain data. A...predictor-correlator procedure for using spectral data and library pole sets for this purpose was developed. Also studied was an iterative method for

Rapid iterative reanalysis for automated design

NASA Technical Reports Server (NTRS)

Bhatia, K. G.

1973-01-01

A method for iterative reanalysis in automated structural design is presented for a finite-element analysis using the direct stiffness approach. A basic feature of the method is that the generalized stiffness and inertia matrices are expressed as functions of structural design parameters, and these generalized matrices are expanded in Taylor series about the initial design. Only the linear terms are retained in the expansions. The method is approximate because it uses static condensation, modal reduction, and the linear Taylor series expansions. The exact linear representation of the expansions of the generalized matrices is also described and a basis for the present method is established. Results of applications of the present method to the recalculation of the natural frequencies of two simple platelike structural models are presented and compared with results obtained by using a commonly applied analysis procedure used as a reference. In general, the results are in good agreement. A comparison of the computer times required for the use of the present method and the reference method indicated that the present method required substantially less time for reanalysis. Although the results presented are for relatively small-order problems, the present method will become more efficient relative to the reference method as the problem size increases. An extension of the present method to static reanalysis is described, ana a basis for unifying the static and dynamic reanalysis procedures is presented.

Fluence map optimization (FMO) with dose-volume constraints in IMRT using the geometric distance sorting method.

PubMed

Lan, Yihua; Li, Cunhua; Ren, Haozheng; Zhang, Yong; Min, Zhifang

2012-10-21

A new heuristic algorithm based on the so-called geometric distance sorting technique is proposed for solving the fluence map optimization with dose-volume constraints which is one of the most essential tasks for inverse planning in IMRT. The framework of the proposed method is basically an iterative process which begins with a simple linear constrained quadratic optimization model without considering any dose-volume constraints, and then the dose constraints for the voxels violating the dose-volume constraints are gradually added into the quadratic optimization model step by step until all the dose-volume constraints are satisfied. In each iteration step, an interior point method is adopted to solve each new linear constrained quadratic programming. For choosing the proper candidate voxels for the current dose constraint adding, a so-called geometric distance defined in the transformed standard quadratic form of the fluence map optimization model was used to guide the selection of the voxels. The new geometric distance sorting technique can mostly reduce the unexpected increase of the objective function value caused inevitably by the constraint adding. It can be regarded as an upgrading to the traditional dose sorting technique. The geometry explanation for the proposed method is also given and a proposition is proved to support our heuristic idea. In addition, a smart constraint adding/deleting strategy is designed to ensure a stable iteration convergence. The new algorithm is tested on four cases including head-neck, a prostate, a lung and an oropharyngeal, and compared with the algorithm based on the traditional dose sorting technique. Experimental results showed that the proposed method is more suitable for guiding the selection of new constraints than the traditional dose sorting method, especially for the cases whose target regions are in non-convex shapes. It is a more efficient optimization technique to some extent for choosing constraints than the dose sorting method. By integrating a smart constraint adding/deleting scheme within the iteration framework, the new technique builds up an improved algorithm for solving the fluence map optimization with dose-volume constraints.

A simple method for low-contrast detectability, image quality and dose optimisation with CT iterative reconstruction algorithms and model observers.

PubMed

Bellesi, Luca; Wyttenbach, Rolf; Gaudino, Diego; Colleoni, Paolo; Pupillo, Francesco; Carrara, Mauro; Braghetti, Antonio; Puligheddu, Carla; Presilla, Stefano

2017-01-01

The aim of this work was to evaluate detection of low-contrast objects and image quality in computed tomography (CT) phantom images acquired at different tube loadings (i.e. mAs) and reconstructed with different algorithms, in order to find appropriate settings to reduce the dose to the patient without any image detriment. Images of supraslice low-contrast objects of a CT phantom were acquired using different mAs values. Images were reconstructed using filtered back projection (FBP), hybrid and iterative model-based methods. Image quality parameters were evaluated in terms of modulation transfer function; noise, and uniformity using two software resources. For the definition of low-contrast detectability, studies based on both human (i.e. four-alternative forced-choice test) and model observers were performed across the various images. Compared to FBP, image quality parameters were improved by using iterative reconstruction (IR) algorithms. In particular, IR model-based methods provided a 60% noise reduction and a 70% dose reduction, preserving image quality and low-contrast detectability for human radiological evaluation. According to the model observer, the diameters of the minimum detectable detail were around 2 mm (up to 100 mAs). Below 100 mAs, the model observer was unable to provide a result. IR methods improve CT protocol quality, providing a potential dose reduction while maintaining a good image detectability. Model observer can in principle be useful to assist human performance in CT low-contrast detection tasks and in dose optimisation.

Estimation of color filter array data from JPEG images for improved demosaicking

NASA Astrophysics Data System (ADS)

Feng, Wei; Reeves, Stanley J.

2006-02-01

On-camera demosaicking algorithms are necessarily simple and therefore do not yield the best possible images. However, off-camera demosaicking algorithms face the additional challenge that the data has been compressed and therefore corrupted by quantization noise. We propose a method to estimate the original color filter array (CFA) data from JPEG-compressed images so that more sophisticated (and better) demosaicking schemes can be applied to get higher-quality images. The JPEG image formation process, including simple demosaicking, color space transformation, chrominance channel decimation and DCT, is modeled as a series of matrix operations followed by quantization on the CFA data, which is estimated by least squares. An iterative method is used to conserve memory and speed computation. Our experiments show that the mean square error (MSE) with respect to the original CFA data is reduced significantly using our algorithm, compared to that of unprocessed JPEG and deblocked JPEG data.

Post-game analysis: An initial experiment for heuristic-based resource management in concurrent systems

NASA Technical Reports Server (NTRS)

Yan, Jerry C.

1987-01-01

In concurrent systems, a major responsibility of the resource management system is to decide how the application program is to be mapped onto the multi-processor. Instead of using abstract program and machine models, a generate-and-test framework known as 'post-game analysis' that is based on data gathered during program execution is proposed. Each iteration consists of (1) (a simulation of) an execution of the program; (2) analysis of the data gathered; and (3) the proposal of a new mapping that would have a smaller execution time. These heuristics are applied to predict execution time changes in response to small perturbations applied to the current mapping. An initial experiment was carried out using simple strategies on 'pipeline-like' applications. The results obtained from four simple strategies demonstrated that for this kind of application, even simple strategies can produce acceptable speed-up with a small number of iterations.

Predictive wall adjustment strategy for two-dimensional flexible walled adaptive wind tunnel: A detailed description of the first one-step method

NASA Technical Reports Server (NTRS)

Wolf, Stephen W. D.; Goodyer, Michael J.

1988-01-01

Following the realization that a simple iterative strategy for bringing the flexible walls of two-dimensional test sections to streamline contours was too slow for practical use, Judd proposed, developed, and placed into service what was the first Predictive Strategy. The Predictive Strategy reduced by 75 percent or more the number of iterations of wall shapes, and therefore the tunnel run-time overhead attributable to the streamlining process, required to reach satisfactory streamlines. The procedures of the Strategy are embodied in the FORTRAN subroutine WAS (standing for Wall Adjustment Strategy) which is written in general form. The essentials of the test section hardware, followed by the underlying aerodynamic theory which forms the basis of the Strategy, are briefly described. The subroutine is then presented as the Appendix, broken down into segments with descriptions of the numerical operations underway in each, with definitions of variables.

Real-Time Optimization for use in a Control Allocation System to Recover from Pilot Induced Oscillations

NASA Technical Reports Server (NTRS)

Leonard, Michael W.

2013-01-01

Integration of the Control Allocation technique to recover from Pilot Induced Oscillations (CAPIO) System into the control system of a Short Takeoff and Landing Mobility Concept Vehicle simulation presents a challenge because the CAPIO formulation requires that constrained optimization problems be solved at the controller operating frequency. We present a solution that utilizes a modified version of the well-known L-BFGS-B solver. Despite the iterative nature of the solver, the method is seen to converge in real time with sufficient reliability to support three weeks of piloted runs at the NASA Ames Vertical Motion Simulator (VMS) facility. The results of the optimization are seen to be excellent in the vast majority of real-time frames. Deficiencies in the quality of the results in some frames are shown to be improvable with simple termination criteria adjustments, though more real-time optimization iterations would be required.

On a multigrid method for the coupled Stokes and porous media flow problem

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2017-07-01

The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linear system. Special treatment is required regarding the discretization at the interface. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on symmetric Gauss-Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a relaxation parameter is part of a Richardson iteration, Local Fourier Analysis (LFA) is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs well for small values of the hydraulic conductivity and fluid viscosity, that are relevant for applications.

Robust non-fragile finite-frequency H∞ static output-feedback control for active suspension systems

NASA Astrophysics Data System (ADS)

Wang, Gang; Chen, Changzheng; Yu, Shenbo

2017-07-01

This paper deals with the problem of non-fragile H∞ static output-feedback control of vehicle active suspension systems with finite-frequency constraint. The control objective is to improve ride comfort within the given frequency range and ensure the hard constraints in the time-domain. Moreover, in order to enhance the robustness of the controller, the control gain perturbation is also considered in controller synthesis. Firstly, a new non-fragile H∞ finite-frequency control condition is established by using generalized Kalman-Yakubovich-Popov (GKYP) lemma. Secondly, the static output-feedback control gain is directly derived by using a non-iteration algorithm. Different from the existing iteration LMI results, the static output-feedback design is simple and less conservative. Finally, the proposed control algorithm is applied to a quarter-car active suspension model with actuator dynamics, numerical results are made to show the effectiveness and merits of the proposed method.

Ground Truth Creation for Complex Clinical NLP Tasks - an Iterative Vetting Approach and Lessons Learned.

PubMed

Liang, Jennifer J; Tsou, Ching-Huei; Devarakonda, Murthy V

2017-01-01

Natural language processing (NLP) holds the promise of effectively analyzing patient record data to reduce cognitive load on physicians and clinicians in patient care, clinical research, and hospital operations management. A critical need in developing such methods is the "ground truth" dataset needed for training and testing the algorithms. Beyond localizable, relatively simple tasks, ground truth creation is a significant challenge because medical experts, just as physicians in patient care, have to assimilate vast amounts of data in EHR systems. To mitigate potential inaccuracies of the cognitive challenges, we present an iterative vetting approach for creating the ground truth for complex NLP tasks. In this paper, we present the methodology, and report on its use for an automated problem list generation task, its effect on the ground truth quality and system accuracy, and lessons learned from the effort.

A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet.

PubMed

Brown, A M

2001-06-01

The objective of this present study was to introduce a simple, easily understood method for carrying out non-linear regression analysis based on user input functions. While it is relatively straightforward to fit data with simple functions such as linear or logarithmic functions, fitting data with more complicated non-linear functions is more difficult. Commercial specialist programmes are available that will carry out this analysis, but these programmes are expensive and are not intuitive to learn. An alternative method described here is to use the SOLVER function of the ubiquitous spreadsheet programme Microsoft Excel, which employs an iterative least squares fitting routine to produce the optimal goodness of fit between data and function. The intent of this paper is to lead the reader through an easily understood step-by-step guide to implementing this method, which can be applied to any function in the form y=f(x), and is well suited to fast, reliable analysis of data in all fields of biology.

Effective Algorithm for Detection and Correction of the Wave Reconstruction Errors Caused by the Tilt of Reference Wave in Phase-shifting Interferometry

NASA Astrophysics Data System (ADS)

Xu, Xianfeng; Cai, Luzhong; Li, Dailin; Mao, Jieying

2010-04-01

In phase-shifting interferometry (PSI) the reference wave is usually supposed to be an on-axis plane wave. But in practice a slight tilt of reference wave often occurs, and this tilt will introduce unexpected errors of the reconstructed object wave-front. Usually the least-square method with iterations, which is time consuming, is employed to analyze the phase errors caused by the tilt of reference wave. Here a simple effective algorithm is suggested to detect and then correct this kind of errors. In this method, only some simple mathematic operation is used, avoiding using least-square equations as needed in most methods reported before. It can be used for generalized phase-shifting interferometry with two or more frames for both smooth and diffusing objects, and the excellent performance has been verified by computer simulations. The numerical simulations show that the wave reconstruction errors can be reduced by 2 orders of magnitude.

Iterative channel decoding of FEC-based multiple-description codes.

PubMed

Chang, Seok-Ho; Cosman, Pamela C; Milstein, Laurence B

2012-03-01

Multiple description coding has been receiving attention as a robust transmission framework for multimedia services. This paper studies the iterative decoding of FEC-based multiple description codes. The proposed decoding algorithms take advantage of the error detection capability of Reed-Solomon (RS) erasure codes. The information of correctly decoded RS codewords is exploited to enhance the error correction capability of the Viterbi algorithm at the next iteration of decoding. In the proposed algorithm, an intradescription interleaver is synergistically combined with the iterative decoder. The interleaver does not affect the performance of noniterative decoding but greatly enhances the performance when the system is iteratively decoded. We also address the optimal allocation of RS parity symbols for unequal error protection. For the optimal allocation in iterative decoding, we derive mathematical equations from which the probability distributions of description erasures can be generated in a simple way. The performance of the algorithm is evaluated over an orthogonal frequency-division multiplexing system. The results show that the performance of the multiple description codes is significantly enhanced.

Supply based on demand dynamical model

NASA Astrophysics Data System (ADS)

Levi, Asaf; Sabuco, Juan; Sanjuán, Miguel A. F.

2018-04-01

We propose and numerically analyze a simple dynamical model that describes the firm behaviors under uncertainty of demand. Iterating this simple model and varying some parameter values, we observe a wide variety of market dynamics such as equilibria, periodic, and chaotic behaviors. Interestingly, the model is also able to reproduce market collapses.

Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

NASA Astrophysics Data System (ADS)

Rangan, Aaditya V.; Cai, David; Tao, Louis

2007-02-01

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of integrate-and-fire neuronal networks.

Superpixel Based Factor Analysis and Target Transformation Method for Martian Minerals Detection

NASA Astrophysics Data System (ADS)

Wu, X.; Zhang, X.; Lin, H.

2018-04-01

The Factor analysis and target transformation (FATT) is an effective method to test for the presence of particular mineral on Martian surface. It has been used both in thermal infrared (Thermal Emission Spectrometer, TES) and near-infrared (Compact Reconnaissance Imaging Spectrometer for Mars, CRISM) hyperspectral data. FATT derived a set of orthogonal eigenvectors from a mixed system and typically selected first 10 eigenvectors to least square fit the library mineral spectra. However, minerals present only in a limited pixels will be ignored because its weak spectral features compared with full image signatures. Here, we proposed a superpixel based FATT method to detect the mineral distributions on Mars. The simple linear iterative clustering (SLIC) algorithm was used to partition the CRISM image into multiple connected image regions with spectral homogeneous to enhance the weak signatures by increasing their proportion in a mixed system. A least square fitting was used in target transformation and performed to each region iteratively. Finally, the distribution of the specific minerals in image was obtained, where fitting residual less than a threshold represent presence and otherwise absence. We validate our method by identifying carbonates in a well analysed CRISM image in Nili Fossae on Mars. Our experimental results indicate that the proposed method work well both in simulated and real data sets.

Calculation of water equivalent thickness of materials of arbitrary density, elemental composition and thickness in proton beam irradiation

NASA Astrophysics Data System (ADS)

Zhang, Rui; Newhauser, Wayne D.

2009-03-01

In proton therapy, the radiological thickness of a material is commonly expressed in terms of water equivalent thickness (WET) or water equivalent ratio (WER). However, the WET calculations required either iterative numerical methods or approximate methods of unknown accuracy. The objective of this study was to develop a simple deterministic formula to calculate WET values with an accuracy of 1 mm for materials commonly used in proton radiation therapy. Several alternative formulas were derived in which the energy loss was calculated based on the Bragg-Kleeman rule (BK), the Bethe-Bloch equation (BB) or an empirical version of the Bethe-Bloch equation (EBB). Alternative approaches were developed for targets that were 'radiologically thin' or 'thick'. The accuracy of these methods was assessed by comparison to values from an iterative numerical method that utilized evaluated stopping power tables. In addition, we also tested the approximate formula given in the International Atomic Energy Agency's dosimetry code of practice (Technical Report Series No 398, 2000, IAEA, Vienna) and stopping power ratio approximation. The results of these comparisons revealed that most methods were accurate for cases involving thin or low-Z targets. However, only the thick-target formulas provided accurate WET values for targets that were radiologically thick and contained high-Z material.

Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

NASA Astrophysics Data System (ADS)

Broedel, Johannes; Duhr, Claude; Dulat, Falko; Tancredi, Lorenzo

2018-05-01

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. We demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.

Capture zones for simple aquifers

USGS Publications Warehouse

McElwee, Carl D.

1991-01-01

Capture zones showing the area influenced by a well within a certain time are useful for both aquifer protection and cleanup. If hydrodynamic dispersion is neglected, a deterministic curve defines the capture zone. Analytical expressions for the capture zones can be derived for simple aquifers. However, the capture zone equations are transcendental and cannot be explicitly solved for the coordinates of the capture zone boundary. Fortunately, an iterative scheme allows the solution to proceed quickly and efficiently even on a modest personal computer. Three forms of the analytical solution must be used in an iterative scheme to cover the entire region of interest, after the extreme values of the x coordinate are determined by an iterative solution. The resulting solution is a discrete one, and usually 100-1000 intervals along the x-axis are necessary for a smooth definition of the capture zone. The presented program is written in FORTRAN and has been used in a variety of computing environments. No graphics capability is included with the program; it is assumed the user has access to a commercial package. The superposition of capture zones for multiple wells is expected to be satisfactory if the spacing is not too close. Because this program deals with simple aquifers, the results rarely will be the final word in a real application.

A General Interface Method for Aeroelastic Analysis of Aircraft

NASA Technical Reports Server (NTRS)

Tzong, T.; Chen, H. H.; Chang, K. C.; Wu, T.; Cebeci, T.

1996-01-01

The aeroelastic analysis of an aircraft requires an accurate and efficient procedure to couple aerodynamics and structures. The procedure needs an interface method to bridge the gap between the aerodynamic and structural models in order to transform loads and displacements. Such an interface method is described in this report. This interface method transforms loads computed by any aerodynamic code to a structural finite element (FE) model and converts the displacements from the FE model to the aerodynamic model. The approach is based on FE technology in which virtual work is employed to transform the aerodynamic pressures into FE nodal forces. The displacements at the FE nodes are then converted back to aerodynamic grid points on the aircraft surface through the reciprocal theorem in structural engineering. The method allows both high and crude fidelities of both models and does not require an intermediate modeling. In addition, the method performs the conversion of loads and displacements directly between individual aerodynamic grid point and its corresponding structural finite element and, hence, is very efficient for large aircraft models. This report also describes the application of this aero-structure interface method to a simple wing and an MD-90 wing. The results show that the aeroelastic effect is very important. For the simple wing, both linear and nonlinear approaches are used. In the linear approach, the deformation of the structural model is considered small, and the loads from the deformed aerodynamic model are applied to the original geometry of the structure. In the nonlinear approach, the geometry of the structure and its stiffness matrix are updated in every iteration and the increments of loads from the previous iteration are applied to the new structural geometry in order to compute the displacement increments. Additional studies to apply the aero-structure interaction procedure to more complicated geometry will be conducted in the second phase of the present contract.

Using generalized additive modeling to empirically identify thresholds within the ITERS in relation to toddlers' cognitive development.

PubMed

Setodji, Claude Messan; Le, Vi-Nhuan; Schaack, Diana

2013-04-01

Research linking high-quality child care programs and children's cognitive development has contributed to the growing popularity of child care quality benchmarking efforts such as quality rating and improvement systems (QRIS). Consequently, there has been an increased interest in and a need for approaches to identifying thresholds, or cutpoints, in the child care quality measures used in these benchmarking efforts that differentiate between different levels of children's cognitive functioning. To date, research has provided little guidance to policymakers as to where these thresholds should be set. Using the Early Childhood Longitudinal Study, Birth Cohort (ECLS-B) data set, this study explores the use of generalized additive modeling (GAM) as a method of identifying thresholds on the Infant/Toddler Environment Rating Scale (ITERS) in relation to toddlers' performance on the Mental Development subscale of the Bayley Scales of Infant Development (the Bayley Mental Development Scale Short Form-Research Edition, or BMDSF-R). The present findings suggest that simple linear models do not always correctly depict the relationships between ITERS scores and BMDSF-R scores and that GAM-derived thresholds were more effective at differentiating among children's performance levels on the BMDSF-R. Additionally, the present findings suggest that there is a minimum threshold on the ITERS that must be exceeded before significant improvements in children's cognitive development can be expected. There may also be a ceiling threshold on the ITERS, such that beyond a certain level, only marginal increases in children's BMDSF-R scores are observed. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

Error Field Assessment from Driven Mode Rotation: Results from Extrap-T2R Reversed-Field-Pinch and Perspectives for ITER

NASA Astrophysics Data System (ADS)

Volpe, F. A.; Frassinetti, L.; Brunsell, P. R.; Drake, J. R.; Olofsson, K. E. J.

2012-10-01

A new ITER-relevant non-disruptive error field (EF) assessment technique not restricted to low density and thus low beta was demonstrated at the Extrap-T2R reversed field pinch. Resistive Wall Modes (RWMs) were generated and their rotation sustained by rotating magnetic perturbations. In particular, stable modes of toroidal mode number n=8 and 10 and unstable modes of n=1 were used in this experiment. Due to finite EFs, and in spite of the applied perturbations rotating uniformly and having constant amplitude, the RWMs were observed to rotate non-uniformly and be modulated in amplitude (in the case of unstable modes, the observed oscillation was superimposed to the mode growth). This behavior was used to infer the amplitude and toroidal phase of n=1, 8 and 10 EFs. The method was first tested against known, deliberately applied EFs, and then against actual intrinsic EFs. Applying equal and opposite corrections resulted in longer discharges and more uniform mode rotation, indicating good EF compensation. The results agree with a simple theoretical model. Extensions to tearing modes, to the non-uniform plasma response to rotating perturbations, and to tokamaks, including ITER, will be discussed.

An Iterative Local Updating Ensemble Smoother for Estimation and Uncertainty Assessment of Hydrologic Model Parameters With Multimodal Distributions

NASA Astrophysics Data System (ADS)

Zhang, Jiangjiang; Lin, Guang; Li, Weixuan; Wu, Laosheng; Zeng, Lingzao

2018-03-01

Ensemble smoother (ES) has been widely used in inverse modeling of hydrologic systems. However, for problems where the distribution of model parameters is multimodal, using ES directly would be problematic. One popular solution is to use a clustering algorithm to identify each mode and update the clusters with ES separately. However, this strategy may not be very efficient when the dimension of parameter space is high or the number of modes is large. Alternatively, we propose in this paper a very simple and efficient algorithm, i.e., the iterative local updating ensemble smoother (ILUES), to explore multimodal distributions of model parameters in nonlinear hydrologic systems. The ILUES algorithm works by updating local ensembles of each sample with ES to explore possible multimodal distributions. To achieve satisfactory data matches in nonlinear problems, we adopt an iterative form of ES to assimilate the measurements multiple times. Numerical cases involving nonlinearity and multimodality are tested to illustrate the performance of the proposed method. It is shown that overall the ILUES algorithm can well quantify the parametric uncertainties of complex hydrologic models, no matter whether the multimodal distribution exists.

3-D imaging of large scale buried structure by 1-D inversion of very early time electromagnetic (VETEM) data

USGS Publications Warehouse

Aydmer, A.A.; Chew, W.C.; Cui, T.J.; Wright, D.L.; Smith, D.V.; Abraham, J.D.

2001-01-01

A simple and efficient method for large scale three-dimensional (3-D) subsurface imaging of inhomogeneous background is presented. One-dimensional (1-D) multifrequency distorted Born iterative method (DBIM) is employed in the inversion. Simulation results utilizing synthetic scattering data are given. Calibration of the very early time electromagnetic (VETEM) experimental waveforms is detailed along with major problems encountered in practice and their solutions. This discussion is followed by the results of a large scale application of the method to the experimental data provided by the VETEM system of the U.S. Geological Survey. The method is shown to have a computational complexity that is promising for on-site inversion.

NOTE: Wobbled splatting—a fast perspective volume rendering method for simulation of x-ray images from CT

NASA Astrophysics Data System (ADS)

Birkfellner, Wolfgang; Seemann, Rudolf; Figl, Michael; Hummel, Johann; Ede, Christopher; Homolka, Peter; Yang, Xinhui; Niederer, Peter; Bergmann, Helmar

2005-05-01

3D/2D registration, the automatic assignment of a global rigid-body transformation matching the coordinate systems of patient and preoperative volume scan using projection images, is an important topic in image-guided therapy and radiation oncology. A crucial part of most 3D/2D registration algorithms is the fast computation of digitally rendered radiographs (DRRs) to be compared iteratively to radiographs or portal images. Since registration is an iterative process, fast generation of DRRs—which are perspective summed voxel renderings—is desired. In this note, we present a simple and rapid method for generation of DRRs based on splat rendering. As opposed to conventional splatting, antialiasing of the resulting images is not achieved by means of computing a discrete point spread function (a so-called footprint), but by stochastic distortion of either the voxel positions in the volume scan or by the simulation of a focal spot of the x-ray tube with non-zero diameter. Our method generates slightly blurred DRRs suitable for registration purposes at framerates of approximately 10 Hz when rendering volume images with a size of 30 MB.

On the joint inversion of geophysical data for models of the coupled core-mantle system

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1991-01-01

Joint inversion of magnetic, earth rotation, geoid, and seismic data for a unified model of the coupled core-mantle system is proposed and shown to be possible. A sample objective function is offered and simplified by targeting results from independent inversions and summary travel time residuals instead of original observations. These data are parameterized in terms of a very simple, closed model of the topographically coupled core-mantle system. Minimization of the simplified objective function leads to a nonlinear inverse problem; an iterative method for solution is presented. Parameterization and method are emphasized; numerical results are not presented.

Query-seeded iterative sequence similarity searching improves selectivity 5–20-fold

PubMed Central

Li, Weizhong; Lopez, Rodrigo

2017-01-01

Abstract Iterative similarity search programs, like psiblast, jackhmmer, and psisearch, are much more sensitive than pairwise similarity search methods like blast and ssearch because they build a position specific scoring model (a PSSM or HMM) that captures the pattern of sequence conservation characteristic to a protein family. But models are subject to contamination; once an unrelated sequence has been added to the model, homologs of the unrelated sequence will also produce high scores, and the model can diverge from the original protein family. Examination of alignment errors during psiblast PSSM contamination suggested a simple strategy for dramatically reducing PSSM contamination. psiblast PSSMs are built from the query-based multiple sequence alignment (MSA) implied by the pairwise alignments between the query model (PSSM, HMM) and the subject sequences in the library. When the original query sequence residues are inserted into gapped positions in the aligned subject sequence, the resulting PSSM rarely produces alignment over-extensions or alignments to unrelated sequences. This simple step, which tends to anchor the PSSM to the original query sequence and slightly increase target percent identity, can reduce the frequency of false-positive alignments more than 20-fold compared with psiblast and jackhmmer, with little loss in search sensitivity. PMID:27923999

A simple predistortion technique for suppression of nonlinear effects in periodic signals generated by nonlinear transducers

NASA Astrophysics Data System (ADS)

Novak, A.; Simon, L.; Lotton, P.

2018-04-01

Mechanical transducers, such as shakers, loudspeakers and compression drivers that are used as excitation devices to excite acoustical or mechanical nonlinear systems under test are imperfect. Due to their nonlinear behaviour, unwanted contributions appear at their output besides the wanted part of the signal. Since these devices are used to study nonlinear systems, it should be required to measure properly the systems under test by overcoming the influence of the nonlinear excitation device. In this paper, a simple method that corrects distorted output signal of the excitation device by means of predistortion of its input signal is presented. A periodic signal is applied to the input of the excitation device and, from analysing the output signal of the device, the input signal is modified in such a way that the undesirable spectral components in the output of the excitation device are cancelled out after few iterations of real-time processing. The experimental results provided on an electrodynamic shaker show that the spectral purity of the generated acceleration output approaches 100 dB after few iterations (1 s). This output signal, applied to the system under test, is thus cleaned from the undesirable components produced by the excitation device; this is an important condition to ensure a correct measurement of the nonlinear system under test.

Eight channel transmit array volume coil using on-coil radiofrequency current sources

PubMed Central

Kurpad, Krishna N.; Boskamp, Eddy B.

2014-01-01

Background At imaging frequencies associated with high-field MRI, the combined effects of increased load-coil interaction and shortened wavelength results in degradation of circular polarization and B1 field homogeneity in the imaging volume. Radio frequency (RF) shimming is known to mitigate the problem of B1 field inhomogeneity. Transmit arrays with well decoupled transmitting elements enable accurate B1 field pattern control using simple, non-iterative algorithms. Methods An eight channel transmit array was constructed. Each channel consisted of a transmitting element driven by a dedicated on-coil RF current source. The coil current distributions of characteristic transverse electromagnetic (TEM) coil resonant modes were non-iteratively set up on each transmitting element and 3T MRI images of a mineral oil phantom were obtained. Results B1 field patterns of several linear and quadrature TEM coil resonant modes that typically occur at different resonant frequencies were replicated at 128 MHz without having to retune the transmit array. The generated B1 field patterns agreed well with simulation in most cases. Conclusions Independent control of current amplitude and phase on each transmitting element was demonstrated. The transmit array with on-coil RF current sources enables B1 field shimming in a simple and predictable manner. PMID:24834418

Real-time restoration of white-light confocal microscope optical sections

PubMed Central

Balasubramanian, Madhusudhanan; Iyengar, S. Sitharama; Beuerman, Roger W.; Reynaud, Juan; Wolenski, Peter

2009-01-01

Confocal microscopes (CM) are routinely used for building 3-D images of microscopic structures. Nonideal imaging conditions in a white-light CM introduce additive noise and blur. The optical section images need to be restored prior to quantitative analysis. We present an adaptive noise filtering technique using Karhunen–Loéve expansion (KLE) by the method of snapshots and a ringing metric to quantify the ringing artifacts introduced in the images restored at various iterations of iterative Lucy–Richardson deconvolution algorithm. The KLE provides a set of basis functions that comprise the optimal linear basis for an ensemble of empirical observations. We show that most of the noise in the scene can be removed by reconstructing the images using the KLE basis vector with the largest eigenvalue. The prefiltering scheme presented is faster and does not require prior knowledge about image noise. Optical sections processed using the KLE prefilter can be restored using a simple inverse restoration algorithm; thus, the methodology is suitable for real-time image restoration applications. The KLE image prefilter outperforms the temporal-average prefilter in restoring CM optical sections. The ringing metric developed uses simple binary morphological operations to quantify the ringing artifacts and confirms with the visual observation of ringing artifacts in the restored images. PMID:20186290

Kirchhoff and Ohm in action: solving electric currents in continuous extended media

NASA Astrophysics Data System (ADS)

Dolinko, A. E.

2018-03-01

In this paper we show a simple and versatile computational simulation method for determining electric currents and electric potential in 2D and 3D media with arbitrary distribution of resistivity. One of the highlights of the proposed method is that the simulation space containing the distribution of resistivity and the points of external applied voltage are introduced by means of digital images or bitmaps, which easily allows simulating any phenomena involving distributions of resistivity. The simulation is based on the Kirchhoff’s laws of electric currents and it is solved by means of an iterative procedure. The method is also generalised to account for media with distributions of reactive impedance. At the end of this work, we show an example of application of the simulation, consisting in reproducing the response obtained with the geophysical method of electric resistivity tomography in presence of soil cracks. This paper is aimed at undergraduate or graduated students interested in computational physics and electricity and also researchers involved in the area of continuous electric media, which could find a simple and powerful tool for investigation.

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

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.

Comparison of different filter methods for data assimilation in the unsaturated zone

NASA Astrophysics Data System (ADS)

Lange, Natascha; Berkhahn, Simon; Erdal, Daniel; Neuweiler, Insa

2016-04-01

The unsaturated zone is an important compartment, which plays a role for the division of terrestrial water fluxes into surface runoff, groundwater recharge and evapotranspiration. For data assimilation in coupled systems it is therefore important to have a good representation of the unsaturated zone in the model. Flow processes in the unsaturated zone have all the typical features of flow in porous media: Processes can have long memory and as observations are scarce, hydraulic model parameters cannot be determined easily. However, they are important for the quality of model predictions. On top of that, the established flow models are highly non-linear. For these reasons, the use of the popular Ensemble Kalman filter as a data assimilation method to estimate state and parameters in unsaturated zone models could be questioned. With respect to the long process memory in the subsurface, it has been suggested that iterative filters and smoothers may be more suitable for parameter estimation in unsaturated media. We test the performance of different iterative filters and smoothers for data assimilation with a focus on parameter updates in the unsaturated zone. In particular we compare the Iterative Ensemble Kalman Filter and Smoother as introduced by Bocquet and Sakov (2013) as well as the Confirming Ensemble Kalman Filter and the modified Restart Ensemble Kalman Filter proposed by Song et al. (2014) to the original Ensemble Kalman Filter (Evensen, 2009). This is done with simple test cases generated numerically. We consider also test examples with layering structure, as a layering structure is often found in natural soils. We assume that observations are water content, obtained from TDR probes or other observation methods sampling relatively small volumes. Particularly in larger data assimilation frameworks, a reasonable balance between computational effort and quality of results has to be found. Therefore, we compare computational costs of the different methods as well as the quality of open loop model predictions and the estimated parameters. Bocquet, M. and P. Sakov, 2013: Joint state and parameter estimation with an iterative ensemble Kalman smoother, Nonlinear Processes in Geophysics 20(5): 803-818. Evensen, G., 2009: Data assimilation: The ensemble Kalman filter. Springer Science & Business Media. Song, X.H., L.S. Shi, M. Ye, J.Z. Yang and I.M. Navon, 2014: Numerical comparison of iterative ensemble Kalman filters for unsaturated flow inverse modeling. Vadose Zone Journal 13(2), 10.2136/vzj2013.05.0083.

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.

Extremely simple holographic projection of color images

NASA Astrophysics Data System (ADS)

Makowski, Michal; Ducin, Izabela; Kakarenko, Karol; Suszek, Jaroslaw; Kolodziejczyk, Andrzej; Sypek, Maciej

2012-03-01

A very simple scheme of holographic projection is presented with some experimental results showing good quality image projection without any imaging lens. This technique can be regarded as an alternative to classic projection methods. It is based on the reconstruction real images from three phase iterated Fourier holograms. The illumination is performed with three laser beams of primary colors. A divergent wavefront geometry is used to achieve an increased throw angle of the projection, compared to plane wave illumination. Light fibers are used as light guidance in order to keep the setup as simple as possible and to provide point-like sources of high quality divergent wave-fronts at optimized position against the light modulator. Absorbing spectral filters are implemented to multiplex three holograms on a single phase-only spatial light modulator. Hence color mixing occurs without any time-division methods, which cause rainbow effects and color flicker. The zero diffractive order with divergent illumination is practically invisible and speckle field is effectively suppressed with phase optimization and time averaging techniques. The main advantages of the proposed concept are: a very simple and highly miniaturizable configuration; lack of lens; a single LCoS (Liquid Crystal on Silicon) modulator; a strong resistance to imperfections and obstructions of the spatial light modulator like dead pixels, dust, mud, fingerprints etc.; simple calculations based on Fast Fourier Transform (FFT) easily processed in real time mode with GPU (Graphic Programming).

A Symmetric Positive Definite Formulation for Monolithic Fluid Structure Interaction

DTIC Science & Technology

2010-08-09

more likely to converge than simply iterating the partitioned approach to convergence in a simple Gauss - Seidel manner. Our approach allows the use of...conditions in a second step. These approaches can also be iterated within a given time step for increased stability, noting that in the limit if one... converges one obtains a monolithic (albeit expensive) approach. Other approaches construct strongly coupled systems and then solve them in one of several

Modelling the Probability of Landslides Impacting Road Networks

NASA Astrophysics Data System (ADS)

Taylor, F. E.; Malamud, B. D.

2012-04-01

During a landslide triggering event, the threat of landslides blocking roads poses a risk to logistics, rescue efforts and communities dependant on those road networks. Here we present preliminary results of a stochastic model we have developed to evaluate the probability of landslides intersecting a simple road network during a landslide triggering event and apply simple network indices to measure the state of the road network in the affected region. A 4000 x 4000 cell array with a 5 m x 5 m resolution was used, with a pre-defined simple road network laid onto it, and landslides 'randomly' dropped onto it. Landslide areas (AL) were randomly selected from a three-parameter inverse gamma probability density function, consisting of a power-law decay of about -2.4 for medium and large values of AL and an exponential rollover for small values of AL; the rollover (maximum probability) occurs at about AL = 400 m2 This statistical distribution was chosen based on three substantially complete triggered landslide inventories recorded in existing literature. The number of landslide areas (NL) selected for each triggered event iteration was chosen to have an average density of 1 landslide km-2, i.e. NL = 400 landslide areas chosen randomly for each iteration, and was based on several existing triggered landslide event inventories. A simple road network was chosen, in a 'T' shape configuration, with one road 1 x 4000 cells (5 m x 20 km) in a 'T' formation with another road 1 x 2000 cells (5 m x 10 km). The landslide areas were then randomly 'dropped' over the road array and indices such as the location, size (ABL) and number of road blockages (NBL) recorded. This process was performed 500 times (iterations) in a Monte-Carlo type simulation. Initial results show that for a landslide triggering event with 400 landslides over a 400 km2 region, the number of road blocks per iteration, NBL,ranges from 0 to 7. The average blockage area for the 500 iterations (A¯ BL) is about 3000 m2, which closely matches the value of A¯ L for the triggered landslide inventories. We further find that over the 500 iterations, the probability of a given number of road blocks occurring on any given iteration, p(NBL) as a function of NBL, follows reasonably well a three-parameter inverse gamma probability density distribution with an exponential rollover (i.e., the most frequent value) at NBL = 1.3. In this paper we have begun to calculate the probability of the number of landslides blocking roads during a triggering event, and have found that this follows an inverse-gamma distribution, which is similar to that found for the statistics of landslide areas resulting from triggers. As we progress to model more realistic road networks, this work will aid in both long-term and disaster management for road networks by allowing probabilistic assessment of road network potential damage during different magnitude landslide triggering event scenarios.

Transportable Maps Software. Volume I.

DTIC Science & Technology

1982-07-01

being collected at the beginning or end of the routine. This allows the interaction to be followed sequentially through its steps by anyone reading the...flow is either simple sequential , simple conditional (the equivalent of ’if-then-else’), simple iteration (’DO-loop’), or the non-linear recursion...input raster images to be in the form of sequential binary files with a SEGMENTED record type. The advantage of this form is that large logical records

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.

Developing a multipoint titration method with a variable dose implementation for anaerobic digestion monitoring.

PubMed

Salonen, K; Leisola, M; Eerikäinen, T

2009-01-01

Determination of metabolites from an anaerobic digester with an acid base titration is considered as superior method for many reasons. This paper describes a practical at line compatible multipoint titration method. The titration procedure was improved by speed and data quality. A simple and novel control algorithm for estimating a variable titrant dose was derived for this purpose. This non-linear PI-controller like algorithm does not require any preliminary information from sample. Performance of this controller is superior compared to traditional linear PI-controllers. In addition, simplification for presenting polyprotic acids as a sum of multiple monoprotic acids is introduced along with a mathematical error examination. A method for inclusion of the ionic strength effect with stepwise iteration is shown. The titration model is presented with matrix notations enabling simple computation of all concentration estimates. All methods and algorithms are illustrated in the experimental part. A linear correlation better than 0.999 was obtained for both acetate and phosphate used as model compounds with slopes of 0.98 and 1.00 and average standard deviations of 0.6% and 0.8%, respectively. Furthermore, insensitivity of the presented method for overlapping buffer capacity curves was shown.

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.

SLIC superpixels compared to state-of-the-art superpixel methods.

PubMed

Achanta, Radhakrishna; Shaji, Appu; Smith, Kevin; Lucchi, Aurelien; Fua, Pascal; Süsstrunk, Sabine

2012-11-01

Computer vision applications have come to rely increasingly on superpixels in recent years, but it is not always clear what constitutes a good superpixel algorithm. In an effort to understand the benefits and drawbacks of existing methods, we empirically compare five state-of-the-art superpixel algorithms for their ability to adhere to image boundaries, speed, memory efficiency, and their impact on segmentation performance. We then introduce a new superpixel algorithm, simple linear iterative clustering (SLIC), which adapts a k-means clustering approach to efficiently generate superpixels. Despite its simplicity, SLIC adheres to boundaries as well as or better than previous methods. At the same time, it is faster and more memory efficient, improves segmentation performance, and is straightforward to extend to supervoxel generation.

Inspiring Examples in Rearrangements of Infinite Products

ERIC Educational Resources Information Center

Ramasinghe, W.

2007-01-01

It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same.…

Design Features of a Friendly Software Environment for Novice Programmers. Technical Report No. 3.

ERIC Educational Resources Information Center

Eisenstadt, Marc

This paper describes the results of a 6-year period of design, implementation, testing, and iterative redesign of a programming language, user aids, and curriculum materials for use by psychology students learning how to write simple computer programs. The SOLO language, which was the resulting product, is primarily a simple, database…

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.

ITER-like antenna capacitors voltage probes: Circuit/electromagnetic calculations and calibrations.

PubMed

Helou, W; Dumortier, P; Durodié, F; Lombard, G; Nicholls, K

2016-10-01

The analyses illustrated in this manuscript have been performed in order to provide the required data for the amplitude-and-phase calibration of the D-dot voltage probes used in the ITER-like antenna at the Joint European Torus tokamak. Their equivalent electrical circuit has been extracted and analyzed, and it has been compared to the one of voltage probes installed in simple transmission lines. A radio-frequency calibration technique has been formulated and exact mathematical relations have been derived. This technique mixes in an elegant fashion data extracted from measurements and numerical calculations to retrieve the calibration factors. The latter have been compared to previous calibration data with excellent agreement proving the robustness of the proposed radio-frequency calibration technique. In particular, it has been stressed that it is crucial to take into account environmental parasitic effects. A low-frequency calibration technique has been in addition formulated and analyzed in depth. The equivalence between the radio-frequency and low-frequency techniques has been rigorously demonstrated. The radio-frequency calibration technique is preferable in the case of the ITER-like antenna due to uncertainties on the characteristics of the cables connected at the inputs of the voltage probes. A method to extract the effect of a mismatched data acquisition system has been derived for both calibration techniques. Finally it has been outlined that in the case of the ITER-like antenna voltage probes can be in addition used to monitor the currents at the inputs of the antenna.

Nonlinear Krylov and moving nodes in the method of lines

NASA Astrophysics Data System (ADS)

Miller, Keith

2005-11-01

We report on some successes and problem areas in the Method of Lines from our work with moving node finite element methods. First, we report on our "nonlinear Krylov accelerator" for the modified Newton's method on the nonlinear equations of our stiff ODE solver. Since 1990 it has been robust, simple, cheap, and automatic on all our moving node computations. We publicize further trials with it here because it should be of great general usefulness to all those solving evolutionary equations. Second, we discuss the need for reliable automatic choice of spatially variable time steps. Third, we discuss the need for robust and efficient iterative solvers for the difficult linearized equations (Jx=b) of our stiff ODE solver. Here, the 1997 thesis of Zulu Xaba has made significant progress.

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

A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems

NASA Astrophysics Data System (ADS)

Pan, Kejia; He, Dongdong; Hu, Hongling; Ren, Zhengyong

2017-09-01

In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H3-regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems.

A simple algorithm for sequentially incorporating gravity observations in seismic traveltime tomography

USGS Publications Warehouse

Parsons, T.; Blakely, R.J.; Brocher, T.M.

2001-01-01

The geologic structure of the Earth's upper crust can be revealed by modeling variation in seismic arrival times and in potential field measurements. We demonstrate a simple method for sequentially satisfying seismic traveltime and observed gravity residuals in an iterative 3-D inversion. The algorithm is portable to any seismic analysis method that uses a gridded representation of velocity structure. Our technique calculates the gravity anomaly resulting from a velocity model by converting to density with Gardner's rule. The residual between calculated and observed gravity is minimized by weighted adjustments to the model velocity-depth gradient where the gradient is steepest and where seismic coverage is least. The adjustments are scaled by the sign and magnitude of the gravity residuals, and a smoothing step is performed to minimize vertical streaking. The adjusted model is then used as a starting model in the next seismic traveltime iteration. The process is repeated until one velocity model can simultaneously satisfy both the gravity anomaly and seismic traveltime observations within acceptable misfits. We test our algorithm with data gathered in the Puget Lowland of Washington state, USA (Seismic Hazards Investigation in Puget Sound [SHIPS] experiment). We perform resolution tests with synthetic traveltime and gravity observations calculated with a checkerboard velocity model using the SHIPS experiment geometry, and show that the addition of gravity significantly enhances resolution. We calculate a new velocity model for the region using SHIPS traveltimes and observed gravity, and show examples where correlation between surface geology and modeled subsurface velocity structure is enhanced.

Iterative Procedures for Exact Maximum Likelihood Estimation in the First-Order Gaussian Moving Average Model

DTIC Science & Technology

1990-11-01

1 = Q- 1 - 1 QlaaQ- 1.1 + a’Q-1a This is a simple case of a general formula called Woodbury’s formula by some authors; see, for example, Phadke and...1 2. The First-Order Moving Average Model ..... .................. 3. Some Approaches to the Iterative...the approximate likelihood function in some time series models. Useful suggestions have been the Cholesky decomposition of the covariance matrix and

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.

Runtime support and compilation methods for user-specified data distributions

NASA Technical Reports Server (NTRS)

Ponnusamy, Ravi; Saltz, Joel; Choudhury, Alok; Hwang, Yuan-Shin; Fox, Geoffrey

1993-01-01

This paper describes two new ideas by which an HPF compiler can deal with irregular computations effectively. The first mechanism invokes a user specified mapping procedure via a set of compiler directives. The directives allow use of program arrays to describe graph connectivity, spatial location of array elements, and computational load. The second mechanism is a simple conservative method that in many cases enables a compiler to recognize that it is possible to reuse previously computed information from inspectors (e.g. communication schedules, loop iteration partitions, information that associates off-processor data copies with on-processor buffer locations). We present performance results for these mechanisms from a Fortran 90D compiler implementation.

How good are the Garvey-Kelson predictions of nuclear masses?

NASA Astrophysics Data System (ADS)

Morales, Irving O.; López Vieyra, J. C.; Hirsch, J. G.; Frank, A.

2009-09-01

The Garvey-Kelson relations are used in an iterative process to predict nuclear masses in the neighborhood of nuclei with measured masses. Average errors in the predicted masses for the first three iteration shells are smaller than those obtained with the best nuclear mass models. Their quality is comparable with the Audi-Wapstra extrapolations, offering a simple and reproducible procedure for short range mass predictions. A systematic study of the way the error grows as a function of the iteration and the distance to the known masses region, shows that a correlation exists between the error and the residual neutron-proton interaction, produced mainly by the implicit assumption that V varies smoothly along the nuclear landscape.

Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory.

PubMed

Bardhan, Jaydeep P

2008-10-14

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

An iterative shrinkage approach to total-variation image restoration.

PubMed

Michailovich, Oleg V

2011-05-01

The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the degradation phenomenon is modeled by an ill-conditioned operator. In such a situation, the presence of noise makes it impossible to recover a valuable approximation of the image of interest without using some a priori information about its properties. Such a priori information--commonly referred to as simply priors--is essential for image restoration, rendering it stable and robust to noise. Moreover, using the priors makes the recovered images exhibit some plausible features of their original counterpart. Particularly, if the original image is known to be a piecewise smooth function, one of the standard priors used in this case is defined by the Rudin-Osher-Fatemi model, which results in total variation (TV) based image restoration. The current arsenal of algorithms for TV-based image restoration is vast. In this present paper, a different approach to the solution of the problem is proposed based upon the method of iterative shrinkage (aka iterated thresholding). In the proposed method, the TV-based image restoration is performed through a recursive application of two simple procedures, viz. linear filtering and soft thresholding. Therefore, the method can be identified as belonging to the group of first-order algorithms which are efficient in dealing with images of relatively large sizes. Another valuable feature of the proposed method consists in its working directly with the TV functional, rather then with its smoothed versions. Moreover, the method provides a single solution for both isotropic and anisotropic definitions of the TV functional, thereby establishing a useful connection between the two formulae. Finally, a number of standard examples of image deblurring are demonstrated, in which the proposed method can provide restoration results of superior quality as compared to the case of sparse-wavelet deconvolution.

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.

Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.

An efficient higher order family of root finders

NASA Astrophysics Data System (ADS)

Petkovic, Ljiljana D.; Rancic, Lidija; Petkovic, Miodrag S.

2008-06-01

A one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial, based on a cubically convergent Hansen-Patrick's family, is studied. We show that the convergence of the basic family of the fourth order can be increased to five and six using Newton's and Halley's corrections, respectively. Since these corrections use the already calculated values, the computational efficiency of the accelerated methods is significantly increased. Further acceleration is achieved by applying the Gauss-Seidel approach (single-step mode). One of the most important problems in solving nonlinear equations, the construction of initial conditions which provide both the guaranteed and fast convergence, is considered for the proposed accelerated family. These conditions are computationally verifiable; they depend only on the polynomial coefficients, its degree and initial approximations, which is of practical importance. Some modifications of the considered family, providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions, are also studied. Numerical examples demonstrate the convergence properties of the presented family of root-finding methods.

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/.

Iterative quantization: a Procrustean approach to learning binary codes for large-scale image retrieval.

PubMed

Gong, Yunchao; Lazebnik, Svetlana; Gordo, Albert; Perronnin, Florent

2013-12-01

This paper addresses the problem of learning similarity-preserving binary codes for efficient similarity search in large-scale image collections. We formulate this problem in terms of finding a rotation of zero-centered data so as to minimize the quantization error of mapping this data to the vertices of a zero-centered binary hypercube, and propose a simple and efficient alternating minimization algorithm to accomplish this task. This algorithm, dubbed iterative quantization (ITQ), has connections to multiclass spectral clustering and to the orthogonal Procrustes problem, and it can be used both with unsupervised data embeddings such as PCA and supervised embeddings such as canonical correlation analysis (CCA). The resulting binary codes significantly outperform several other state-of-the-art methods. We also show that further performance improvements can result from transforming the data with a nonlinear kernel mapping prior to PCA or CCA. Finally, we demonstrate an application of ITQ to learning binary attributes or "classemes" on the ImageNet data set.

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; An Iterative Decoding Algorithm for Linear Block Codes Based on a Low-Weight Trellis Search

NASA Technical Reports Server (NTRS)

Lin, Shu; Fossorier, Marc

1998-01-01

For long linear block codes, maximum likelihood decoding based on full code trellises would be very hard to implement if not impossible. In this case, we may wish to trade error performance for the reduction in decoding complexity. Sub-optimum soft-decision decoding of a linear block code based on a low-weight sub-trellis can be devised to provide an effective trade-off between error performance and decoding complexity. This chapter presents such a suboptimal decoding algorithm for linear block codes. This decoding algorithm is iterative in nature and based on an optimality test. It has the following important features: (1) a simple method to generate a sequence of candidate code-words, one at a time, for test; (2) a sufficient condition for testing a candidate code-word for optimality; and (3) a low-weight sub-trellis search for finding the most likely (ML) code-word.

Simple method to set up low eccentricity initial data for moving puncture simulations

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

Tichy, Wolfgang; Marronetti, Pedro

2011-01-15

We introduce two new eccentricity measures to analyze numerical simulations. Unlike earlier definitions these eccentricity measures do not involve any free parameters which makes them easy to use. We show how relatively inexpensive grid setups can be used to estimate the eccentricity during the early inspiral phase. Furthermore, we compare standard puncture data and post-Newtonian data in ADMTT gauge. We find that both use different coordinates. Thus low eccentricity initial momentum parameters for a certain separation measured in ADMTT coordinates are hard to use in puncture data, because it is not known how the separation in puncture coordinates is relatedmore » to the separation in ADMTT coordinates. As a remedy we provide a simple approach which allows us to iterate the momentum parameters until our numerical simulations result in acceptably low eccentricities.« less

If SWORD Is the Answer, What Is the Question?: Use of the Simple Web-Service Offering Repository Deposit Protocol

ERIC Educational Resources Information Center

Lewis, Stuart; Hayes, Leonie; Newton-Wade, Vanessa; Corfield, Antony; Davis, Richard; Donohue, Tim; Wilson, Scott

2009-01-01

Purpose: The purpose of this paper is to describe the repository deposit protocol, Simple Web-service Offering Repository Deposit (SWORD), its development iteration, and some of its potential use cases. In addition, seven case studies of institutional use of SWORD are provided. Design/methodology/approach: The paper describes the recent…

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.

Stochastic optimal operation of reservoirs based on copula functions

NASA Astrophysics Data System (ADS)

Lei, Xiao-hui; Tan, Qiao-feng; Wang, Xu; Wang, Hao; Wen, Xin; Wang, Chao; Zhang, Jing-wen

2018-02-01

Stochastic dynamic programming (SDP) has been widely used to derive operating policies for reservoirs considering streamflow uncertainties. In SDP, there is a need to calculate the transition probability matrix more accurately and efficiently in order to improve the economic benefit of reservoir operation. In this study, we proposed a stochastic optimization model for hydropower generation reservoirs, in which 1) the transition probability matrix was calculated based on copula functions; and 2) the value function of the last period was calculated by stepwise iteration. Firstly, the marginal distribution of stochastic inflow in each period was built and the joint distributions of adjacent periods were obtained using the three members of the Archimedean copulas, based on which the conditional probability formula was derived. Then, the value in the last period was calculated by a simple recursive equation with the proposed stepwise iteration method and the value function was fitted with a linear regression model. These improvements were incorporated into the classic SDP and applied to the case study in Ertan reservoir, China. The results show that the transition probability matrix can be more easily and accurately obtained by the proposed copula function based method than conventional methods based on the observed or synthetic streamflow series, and the reservoir operation benefit can also be increased.

MAP: an iterative experimental design methodology for the optimization of catalytic search space structure modeling.

PubMed

Baumes, Laurent A

2006-01-01

One of the main problems in high-throughput research for materials is still the design of experiments. At early stages of discovery programs, purely exploratory methodologies coupled with fast screening tools should be employed. This should lead to opportunities to find unexpected catalytic results and identify the "groups" of catalyst outputs, providing well-defined boundaries for future optimizations. However, very few new papers deal with strategies that guide exploratory studies. Mostly, traditional designs, homogeneous covering, or simple random samplings are exploited. Typical catalytic output distributions exhibit unbalanced datasets for which an efficient learning is hardly carried out, and interesting but rare classes are usually unrecognized. Here is suggested a new iterative algorithm for the characterization of the search space structure, working independently of learning processes. It enhances recognition rates by transferring catalysts to be screened from "performance-stable" space zones to "unsteady" ones which necessitate more experiments to be well-modeled. The evaluation of new algorithm attempts through benchmarks is compulsory due to the lack of past proofs about their efficiency. The method is detailed and thoroughly tested with mathematical functions exhibiting different levels of complexity. The strategy is not only empirically evaluated, the effect or efficiency of sampling on future Machine Learning performances is also quantified. The minimum sample size required by the algorithm for being statistically discriminated from simple random sampling is investigated.

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.

Image segmentation-based robust feature extraction for color image watermarking

NASA Astrophysics Data System (ADS)

Li, Mianjie; Deng, Zeyu; Yuan, Xiaochen

2018-04-01

This paper proposes a local digital image watermarking method based on Robust Feature Extraction. The segmentation is achieved by Simple Linear Iterative Clustering (SLIC) based on which an Image Segmentation-based Robust Feature Extraction (ISRFE) method is proposed for feature extraction. Our method can adaptively extract feature regions from the blocks segmented by SLIC. This novel method can extract the most robust feature region in every segmented image. Each feature region is decomposed into low-frequency domain and high-frequency domain by Discrete Cosine Transform (DCT). Watermark images are then embedded into the coefficients in the low-frequency domain. The Distortion-Compensated Dither Modulation (DC-DM) algorithm is chosen as the quantization method for embedding. The experimental results indicate that the method has good performance under various attacks. Furthermore, the proposed method can obtain a trade-off between high robustness and good image quality.

Improved pressure-velocity coupling algorithm based on minimization of global residual norm

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

Chatwani, A.U.; Turan, A.

1991-01-01

In this paper an improved pressure velocity coupling algorithm is proposed based on the minimization of the global residual norm. The procedure is applied to SIMPLE and SIMPLEC algorithms to automatically select the pressure underrelaxation factor to minimize the global residual norm at each iteration level. Test computations for three-dimensional turbulent, isothermal flow is a toroidal vortex combustor indicate that velocity underrelaxation factors as high as 0.7 can be used to obtain a converged solution in 300 iterations.

Simultaneous deblurring and iterative reconstruction of CBCT for image guided brain radiosurgery.

PubMed

Hashemi, SayedMasoud; Song, William Y; Sahgal, Arjun; Lee, Young; Huynh, Christopher; Grouza, Vladimir; Nordström, Håkan; Eriksson, Markus; Dorenlot, Antoine; Régis, Jean Marie; Mainprize, James G; Ruschin, Mark

2017-04-07

One of the limiting factors in cone-beam CT (CBCT) image quality is system blur, caused by detector response, x-ray source focal spot size, azimuthal blurring, and reconstruction algorithm. In this work, we develop a novel iterative reconstruction algorithm that improves spatial resolution by explicitly accounting for image unsharpness caused by different factors in the reconstruction formulation. While the model-based iterative reconstruction techniques use prior information about the detector response and x-ray source, our proposed technique uses a simple measurable blurring model. In our reconstruction algorithm, denoted as simultaneous deblurring and iterative reconstruction (SDIR), the blur kernel can be estimated using the modulation transfer function (MTF) slice of the CatPhan phantom or any other MTF phantom, such as wire phantoms. The proposed image reconstruction formulation includes two regularization terms: (1) total variation (TV) and (2) nonlocal regularization, solved with a split Bregman augmented Lagrangian iterative method. The SDIR formulation preserves edges, eases the parameter adjustments to achieve both high spatial resolution and low noise variances, and reduces the staircase effect caused by regular TV-penalized iterative algorithms. The proposed algorithm is optimized for a point-of-care head CBCT unit for image-guided radiosurgery and is tested with CatPhan phantom, an anthropomorphic head phantom, and 6 clinical brain stereotactic radiosurgery cases. Our experiments indicate that SDIR outperforms the conventional filtered back projection and TV penalized simultaneous algebraic reconstruction technique methods (represented by adaptive steepest-descent POCS algorithm, ASD-POCS) in terms of MTF and line pair resolution, and retains the favorable properties of the standard TV-based iterative reconstruction algorithms in improving the contrast and reducing the reconstruction artifacts. It improves the visibility of the high contrast details in bony areas and the brain soft-tissue. For example, the results show the ventricles and some brain folds become visible in SDIR reconstructed images and the contrast of the visible lesions is effectively improved. The line-pair resolution was improved from 12 line-pair/cm in FBP to 14 line-pair/cm in SDIR. Adjusting the parameters of the ASD-POCS to achieve 14 line-pair/cm caused the noise variance to be higher than the SDIR. Using these parameters for ASD-POCS, the MTF of FBP and ASD-POCS were very close and equal to 0.7 mm -1 which was increased to 1.2 mm -1 by SDIR, at half maximum.

Simultaneous deblurring and iterative reconstruction of CBCT for image guided brain radiosurgery

NASA Astrophysics Data System (ADS)

Hashemi, SayedMasoud; Song, William Y.; Sahgal, Arjun; Lee, Young; Huynh, Christopher; Grouza, Vladimir; Nordström, Håkan; Eriksson, Markus; Dorenlot, Antoine; Régis, Jean Marie; Mainprize, James G.; Ruschin, Mark

2017-04-01

One of the limiting factors in cone-beam CT (CBCT) image quality is system blur, caused by detector response, x-ray source focal spot size, azimuthal blurring, and reconstruction algorithm. In this work, we develop a novel iterative reconstruction algorithm that improves spatial resolution by explicitly accounting for image unsharpness caused by different factors in the reconstruction formulation. While the model-based iterative reconstruction techniques use prior information about the detector response and x-ray source, our proposed technique uses a simple measurable blurring model. In our reconstruction algorithm, denoted as simultaneous deblurring and iterative reconstruction (SDIR), the blur kernel can be estimated using the modulation transfer function (MTF) slice of the CatPhan phantom or any other MTF phantom, such as wire phantoms. The proposed image reconstruction formulation includes two regularization terms: (1) total variation (TV) and (2) nonlocal regularization, solved with a split Bregman augmented Lagrangian iterative method. The SDIR formulation preserves edges, eases the parameter adjustments to achieve both high spatial resolution and low noise variances, and reduces the staircase effect caused by regular TV-penalized iterative algorithms. The proposed algorithm is optimized for a point-of-care head CBCT unit for image-guided radiosurgery and is tested with CatPhan phantom, an anthropomorphic head phantom, and 6 clinical brain stereotactic radiosurgery cases. Our experiments indicate that SDIR outperforms the conventional filtered back projection and TV penalized simultaneous algebraic reconstruction technique methods (represented by adaptive steepest-descent POCS algorithm, ASD-POCS) in terms of MTF and line pair resolution, and retains the favorable properties of the standard TV-based iterative reconstruction algorithms in improving the contrast and reducing the reconstruction artifacts. It improves the visibility of the high contrast details in bony areas and the brain soft-tissue. For example, the results show the ventricles and some brain folds become visible in SDIR reconstructed images and the contrast of the visible lesions is effectively improved. The line-pair resolution was improved from 12 line-pair/cm in FBP to 14 line-pair/cm in SDIR. Adjusting the parameters of the ASD-POCS to achieve 14 line-pair/cm caused the noise variance to be higher than the SDIR. Using these parameters for ASD-POCS, the MTF of FBP and ASD-POCS were very close and equal to 0.7 mm-1 which was increased to 1.2 mm-1 by SDIR, at half maximum.

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.

Computing the optimal path in stochastic dynamical systems

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

Bauver, Martha; Forgoston, Eric, E-mail: eric.forgoston@montclair.edu; Billings, Lora

2016-08-15

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensionalmore » system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.« less

Collisional-radiative switching - A powerful technique for converging non-LTE calculations

NASA Technical Reports Server (NTRS)

Hummer, D. G.; Voels, S. A.

1988-01-01

A very simple technique has been developed to converge statistical equilibrium and model atmospheric calculations in extreme non-LTE conditions when the usual iterative methods fail to converge from an LTE starting model. The proposed technique is based on a smooth transition from a collision-dominated LTE situation to the desired non-LTE conditions in which radiation dominates, at least in the most important transitions. The proposed approach was used to successfully compute stellar models with He abundances of 0.20, 0.30, and 0.50; Teff = 30,000 K, and log g = 2.9.

How children perceive fractals: Hierarchical self-similarity and cognitive development

PubMed Central

Martins, Maurício Dias; Laaha, Sabine; Freiberger, Eva Maria; Choi, Soonja; Fitch, W. Tecumseh

2014-01-01

The ability to understand and generate hierarchical structures is a crucial component of human cognition, available in language, music, mathematics and problem solving. Recursion is a particularly useful mechanism for generating complex hierarchies by means of self-embedding rules. In the visual domain, fractals are recursive structures in which simple transformation rules generate hierarchies of infinite depth. Research on how children acquire these rules can provide valuable insight into the cognitive requirements and learning constraints of recursion. Here, we used fractals to investigate the acquisition of recursion in the visual domain, and probed for correlations with grammar comprehension and general intelligence. We compared second (n = 26) and fourth graders (n = 26) in their ability to represent two types of rules for generating hierarchical structures: Recursive rules, on the one hand, which generate new hierarchical levels; and iterative rules, on the other hand, which merely insert items within hierarchies without generating new levels. We found that the majority of fourth graders, but not second graders, were able to represent both recursive and iterative rules. This difference was partially accounted by second graders’ impairment in detecting hierarchical mistakes, and correlated with between-grade differences in grammar comprehension tasks. Empirically, recursion and iteration also differed in at least one crucial aspect: While the ability to learn recursive rules seemed to depend on the previous acquisition of simple iterative representations, the opposite was not true, i.e., children were able to acquire iterative rules before they acquired recursive representations. These results suggest that the acquisition of recursion in vision follows learning constraints similar to the acquisition of recursion in language, and that both domains share cognitive resources involved in hierarchical processing. PMID:24955884

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

Anisotropic modeling and joint-MAP stitching for improved ultrasound model-based iterative reconstruction of large and thick specimens

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

Almansouri, Hani; Venkatakrishnan, Singanallur V.; Clayton, Dwight A.

One-sided non-destructive evaluation (NDE) is widely used to inspect materials, such as concrete structures in nuclear power plants (NPP). A widely used method for one-sided NDE is the synthetic aperture focusing technique (SAFT). The SAFT algorithm produces reasonable results when inspecting simple structures. However, for complex structures, such as heavily reinforced thick concrete structures, SAFT results in artifacts and hence there is a need for a more sophisticated inversion technique. Model-based iterative reconstruction (MBIR) algorithms, which are typically equivalent to regularized inversion techniques, offer a powerful framework to incorporate complex models for the physics, detector miscalibrations and the materials beingmore » imaged to obtain high quality reconstructions. Previously, we have proposed an ultrasonic MBIR method that signifcantly improves reconstruction quality compared to SAFT. However, the method made some simplifying assumptions on the propagation model and did not disucss ways to handle data that is obtained by raster scanning a system over a surface to inspect large regions. In this paper, we propose a novel MBIR algorithm that incorporates an anisotropic forward model and allows for the joint processing of data obtained from a system that raster scans a large surface. We demonstrate that the new MBIR method can produce dramatic improvements in reconstruction quality compared to SAFT and suppresses articfacts compared to the perviously presented MBIR approach.« less

Anisotropic modeling and joint-MAP stitching for improved ultrasound model-based iterative reconstruction of large and thick specimens

NASA Astrophysics Data System (ADS)

Almansouri, Hani; Venkatakrishnan, Singanallur; Clayton, Dwight; Polsky, Yarom; Bouman, Charles; Santos-Villalobos, Hector

2018-04-01

One-sided non-destructive evaluation (NDE) is widely used to inspect materials, such as concrete structures in nuclear power plants (NPP). A widely used method for one-sided NDE is the synthetic aperture focusing technique (SAFT). The SAFT algorithm produces reasonable results when inspecting simple structures. However, for complex structures, such as heavily reinforced thick concrete structures, SAFT results in artifacts and hence there is a need for a more sophisticated inversion technique. Model-based iterative reconstruction (MBIR) algorithms, which are typically equivalent to regularized inversion techniques, offer a powerful framework to incorporate complex models for the physics, detector miscalibrations and the materials being imaged to obtain high quality reconstructions. Previously, we have proposed an ultrasonic MBIR method that signifcantly improves reconstruction quality compared to SAFT. However, the method made some simplifying assumptions on the propagation model and did not disucss ways to handle data that is obtained by raster scanning a system over a surface to inspect large regions. In this paper, we propose a novel MBIR algorithm that incorporates an anisotropic forward model and allows for the joint processing of data obtained from a system that raster scans a large surface. We demonstrate that the new MBIR method can produce dramatic improvements in reconstruction quality compared to SAFT and suppresses articfacts compared to the perviously presented MBIR approach.

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

Wu, Baisheng; Liu, Weijia; Lim, C. W.

2017-07-01

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

A second order discontinuous Galerkin fast sweeping method for Eikonal equations

NASA Astrophysics Data System (ADS)

Li, Fengyan; Shu, Chi-Wang; Zhang, Yong-Tao; Zhao, Hongkai

2008-09-01

In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.

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.

Improving cerebellar segmentation with statistical fusion

NASA Astrophysics Data System (ADS)

Plassard, Andrew J.; Yang, Zhen; Prince, Jerry L.; Claassen, Daniel O.; Landman, Bennett A.

2016-03-01

The cerebellum is a somatotopically organized central component of the central nervous system well known to be involved with motor coordination and increasingly recognized roles in cognition and planning. Recent work in multiatlas labeling has created methods that offer the potential for fully automated 3-D parcellation of the cerebellar lobules and vermis (which are organizationally equivalent to cortical gray matter areas). This work explores the trade offs of using different statistical fusion techniques and post hoc optimizations in two datasets with distinct imaging protocols. We offer a novel fusion technique by extending the ideas of the Selective and Iterative Method for Performance Level Estimation (SIMPLE) to a patch-based performance model. We demonstrate the effectiveness of our algorithm, Non- Local SIMPLE, for segmentation of a mixed population of healthy subjects and patients with severe cerebellar anatomy. Under the first imaging protocol, we show that Non-Local SIMPLE outperforms previous gold-standard segmentation techniques. In the second imaging protocol, we show that Non-Local SIMPLE outperforms previous gold standard techniques but is outperformed by a non-locally weighted vote with the deeper population of atlases available. This work advances the state of the art in open source cerebellar segmentation algorithms and offers the opportunity for routinely including cerebellar segmentation in magnetic resonance imaging studies that acquire whole brain T1-weighted volumes with approximately 1 mm isotropic resolution.

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.

Large-scale computation of incompressible viscous flow by least-squares finite element method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, T. L.; Povinelli, Louis A.

1993-01-01

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

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.

How does culture affect experiential training feedback in exported Canadian health professional curricula?

PubMed Central

Mousa Bacha, Rasha; Abdelaziz, Somaia

2017-01-01

Objectives To explore feedback processes of Western-based health professional student training curricula conducted in an Arab clinical teaching setting. Methods This qualitative study employed document analysis of in-training evaluation reports (ITERs) used by Canadian nursing, pharmacy, respiratory therapy, paramedic, dental hygiene, and pharmacy technician programs established in Qatar. Six experiential training program coordinators were interviewed between February and May 2016 to explore how national cultural differences are perceived to affect feedback processes between students and clinical supervisors. Interviews were recorded, transcribed, and coded according to a priori cultural themes. Results Document analysis found all programs’ ITERs outlined competency items for students to achieve. Clinical supervisors choose a response option corresponding to their judgment of student performance and may provide additional written feedback in spaces provided. Only one program required formal face-to-face feedback exchange between students and clinical supervisors. Experiential training program coordinators identified that no ITER was expressly culturally adapted, although in some instances, modifications were made for differences in scopes of practice between Canada and Qatar.  Power distance was recognized by all coordinators who also identified both student and supervisor reluctance to document potentially negative feedback in ITERs. Instances of collectivism were described as more lenient student assessment by clinical supervisors of the same cultural background. Uncertainty avoidance did not appear to impact feedback processes. Conclusions Our findings suggest that differences in specific cultural dimensions between Qatar and Canada have implications on the feedback process in experiential training which may be addressed through simple measures to accommodate communication preferences. PMID:28315858

An iterative truncation method for unbounded electromagnetic problems using varying order finite elements

NASA Astrophysics Data System (ADS)

Paul, Prakash

2009-12-01

The finite element method (FEM) is used to solve three-dimensional electromagnetic scattering and radiation problems. Finite element (FE) solutions of this kind contain two main types of error: discretization error and boundary error. Discretization error depends on the number of free parameters used to model the problem, and on how effectively these parameters are distributed throughout the problem space. To reduce the discretization error, the polynomial order of the finite elements is increased, either uniformly over the problem domain or selectively in those areas with the poorest solution quality. Boundary error arises from the condition applied to the boundary that is used to truncate the computational domain. To reduce the boundary error, an iterative absorbing boundary condition (IABC) is implemented. The IABC starts with an inexpensive boundary condition and gradually improves the quality of the boundary condition as the iteration continues. An automatic error control (AEC) is implemented to balance the two types of error. With the AEC, the boundary condition is improved when the discretization error has fallen to a low enough level to make this worth doing. The AEC has these characteristics: (i) it uses a very inexpensive truncation method initially; (ii) it allows the truncation boundary to be very close to the scatterer/radiator; (iii) it puts more computational effort on the parts of the problem domain where it is most needed; and (iv) it can provide as accurate a solution as needed depending on the computational price one is willing to pay. To further reduce the computational cost, disjoint scatterers and radiators that are relatively far from each other are bounded separately and solved using a multi-region method (MRM), which leads to savings in computational cost. A simple analytical way to decide whether the MRM or the single region method will be computationally cheaper is also described. To validate the accuracy and savings in computation time, different shaped metallic and dielectric obstacles (spheres, ogives, cube, flat plate, multi-layer slab etc.) are used for the scattering problems. For the radiation problems, waveguide excited antennas (horn antenna, waveguide with flange, microstrip patch antenna) are used. Using the AEC the peak reduction in computation time during the iteration is typically a factor of 2, compared to the IABC using the same element orders throughout. In some cases, it can be as high as a factor of 4.

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.

Threshold-driven optimization for reference-based auto-planning

NASA Astrophysics Data System (ADS)

Long, Troy; Chen, Mingli; Jiang, Steve; Lu, Weiguo

2018-02-01

We study threshold-driven optimization methodology for automatically generating a treatment plan that is motivated by a reference DVH for IMRT treatment planning. We present a framework for threshold-driven optimization for reference-based auto-planning (TORA). Commonly used voxel-based quadratic penalties have two components for penalizing under- and over-dosing of voxels: a reference dose threshold and associated penalty weight. Conventional manual- and auto-planning using such a function involves iteratively updating the preference weights while keeping the thresholds constant, an unintuitive and often inconsistent method for planning toward some reference DVH. However, driving a dose distribution by threshold values instead of preference weights can achieve similar plans with less computational effort. The proposed methodology spatially assigns reference DVH information to threshold values, and iteratively improves the quality of that assignment. The methodology effectively handles both sub-optimal and infeasible DVHs. TORA was applied to a prostate case and a liver case as a proof-of-concept. Reference DVHs were generated using a conventional voxel-based objective, then altered to be either infeasible or easy-to-achieve. TORA was able to closely recreate reference DVHs in 5-15 iterations of solving a simple convex sub-problem. TORA has the potential to be effective for auto-planning based on reference DVHs. As dose prediction and knowledge-based planning becomes more prevalent in the clinical setting, incorporating such data into the treatment planning model in a clear, efficient way will be crucial for automated planning. A threshold-focused objective tuning should be explored over conventional methods of updating preference weights for DVH-guided treatment planning.

Fast iterative image reconstruction using sparse matrix factorization with GPU acceleration

NASA Astrophysics Data System (ADS)

Zhou, Jian; Qi, Jinyi

2011-03-01

Statistically based iterative approaches for image reconstruction have gained much attention in medical imaging. An accurate system matrix that defines the mapping from the image space to the data space is the key to high-resolution image reconstruction. However, an accurate system matrix is often associated with high computational cost and huge storage requirement. Here we present a method to address this problem by using sparse matrix factorization and parallel computing on a graphic processing unit (GPU).We factor the accurate system matrix into three sparse matrices: a sinogram blurring matrix, a geometric projection matrix, and an image blurring matrix. The sinogram blurring matrix models the detector response. The geometric projection matrix is based on a simple line integral model. The image blurring matrix is to compensate for the line-of-response (LOR) degradation due to the simplified geometric projection matrix. The geometric projection matrix is precomputed, while the sinogram and image blurring matrices are estimated by minimizing the difference between the factored system matrix and the original system matrix. The resulting factored system matrix has much less number of nonzero elements than the original system matrix and thus substantially reduces the storage and computation cost. The smaller size also allows an efficient implement of the forward and back projectors on GPUs, which have limited amount of memory. Our simulation studies show that the proposed method can dramatically reduce the computation cost of high-resolution iterative image reconstruction. The proposed technique is applicable to image reconstruction for different imaging modalities, including x-ray CT, PET, and SPECT.

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.

Determination of the mechanical indices of composite materials by testing multilayered samples

NASA Astrophysics Data System (ADS)

Teregulov, I. G.; Kayumov, R. A.; Butenko, Yu. I.; Safiullin, D. Kh.

1996-09-01

The mechanical indices of materials such as composites reinforced by braids and ribbons are difficult to determine by standard methods. Moreover, the indices of such materials may be greatly altered when they are converted into various structures. It has been suggested that these indices be determined by analyzing the structure testing data. The determination of linear and nonlinear elastic, plastic, and viscoelastic parameters of reinforced materials is discussed. A very simple structure, namely, cylindrical shells made by symmetric winding, is studied as an example. Equilibrium conditions are used to obtain resolving equations relative to the mechanical indices. Convergence of iteration methods is examined. The effect of the scatter of experimental data on the calculated results is analyzed.

Quasi solution of radiation transport equation

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

Pogosbekyan, L.R.; Lysov, D.A.

There is uncertainty with experimental data as well as with input data of theoretical calculations. The neutron distribution from the variational principle, which takes into account both theoretical and experimental data, is obtained to increase the accuracy and speed of neutronic calculations. The neutron imbalance in mesh cells and the discrepancy between experimentally measured and calculated functional of the neutron distribution are simultaneously minimized. A fast-working and simple-programming iteration method is developed to minimize the objective functional. The method can be used in the core monitoring and control system for (a) power distribution calculations, (b) in- and ex-core detector calibration,more » (c) macro-cross sections or isotope distribution correction by experimental data, and (d) core and detector diagnostics.« less

Uniscale multi-view registration using double dog-leg method

NASA Astrophysics Data System (ADS)

Chen, Chao-I.; Sargent, Dusty; Tsai, Chang-Ming; Wang, Yuan-Fang; Koppel, Dan

2009-02-01

3D computer models of body anatomy can have many uses in medical research and clinical practices. This paper describes a robust method that uses videos of body anatomy to construct multiple, partial 3D structures and then fuse them to form a larger, more complete computer model using the structure-from-motion framework. We employ the Double Dog-Leg (DDL) method, a trust-region based nonlinear optimization method, to jointly optimize the camera motion parameters (rotation and translation) and determine a global scale that all partial 3D structures should agree upon. These optimized motion parameters are used for constructing local structures, and the global scale is essential for multi-view registration after all these partial structures are built. In order to provide a good initial guess of the camera movement parameters and outlier free 2D point correspondences for DDL, we also propose a two-stage scheme where multi-RANSAC with a normalized eight-point algorithm is first performed and then a few iterations of an over-determined five-point algorithm is used to polish the results. Our experimental results using colonoscopy video show that the proposed scheme always produces more accurate outputs than the standard RANSAC scheme. Furthermore, since we have obtained many reliable point correspondences, time-consuming and error-prone registration methods like the iterative closest points (ICP) based algorithms can be replaced by a simple rigid-body transformation solver when merging partial structures into a larger model.

Bending and buckling formulation of graphene sheets based on nonlocal simple first-order shear deformation theory

NASA Astrophysics Data System (ADS)

Golmakani, M. E.; Malikan, M.; Sadraee Far, M. N.; Majidi, H. R.

2018-06-01

This paper presents a formulation based on simple first-order shear deformation theory (S-FSDT) for large deflection and buckling of orthotropic single-layered graphene sheets (SLGSs). The S-FSDT has many advantages compared to the classical plate theory (CPT) and conventional FSDT such as needless of shear correction factor, containing less number of unknowns than the existing FSDT and strong similarities with the CPT. Governing equations and boundary conditions are derived based on Hamilton’s principle using the nonlocal differential constitutive relations of Eringen and von Kármán geometrical model. Numerical results are obtained using differential quadrature (DQ) method and the Newton–Raphson iterative scheme. Finally, some comparison studies are carried out to show the high accuracy and reliability of the present formulations compared to the nonlocal CPT and FSDT for different thicknesses, elastic foundations and nonlocal parameters.

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.

Physics Notes.

ERIC Educational Resources Information Center

School Science Review, 1984

1984-01-01

Discusses: (1) Brewster's angle in the elementary laboratory; (2) color mixing by computer; (3) computer iteration at A-level; (4) a simple probe for pressure measurement; (5) the measurement of distance using a laser; and (6) an activity on Archimede's principle. (JN)

3D modelling of non-linear visco-elasto-plastic crustal and lithospheric processes using LaMEM

NASA Astrophysics Data System (ADS)

Popov, Anton; Kaus, Boris

2016-04-01

LaMEM (Lithosphere and Mantle Evolution Model) is a three-dimensional thermo-mechanical numerical code to simulate crustal and lithospheric deformation. The code is based on a staggered finite difference (FDSTAG) discretization in space, which is a stable and very efficient technique to solve the (nearly) incompressible Stokes equations that does not suffer from spurious pressure modes or artificial compressibility (a typical feature of low-order finite element techniques). Higher order finite element methods are more accurate than FDSTAG methods under idealized test cases where the jump in viscosity is exactly aligned with the boundaries of the elements. Yet, geodynamically more realistic cases involve evolving subduction zones, nonlinear rheologies or localized plastic shear bands. In these cases, the viscosity pattern evolves spontaneously during a simulation or even during nonlinear iterations, and the advantages of higher order methods disappear and they all converge with approximately first order accuracy, similar to that of FDSTAG [1]. Yet, since FDSTAG methods have considerably less degrees of freedom than quadratic finite element methods, they require about an order of magnitude less memory for the same number of nodes in 3D which also implies that every matrix-vector multiplication is significantly faster. LaMEM is build on top of the PETSc library and uses the particle-in-cell technique to track material properties, history variables which makes it straightforward to incorporate effects like phase changes or chemistry. An internal free surface is present, together with (simple) erosion and sedimentation processes, and a number of methods are available to import complex geometries into the code (e.g, http://geomio.bitbucket.org). Customized Galerkin coupled geometric multigrid preconditioners are implemented which resulted in a good parallel scalability of the code (we have tested LaMEM on 458'752 cores [2]). Yet, the drawback of using FDSTAG discretizations is that the Jacobian, which is a key component for fast and robust convergence of Newton-Raphson nonlinear iterative solvers, is more difficult to implement than in FE codes and actually results in a larger stencil. Rather than discretizing it explicitly, we therefore developed a matrix-free analytical Jacobian implementation for the coupled sets of momentum, mass, and energy conservation equations, combined with visco-elasto-plastic rheologies. Tests show that for simple nonlinear viscous rheologies there is little advantage of the MF approach over the standard MFFD PETSc approach, but that iterations converge slightly faster if plasticity is present. Results also show that the Newton solver usually converges in a quadratic manner even for pressure-dependent Drucker-Prager rheologies and without harmonic viscosity averaging of plastic and viscous rheologies. Yet, if the timestep is too large (and the model becomes effectively viscoplastic), or if the shear band pattern changes dramatically, stagnation of iterations might occur. This can be remedied with an appropriate regularization, which we discuss. LaMEM is available as open source software. [1] Thielmann, M., May, D.A., and Kaus, B., 2014, Discretization Errors in the Hybrid Finite Element Particle-in-cell Method: Pure and Applied Geophysics,, doi: 10.1007/s00024-014-0808-9. [2] Kaus B.J.P., Popov A.A., Baumann T.S., Püsök A.E., Bauville A., Fernandez N., Collignon M. (2015) Forward and inverse modelling of lithospheric deformation on geological timescales. NIC Symposium 2016 - Proceedings. NIC Series. Vol. 48.

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.

Variational data assimilation for limited-area models: solution of the open boundary control problem and its application for the Gulf of Finland

NASA Astrophysics Data System (ADS)

Sheloput, Tatiana; Agoshkov, Valery

2017-04-01

The problem of modeling water areas with `liquid' (open) lateral boundaries is discussed. There are different known methods dealing with open boundaries in limited-area models, and one of the most efficient is data assimilation. Although this method is popular, there are not so many articles concerning its implementation for recovering boundary functions. However, the problem of specifying boundary conditions at the open boundary of a limited area is still actual and important. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. It is based on the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations. The splitting method that is used for time approximation in the model allows to consider the data assimilation problem as a sequence of linear problems. One of such `simple' temperature (salinity) assimilation problem is investigated in the study. Using well known techniques of study and solution of inverse problems and optimal control problems [1], we propose an iterative solution algorithm and we obtain conditions for existence of the solution, for unique and dense solvability of the problem and for convergence of the iterative algorithm. The investigation shows that if observations satisfy certain conditions, the proposed algorithm converges to the solution of the boundary control problem. Particularly, it converges when observational data are given on the `liquid' boundary [2]. Theoretical results are confirmed by the results of numerical experiments. The numerical algorithm was implemented to water area of the Baltic Sea. Two numerical experiments were carried out in the Gulf of Finland: one with the application of the assimilation procedure and the other without. The analyses have shown that the surface temperature field in the first experiment is close to the observed one, while the result of the second experiment misfits. Number of iterations depends on the regularisation parameter, but generally the algorithm converges after 10 iterations. The results of the numerical experiments show that the usage of the proposed method makes sense. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments) and by the Russian Foundation for Basic Research (project 16-01-00548, the formulation of the problem and its study). [1] Agoshkov V. I. Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). [2] Agoshkov V.I., Sheloput T.O. The study and numerical solution of the problem of heat and salinity transfer assuming 'liquid' boundaries // Russ. J. Numer. Anal. Math. Modelling. 2016. Vol. 31, No. 2. P. 71-80.

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.

Efficient multi-atlas abdominal segmentation on clinically acquired CT with SIMPLE context learning.

PubMed

Xu, Zhoubing; Burke, Ryan P; Lee, Christopher P; Baucom, Rebeccah B; Poulose, Benjamin K; Abramson, Richard G; Landman, Bennett A

2015-08-01

Abdominal segmentation on clinically acquired computed tomography (CT) has been a challenging problem given the inter-subject variance of human abdomens and complex 3-D relationships among organs. Multi-atlas segmentation (MAS) provides a potentially robust solution by leveraging label atlases via image registration and statistical fusion. We posit that the efficiency of atlas selection requires further exploration in the context of substantial registration errors. The selective and iterative method for performance level estimation (SIMPLE) method is a MAS technique integrating atlas selection and label fusion that has proven effective for prostate radiotherapy planning. Herein, we revisit atlas selection and fusion techniques for segmenting 12 abdominal structures using clinically acquired CT. Using a re-derived SIMPLE algorithm, we show that performance on multi-organ classification can be improved by accounting for exogenous information through Bayesian priors (so called context learning). These innovations are integrated with the joint label fusion (JLF) approach to reduce the impact of correlated errors among selected atlases for each organ, and a graph cut technique is used to regularize the combined segmentation. In a study of 100 subjects, the proposed method outperformed other comparable MAS approaches, including majority vote, SIMPLE, JLF, and the Wolz locally weighted vote technique. The proposed technique provides consistent improvement over state-of-the-art approaches (median improvement of 7.0% and 16.2% in DSC over JLF and Wolz, respectively) and moves toward efficient segmentation of large-scale clinically acquired CT data for biomarker screening, surgical navigation, and data mining. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

Pump-dump iterative squeezing of vibrational wave packets.

PubMed

Chang, Bo Y; Sola, Ignacio R

2005-12-22

The free motion of a nonstationary vibrational wave packet in an electronic potential is a source of interesting quantum properties. In this work we propose an iterative scheme that allows continuous stretching and squeezing of a wave packet in the ground or in an excited electronic state, by switching the wave function between both potentials with pi pulses at certain times. Using a simple model of displaced harmonic oscillators and delta pulses, we derive the analytical solution and the conditions for its possible implementation and optimization in different molecules and electronic states. We show that the main constraining parameter is the pulse bandwidth. Although in principle the degree of squeezing (or stretching) is not bounded, the physical resources increase quadratically with the number of iterations, while the achieved squeezing only increases linearly.

ShareSync: A Solution for Deterministic Data Sharing over Ethernet

NASA Technical Reports Server (NTRS)

Dunn, Daniel J., II; Koons, William A.; Kennedy, Richard D.; Davis, Philip A.

2007-01-01

As part of upgrading the Contact Dynamics Simulation Laboratory (CDSL) at the NASA Marshall Space Flight Center (MSFC), a simple, cost effective method was needed to communicate data among the networked simulation machines and I/O controllers used to run the facility. To fill this need and similar applicable situations, a generic protocol was developed, called ShareSync. ShareSync is a lightweight, real-time, publish-subscribe Ethernet protocol for simple and deterministic data sharing across diverse machines and operating systems. ShareSync provides a simple Application Programming Interface (API) for simulation programmers to incorporate into their code. The protocol is compatible with virtually all Ethernet-capable machines, is flexible enough to support a variety of applications, is fast enough to provide soft real-time determinism, and is a low-cost resource for distributed simulation development, deployment, and maintenance. The first design cycle iteration of ShareSync has been completed, and the protocol has undergone several testing procedures including endurance and benchmarking tests and approaches the 2001ts data synchronization design goal for the CDSL.

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.

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

Retinal artery-vein classification via topology estimation

PubMed Central

Estrada, Rolando; Allingham, Michael J.; Mettu, Priyatham S.; Cousins, Scott W.; Tomasi, Carlo; Farsiu, Sina

2015-01-01

We propose a novel, graph-theoretic framework for distinguishing arteries from veins in a fundus image. We make use of the underlying vessel topology to better classify small and midsized vessels. We extend our previously proposed tree topology estimation framework by incorporating expert, domain-specific features to construct a simple, yet powerful global likelihood model. We efficiently maximize this model by iteratively exploring the space of possible solutions consistent with the projected vessels. We tested our method on four retinal datasets and achieved classification accuracies of 91.0%, 93.5%, 91.7%, and 90.9%, outperforming existing methods. Our results show the effectiveness of our approach, which is capable of analyzing the entire vasculature, including peripheral vessels, in wide field-of-view fundus photographs. This topology-based method is a potentially important tool for diagnosing diseases with retinal vascular manifestation. PMID:26068204

Transient temperature distributions in simple conducting bodies steadily heated through a laminar boundary layer

NASA Technical Reports Server (NTRS)

Parker, Hermon M

1953-01-01

An analysis is made of the transient heat-conduction effects in three simple semi-infinite bodies: the flat insulated plate, the conical shell, and the slender solid cone. The bodies are assumed to have constant initial temperatures and, at zero time, to begin to move at a constant speed and zero angle of attack through a homogeneous atmosphere. The heat input is taken as that through a laminar boundary layer. Radiation heat transfer and transverse temperature gradients are assumed to be zero. The appropriate heat-conduction equations are solved by an iteration method, the zeroeth-order terms describing the situation in the limit of small time. The method is presented and the solutions are calculated to three orders which are sufficient to give reasonably accurate results when the forward edge has attained one-half the total temperature rise (nose half-rise time). Flight Mach number and air properties occur as parameters in the result. Approximate expressions for the extent of the conduction region and nose half-rise times as functions of the parameters of the problem are presented. (author)

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…

Multigrid methods for isogeometric discretization

PubMed Central

Gahalaut, K.P.S.; Kraus, J.K.; Tomar, S.K.

2013-01-01

We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels ℓ, whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order p=4, and for C0 and Cp-1 smoothness. PMID:24511168

Real-Time Exponential Curve Fits Using Discrete Calculus

NASA Technical Reports Server (NTRS)

Rowe, Geoffrey

2010-01-01

An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.

Validation of a method for in vivo 3D dose reconstruction for IMRT and VMAT treatments using on-treatment EPID images and a model-based forward-calculation algorithm

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

Van Uytven, Eric, E-mail: eric.vanuytven@cancercare.mb.ca; Van Beek, Timothy; McCowan, Peter M.

2015-12-15

Purpose: Radiation treatments are trending toward delivering higher doses per fraction under stereotactic radiosurgery and hypofractionated treatment regimens. There is a need for accurate 3D in vivo patient dose verification using electronic portal imaging device (EPID) measurements. This work presents a model-based technique to compute full three-dimensional patient dose reconstructed from on-treatment EPID portal images (i.e., transmission images). Methods: EPID dose is converted to incident fluence entering the patient using a series of steps which include converting measured EPID dose to fluence at the detector plane and then back-projecting the primary source component of the EPID fluence upstream of themore » patient. Incident fluence is then recombined with predicted extra-focal fluence and used to calculate 3D patient dose via a collapsed-cone convolution method. This method is implemented in an iterative manner, although in practice it provides accurate results in a single iteration. The robustness of the dose reconstruction technique is demonstrated with several simple slab phantom and nine anthropomorphic phantom cases. Prostate, head and neck, and lung treatments are all included as well as a range of delivery techniques including VMAT and dynamic intensity modulated radiation therapy (IMRT). Results: Results indicate that the patient dose reconstruction algorithm compares well with treatment planning system computed doses for controlled test situations. For simple phantom and square field tests, agreement was excellent with a 2%/2 mm 3D chi pass rate ≥98.9%. On anthropomorphic phantoms, the 2%/2 mm 3D chi pass rates ranged from 79.9% to 99.9% in the planning target volume (PTV) region and 96.5% to 100% in the low dose region (>20% of prescription, excluding PTV and skin build-up region). Conclusions: An algorithm to reconstruct delivered patient 3D doses from EPID exit dosimetry measurements was presented. The method was applied to phantom and patient data sets, as well as for dynamic IMRT and VMAT delivery techniques. Results indicate that the EPID dose reconstruction algorithm presented in this work is suitable for clinical implementation.« less

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.

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.

Hyperspectral chemical plume detection algorithms based on multidimensional iterative filtering decomposition.

PubMed

Cicone, A; Liu, J; Zhou, H

2016-04-13

Chemicals released in the air can be extremely dangerous for human beings and the environment. Hyperspectral images can be used to identify chemical plumes, however the task can be extremely challenging. Assuming we know a priori that some chemical plume, with a known frequency spectrum, has been photographed using a hyperspectral sensor, we can use standard techniques such as the so-called matched filter or adaptive cosine estimator, plus a properly chosen threshold value, to identify the position of the chemical plume. However, due to noise and inadequate sensing, the accurate identification of chemical pixels is not easy even in this apparently simple situation. In this paper, we present a post-processing tool that, in a completely adaptive and data-driven fashion, allows us to improve the performance of any classification methods in identifying the boundaries of a plume. This is done using the multidimensional iterative filtering (MIF) algorithm (Cicone et al. 2014 (http://arxiv.org/abs/1411.6051); Cicone & Zhou 2015 (http://arxiv.org/abs/1507.07173)), which is a non-stationary signal decomposition method like the pioneering empirical mode decomposition method (Huang et al. 1998 Proc. R. Soc. Lond. A 454, 903. (doi:10.1098/rspa.1998.0193)). Moreover, based on the MIF technique, we propose also a pre-processing method that allows us to decorrelate and mean-centre a hyperspectral dataset. The cosine similarity measure, which often fails in practice, appears to become a successful and outperforming classifier when equipped with such a pre-processing method. We show some examples of the proposed methods when applied to real-life problems. © 2016 The Author(s).

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

Decentralized Control of Sound Radiation from an Aircraft-Style Panel Using Iterative Loop Recovery

NASA Technical Reports Server (NTRS)

Schiller, Noah H.; Cabell, Randolph H.; Fuller, Chris R.

2008-01-01

A decentralized LQG-based control strategy is designed to reduce low-frequency sound transmission through periodically stiffened panels. While modern control strategies have been used to reduce sound radiation from relatively simple structural acoustic systems, significant implementation issues have to be addressed before these control strategies can be extended to large systems such as the fuselage of an aircraft. For instance, centralized approaches typically require a high level of connectivity and are computationally intensive, while decentralized strategies face stability problems caused by the unmodeled interaction between neighboring control units. Since accurate uncertainty bounds are not known a priori, it is difficult to ensure the decentralized control system will be robust without making the controller overly conservative. Therefore an iterative approach is suggested, which utilizes frequency-shaped loop recovery. The approach accounts for modeling error introduced by neighboring control loops, requires no communication between subsystems, and is relatively simple. The control strategy is validated using real-time control experiments performed on a built-up aluminum test structure representative of the fuselage of an aircraft. Experiments demonstrate that the iterative approach is capable of achieving 12 dB peak reductions and a 3.6 dB integrated reduction in radiated sound power from the stiffened panel.

Feynman formulas for semigroups generated by an iterated Laplace operator

NASA Astrophysics Data System (ADS)

Buzinov, M. S.

2017-04-01

In the present paper, we find representations of a one-parameter semigroup generated by a finite sum of iterated Laplace operators and an additive perturbation (the potential). Such semigroups and the evolution equations corresponding to them find applications in the field of physics, chemistry, biology, and pattern recognition. The representations mentioned above are obtained in the form of Feynman formulas, i.e., in the form of a limit of multiple integrals as the multiplicity tends to infinity. The term "Feynman formula" was proposed by Smolyanov. Smolyanov's approach uses Chernoff's theorems. A simple form of representations thus obtained enables one to use them for numerical modeling the dynamics of the evolution system as a method for the approximation of solutions of equations. The problems considered in this note can be treated using the approach suggested by Remizov (see also the monograph of Smolyanov and Shavgulidze on path integrals). The representations (of semigroups) obtained in this way are more complicated than those given by the Feynman formulas; however, it is possible to bypass some analytical difficulties.

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

NASA Astrophysics Data System (ADS)

Yu, Hua-Gen

2016-08-01

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH4 and H2CO are given, together with a comparison with previous results.

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

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

Yu, Hua-Gen, E-mail: hgy@bnl.gov

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using amore » multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH{sub 4} and H{sub 2}CO are given, together with a comparison with previous results.« less

An iterative network partition algorithm for accurate identification of dense network modules

PubMed Central

Sun, Siqi; Dong, Xinran; Fu, Yao; Tian, Weidong

2012-01-01

A key step in network analysis is to partition a complex network into dense modules. Currently, modularity is one of the most popular benefit functions used to partition network modules. However, recent studies suggested that it has an inherent limitation in detecting dense network modules. In this study, we observed that despite the limitation, modularity has the advantage of preserving the primary network structure of the undetected modules. Thus, we have developed a simple iterative Network Partition (iNP) algorithm to partition a network. The iNP algorithm provides a general framework in which any modularity-based algorithm can be implemented in the network partition step. Here, we tested iNP with three modularity-based algorithms: multi-step greedy (MSG), spectral clustering and Qcut. Compared with the original three methods, iNP achieved a significant improvement in the quality of network partition in a benchmark study with simulated networks, identified more modules with significantly better enrichment of functionally related genes in both yeast protein complex network and breast cancer gene co-expression network, and discovered more cancer-specific modules in the cancer gene co-expression network. As such, iNP should have a broad application as a general method to assist in the analysis of biological networks. PMID:22121225

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.

High speed phase retrieval of in-line holograms by the assistance of corresponding off-axis holograms.

PubMed

Orzó, László

2015-06-29

Retrieving correct phase information from an in-line hologram is difficult as the object wave field and the diffractions of the zero order and the conjugate object term overlap. The existing iterative numerical phase retrieval methods are slow, especially in the case of high Fresnel number systems. Conversely, the reconstruction of the object wave field from an off-axis hologram is simple, but due to the applied spatial frequency filtering the achievable resolution is confined. Here, a new, high-speed algorithm is introduced that efficiently incorporates the data of an auxiliary off-axis hologram in the phase retrieval of the corresponding in-line hologram. The efficiency of the introduced combined phase retrieval method is demonstrated by simulated and measured holograms.

Automated IMRT planning with regional optimization using planning scripts

PubMed Central

Wong, Eugene; Bzdusek, Karl; Lock, Michael; Chen, Jeff Z.

2013-01-01

Intensity‐modulated radiation therapy (IMRT) has become a standard technique in radiation therapy for treating different types of cancers. Various class solutions have been developed for simple cases (e.g., localized prostate, whole breast) to generate IMRT plans efficiently. However, for more complex cases (e.g., head and neck, pelvic nodes), it can be time‐consuming for a planner to generate optimized IMRT plans. To generate optimal plans in these more complex cases which generally have multiple target volumes and organs at risk, it is often required to have additional IMRT optimization structures such as dose limiting ring structures, adjust beam geometry, select inverse planning objectives and associated weights, and additional IMRT objectives to reduce cold and hot spots in the dose distribution. These parameters are generally manually adjusted with a repeated trial and error approach during the optimization process. To improve IMRT planning efficiency in these more complex cases, an iterative method that incorporates some of these adjustment processes automatically in a planning script is designed, implemented, and validated. In particular, regional optimization has been implemented in an iterative way to reduce various hot or cold spots during the optimization process that begins with defining and automatic segmentation of hot and cold spots, introducing new objectives and their relative weights into inverse planning, and turn this into an iterative process with termination criteria. The method has been applied to three clinical sites: prostate with pelvic nodes, head and neck, and anal canal cancers, and has shown to reduce IMRT planning time significantly for clinical applications with improved plan quality. The IMRT planning scripts have been used for more than 500 clinical cases. PACS numbers: 87.55.D, 87.55.de PMID:23318393

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.

Guided Iterative Substructure Search (GI-SSS) - A New Trick for an Old Dog.

PubMed

Weskamp, Nils

2016-07-01

Substructure search (SSS) is a fundamental technique supported by various chemical information systems. Many users apply it in an iterative manner: they modify their queries to shape the composition of the retrieved hit sets according to their needs. We propose and evaluate two heuristic extensions of SSS aimed at simplifying these iterative query modifications by collecting additional information during query processing and visualizing this information in an intuitive way. This gives the user a convenient feedback on how certain changes to the query would affect the retrieved hit set and reduces the number of trial-and-error cycles needed to generate an optimal search result. The proposed heuristics are simple, yet surprisingly effective and can be easily added to existing SSS implementations. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent

PubMed Central

Press, William H.; Dyson, Freeman J.

2012-01-01

The two-player Iterated Prisoner’s Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministically set her opponent Y’s score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores. Against such a player, an evolutionary player’s best response is to accede to the extortion. Only a player with a theory of mind about his opponent can do better, in which case Iterated Prisoner’s Dilemma is an Ultimatum Game. PMID:22615375

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

Uncertainty Footprint: Visualization of Nonuniform Behavior of Iterative Algorithms Applied to 4D Cell Tracking

PubMed Central

Wan, Y.; Hansen, C.

2018-01-01

Research on microscopy data from developing biological samples usually requires tracking individual cells over time. When cells are three-dimensionally and densely packed in a time-dependent scan of volumes, tracking results can become unreliable and uncertain. Not only are cell segmentation results often inaccurate to start with, but it also lacks a simple method to evaluate the tracking outcome. Previous cell tracking methods have been validated against benchmark data from real scans or artificial data, whose ground truth results are established by manual work or simulation. However, the wide variety of real-world data makes an exhaustive validation impossible. Established cell tracking tools often fail on new data, whose issues are also difficult to diagnose with only manual examinations. Therefore, data-independent tracking evaluation methods are desired for an explosion of microscopy data with increasing scale and resolution. In this paper, we propose the uncertainty footprint, an uncertainty quantification and visualization technique that examines nonuniformity at local convergence for an iterative evaluation process on a spatial domain supported by partially overlapping bases. We demonstrate that the patterns revealed by the uncertainty footprint indicate data processing quality in two algorithms from a typical cell tracking workflow – cell identification and association. A detailed analysis of the patterns further allows us to diagnose issues and design methods for improvements. A 4D cell tracking workflow equipped with the uncertainty footprint is capable of self diagnosis and correction for a higher accuracy than previous methods whose evaluation is limited by manual examinations. PMID:29456279

Evaluation of simulation alternatives for the brute-force ray-tracing approach used in backlight design

NASA Astrophysics Data System (ADS)

Desnijder, Karel; Hanselaer, Peter; Meuret, Youri

2016-04-01

A key requirement to obtain a uniform luminance for a side-lit LED backlight is the optimised spatial pattern of structures on the light guide that extract the light. The generation of such a scatter pattern is usually performed by applying an iterative approach. In each iteration, the luminance distribution of the backlight with a particular scatter pattern is analysed. This is typically performed with a brute-force ray-tracing algorithm, although this approach results in a time-consuming optimisation process. In this study, the Adding-Doubling method is explored as an alternative way for evaluating the luminance of a backlight. Due to the similarities between light propagating in a backlight with extraction structures and light scattering in a cloud of light scatterers, the Adding-Doubling method which is used to model the latter could also be used to model the light distribution in a backlight. The backlight problem is translated to a form upon which the Adding-Doubling method is directly applicable. The calculated luminance for a simple uniform extraction pattern with the Adding-Doubling method matches the luminance generated by a commercial raytracer very well. Although successful, no clear computational advantage over ray tracers is realised. However, the dynamics of light propagation in a light guide as used the Adding-Doubling method, also allow to enhance the efficiency of brute-force ray-tracing algorithms. The performance of this enhanced ray-tracing approach for the simulation of backlights is also evaluated against a typical brute-force ray-tracing approach.

Computational efficiency for the surface renewal method

NASA Astrophysics Data System (ADS)

Kelley, Jason; Higgins, Chad

2018-04-01

Measuring surface fluxes using the surface renewal (SR) method requires programmatic algorithms for tabulation, algebraic calculation, and data quality control. A number of different methods have been published describing automated calibration of SR parameters. Because the SR method utilizes high-frequency (10 Hz+) measurements, some steps in the flux calculation are computationally expensive, especially when automating SR to perform many iterations of these calculations. Several new algorithms were written that perform the required calculations more efficiently and rapidly, and that tested for sensitivity to length of flux averaging period, ability to measure over a large range of lag timescales, and overall computational efficiency. These algorithms utilize signal processing techniques and algebraic simplifications that demonstrate simple modifications that dramatically improve computational efficiency. The results here complement efforts by other authors to standardize a robust and accurate computational SR method. Increased speed of computation time grants flexibility to implementing the SR method, opening new avenues for SR to be used in research, for applied monitoring, and in novel field deployments.

The hyperbolic problem

NASA Astrophysics Data System (ADS)

Gualdesi, Lavinio

2017-04-01

Mooring lines in the Ocean might be seen as a pretty simple seamanlike activity. Connecting valuable scientific instrumentation to it transforms this simple activity into a sophisticated engineering support which needs to be accurately designed, developed, deployed, monitored and hopefully recovered with its precious load of scientific data. This work is an historical travel along the efforts carried out by scientists all over the world to successfully predict mooring line behaviour through both mathematical simulation and experimental verifications. It is at first glance unexpected how many factors one must observe to get closer and closer to a real ocean situation. Most models have dual applications for mooring lines and towed bodies lines equations. Numerous references are provided starting from the oldest one due to Isaac Newton. In his "Philosophiae Naturalis Principia Matematica" (1687) the English scientist, while discussing about the law of motion for bodies in resistant medium, is envisaging a hyperbolic fitting to the phenomenon including asymptotic behaviour in non-resistant media. A non-exhaustive set of mathematical simulations of the mooring lines trajectory prediction is listed hereunder to document how the subject has been under scientific focus over almost a century. Pode (1951) Prior personal computers diffusion a tabular form of calculus of cable geometry was used by generations of engineers keeping in mind the following limitations and approximations: tangential drag coefficients were assumed to be negligible. A steady current flow was assumed as in the towed configuration. Cchabra (1982) Finite Element Method that assumes an arbitrary deflection angle for the top first section and calculates equilibrium equations down to the sea floor iterating up to a compliant solution. Gualdesi (1987) ANAMOOR. A Fortran Program based on iterative methods above including experimental data from intensive mooring campaign. Database of experimental drag coefficients obtained in wind tunnel for the instrumentation verified in ocean mooring. Dangov (1987) A set of Fortran routines, due to a Canadian scientist, to analyse discrepancies between model and experimental data due to strumming effect on mooring line. Acoustic Doppler Current Profiler's data were adopted for the first time as an input for the model. Skop and O' Hara (1968) Static analysis of a three dimensional multi-leg model Knutson (1987) A model developed at David taylor Model basin based on towed models. Henry Berteaux (1990) SFMOOR Iterative FEM analysis fully fitted with mooring components data base developed by a WHOI scientist. Henry Berteaux (1990) SSMOOR Same model applied to sub-surface moorings. Gobats and Grosenbaugh (1998) Fully developed Method based on Strip Theory developed by WHOI scientists. Experimental validation results are not known.

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.

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

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Pseudo-orthogonalization of memory patterns for associative memory.

PubMed

Oku, Makito; Makino, Takaki; Aihara, Kazuyuki

2013-11-01

A new method for improving the storage capacity of associative memory models on a neural network is proposed. The storage capacity of the network increases in proportion to the network size in the case of random patterns, but, in general, the capacity suffers from correlation among memory patterns. Numerous solutions to this problem have been proposed so far, but their high computational cost limits their scalability. In this paper, we propose a novel and simple solution that is locally computable without any iteration. Our method involves XNOR masking of the original memory patterns with random patterns, and the masked patterns and masks are concatenated. The resulting decorrelated patterns allow higher storage capacity at the cost of the pattern length. Furthermore, the increase in the pattern length can be reduced through blockwise masking, which results in a small amount of capacity loss. Movie replay and image recognition are presented as examples to demonstrate the scalability of the proposed method.

The design of supercritical wings by the use of three-dimensional transonic theory

NASA Technical Reports Server (NTRS)

Mann, M. J.

1979-01-01

A procedure was developed for the design of transonic wings by the iterative use of three dimensional, inviscid, transonic analysis methods. The procedure was based on simple principles of supersonic flow and provided the designer with a set of guidelines for the systematic alteration of wing profile shapes to achieve some desired pressure distribution. The method was generally applicable to wing design at conditions involving a large region of supercriterical flow. To illustrate the method, it was applied to the design of a wing for a supercritical maneuvering fighter that operates at high lift and transonic Mach number. The wing profiles were altered to produce a large region of supercritical flow which was terminated by a weak shock wave. The spanwise variation of drag of this wing and some principles for selecting the streamwise pressure distribution are also discussed.

In-Flight System Identification

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

1998-01-01

A method is proposed and studied whereby the system identification cycle consisting of experiment design and data analysis can be repeatedly implemented aboard a test aircraft in real time. This adaptive in-flight system identification scheme has many advantages, including increased flight test efficiency, adaptability to dynamic characteristics that are imperfectly known a priori, in-flight improvement of data quality through iterative input design, and immediate feedback of the quality of flight test results. The technique uses equation error in the frequency domain with a recursive Fourier transform for the real time data analysis, and simple design methods employing square wave input forms to design the test inputs in flight. Simulation examples are used to demonstrate that the technique produces increasingly accurate model parameter estimates resulting from sequentially designed and implemented flight test maneuvers. The method has reasonable computational requirements, and could be implemented aboard an aircraft in real time.

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

NASA Astrophysics Data System (ADS)

Witte, J. H.; Reisinger, C.

2010-09-01

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

Deep Learning Nuclei Detection in Digitized Histology Images by Superpixels

PubMed Central

Sornapudi, Sudhir; Stanley, Ronald Joe; Stoecker, William V.; Almubarak, Haidar; Long, Rodney; Antani, Sameer; Thoma, George; Zuna, Rosemary; Frazier, Shelliane R.

2018-01-01

Background: Advances in image analysis and computational techniques have facilitated automatic detection of critical features in histopathology images. Detection of nuclei is critical for squamous epithelium cervical intraepithelial neoplasia (CIN) classification into normal, CIN1, CIN2, and CIN3 grades. Methods: In this study, a deep learning (DL)-based nuclei segmentation approach is investigated based on gathering localized information through the generation of superpixels using a simple linear iterative clustering algorithm and training with a convolutional neural network. Results: The proposed approach was evaluated on a dataset of 133 digitized histology images and achieved an overall nuclei detection (object-based) accuracy of 95.97%, with demonstrated improvement over imaging-based and clustering-based benchmark techniques. Conclusions: The proposed DL-based nuclei segmentation Method with superpixel analysis has shown improved segmentation results in comparison to state-of-the-art methods. PMID:29619277

Preconditioner-free Wiener filtering with a dense noise matrix

NASA Astrophysics Data System (ADS)

Huffenberger, Kevin M.

2018-05-01

This work extends the Elsner & Wandelt (2013) iterative method for efficient, preconditioner-free Wiener filtering to cases in which the noise covariance matrix is dense, but can be decomposed into a sum whose parts are sparse in convenient bases. The new method, which uses multiple messenger fields, reproduces Wiener-filter solutions for test problems, and we apply it to a case beyond the reach of the Elsner & Wandelt (2013) method. We compute the Wiener-filter solution for a simulated Cosmic Microwave Background (CMB) map that contains spatially varying, uncorrelated noise, isotropic 1/f noise, and large-scale horizontal stripes (like those caused by atmospheric noise). We discuss simple extensions that can filter contaminated modes or inverse-noise-filter the data. These techniques help to address complications in the noise properties of maps from current and future generations of ground-based Microwave Background experiments, like Advanced ACTPol, Simons Observatory, and CMB-S4.

The Parker-Sochacki Method of Solving Differential Equations: Applications and Limitations

NASA Astrophysics Data System (ADS)

Rudmin, Joseph W.

2006-11-01

The Parker-Sochacki method is a powerful but simple technique of solving systems of differential equations, giving either analytical or numerical results. It has been in use for about 10 years now since its discovery by G. Edgar Parker and James Sochacki of the James Madison University Dept. of Mathematics and Statistics. It is being presented here because it is still not widely known and can benefit the listeners. It is a method of rapidly generating the Maclauren series to high order, non-iteratively. It has been successfully applied to more than a hundred systems of equations, including the classical many-body problem. Its advantages include its speed of calculation, its simplicity, and the fact that it uses only addition, subtraction and multiplication. It is not just a polynomial approximation, because it yields the Maclaurin series, and therefore exhibits the advantages and disadvantages of that series. A few applications will be presented.

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.

1-D DC Resistivity Modeling and Interpretation in Anisotropic Media Using Particle Swarm Optimization

NASA Astrophysics Data System (ADS)

Pekşen, Ertan; Yas, Türker; Kıyak, Alper

2014-09-01

We examine the one-dimensional direct current method in anisotropic earth formation. We derive an analytic expression of a simple, two-layered anisotropic earth model. Further, we also consider a horizontally layered anisotropic earth response with respect to the digital filter method, which yields a quasi-analytic solution over anisotropic media. These analytic and quasi-analytic solutions are useful tests for numerical codes. A two-dimensional finite difference earth model in anisotropic media is presented in order to generate a synthetic data set for a simple one-dimensional earth. Further, we propose a particle swarm optimization method for estimating the model parameters of a layered anisotropic earth model such as horizontal and vertical resistivities, and thickness. The particle swarm optimization is a naturally inspired meta-heuristic algorithm. The proposed method finds model parameters quite successfully based on synthetic and field data. However, adding 5 % Gaussian noise to the synthetic data increases the ambiguity of the value of the model parameters. For this reason, the results should be controlled by a number of statistical tests. In this study, we use probability density function within 95 % confidence interval, parameter variation of each iteration and frequency distribution of the model parameters to reduce the ambiguity. The result is promising and the proposed method can be used for evaluating one-dimensional direct current data in anisotropic media.

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

Cyclic Game Dynamics Driven by Iterated Reasoning

PubMed Central

Frey, Seth; Goldstone, Robert L.

2013-01-01

Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated. However, economists have argued that iterated reasoning–what you think I think you think–will suppress complex dynamics by stabilizing or accelerating convergence to Nash equilibrium. We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point solution concept. These cycles are driven by a “hopping” behavior that is consistent with other accounts of iterated reasoning: agents are constrained to about two steps of iterated reasoning and learn an additional one-half step with each session. If higher-order reasoning can be complicit in complex emergent dynamics, then cyclic and chaotic patterns may be endogenous features of real-world social and economic systems. PMID:23441191

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.

In-class Simulations of the Iterated Prisoner's Dilemma Game.

ERIC Educational Resources Information Center

Bodo, Peter

2002-01-01

Developed a simple computer program for the in-class simulation of the repeated prisoner's dilemma game with student-designed strategies. Describes the basic features of the software. Presents two examples using the program to teach the problems of cooperation among profit-maximizing agents. (JEH)

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.

Incorporation of star measurements for the determination of orbit and attitude parameters of a geosynchronous satellite: An iterative application of linear regression

NASA Astrophysics Data System (ADS)

Phillips, D.

1980-10-01

Currently on NOAA/NESS's VIRGS system at the World Weather Building star images are being ingested on a daily basis. The image coordinates of the star locations are measured and stored. Subsequently, the information is used to determine the attitude, the misalignment angles between the spin axis and the principal axis of the satellite, and the precession rate and direction. This is done for both the 'East' and 'West' operational geosynchronous satellites. This orientation information is then combined with image measurements of earth based landmarks to determine the orbit of each satellite. The method for determining the orbit is simple. For each landmark measurement one determines a nominal position vector for the satellite by extending a ray from the landmark's position towards the satellite and intersecting the ray with a sphere with center coinciding with the Earth's center and with radius equal to the nominal height for a geosynchronous satellite. The apparent motion of the satellite around the Earth's center is then approximated with a Keplerian model. In turn the variations of the satellite's height, as a function of time found by using this model, are used to redetermine the successive satellite positions by again using the Earth based landmark measurements and intersecting rays from these landmarks with the newly determined spheres. This process is performed iteratively until convergence is achieved. Only three iterations are required.

Designing Hyperchaotic Cat Maps With Any Desired Number of Positive Lyapunov Exponents.

PubMed

Hua, Zhongyun; Yi, Shuang; Zhou, Yicong; Li, Chengqing; Wu, Yue

2018-02-01

Generating chaotic maps with expected dynamics of users is a challenging topic. Utilizing the inherent relation between the Lyapunov exponents (LEs) of the Cat map and its associated Cat matrix, this paper proposes a simple but efficient method to construct an -dimensional ( -D) hyperchaotic Cat map (HCM) with any desired number of positive LEs. The method first generates two basic -D Cat matrices iteratively and then constructs the final -D Cat matrix by performing similarity transformation on one basic -D Cat matrix by the other. Given any number of positive LEs, it can generate an -D HCM with desired hyperchaotic complexity. Two illustrative examples of -D HCMs were constructed to show the effectiveness of the proposed method, and to verify the inherent relation between the LEs and Cat matrix. Theoretical analysis proves that the parameter space of the generated HCM is very large. Performance evaluations show that, compared with existing methods, the proposed method can construct -D HCMs with lower computation complexity and their outputs demonstrate strong randomness and complex ergodicity.

Measuring the density of a molecular cluster injector via visible emission from an electron beam.

PubMed

Lundberg, D P; Kaita, R; Majeski, R; Stotler, D P

2010-10-01

A method to measure the density distribution of a dense hydrogen gas jet is presented. A Mach 5.5 nozzle is cooled to 80 K to form a flow capable of molecular cluster formation. A 250 V, 10 mA electron beam collides with the jet and produces H(α) emission that is viewed by a fast camera. The high density of the jet, several 10(16) cm(-3), results in substantial electron depletion, which attenuates the H(α) emission. The attenuated emission measurement, combined with a simplified electron-molecule collision model, allows us to determine the molecular density profile via a simple iterative calculation.

K-Partite RNA Secondary Structures

NASA Astrophysics Data System (ADS)

Jiang, Minghui; Tejada, Pedro J.; Lasisi, Ramoni O.; Cheng, Shanhong; Fechser, D. Scott

RNA secondary structure prediction is a fundamental problem in structural bioinformatics. The prediction problem is difficult because RNA secondary structures may contain pseudoknots formed by crossing base pairs. We introduce k-partite secondary structures as a simple classification of RNA secondary structures with pseudoknots. An RNA secondary structure is k-partite if it is the union of k pseudoknot-free sub-structures. Most known RNA secondary structures are either bipartite or tripartite. We show that there exists a constant number k such that any secondary structure can be modified into a k-partite secondary structure with approximately the same free energy. This offers a partial explanation of the prevalence of k-partite secondary structures with small k. We give a complete characterization of the computational complexities of recognizing k-partite secondary structures for all k ≥ 2, and show that this recognition problem is essentially the same as the k-colorability problem on circle graphs. We present two simple heuristics, iterated peeling and first-fit packing, for finding k-partite RNA secondary structures. For maximizing the number of base pair stackings, our iterated peeling heuristic achieves a constant approximation ratio of at most k for 2 ≤ k ≤ 5, and at most frac6{1-(1-6/k)^k} le frac6{1-e^{-6}} < 6.01491 for k ≥ 6. Experiment on sequences from PseudoBase shows that our first-fit packing heuristic outperforms the leading method HotKnots in predicting RNA secondary structures with pseudoknots. Source code, data set, and experimental results are available at http://www.cs.usu.edu/ mjiang/rna/kpartite/.

Stokes space modulation format classification based on non-iterative clustering algorithm for coherent optical receivers.

PubMed

Mai, Xiaofeng; Liu, Jie; Wu, Xiong; Zhang, Qun; Guo, Changjian; Yang, Yanfu; Li, Zhaohui

2017-02-06

A Stokes-space modulation format classification (MFC) technique is proposed for coherent optical receivers by using a non-iterative clustering algorithm. In the clustering algorithm, two simple parameters are calculated to help find the density peaks of the data points in Stokes space and no iteration is required. Correct MFC can be realized in numerical simulations among PM-QPSK, PM-8QAM, PM-16QAM, PM-32QAM and PM-64QAM signals within practical optical signal-to-noise ratio (OSNR) ranges. The performance of the proposed MFC algorithm is also compared with those of other schemes based on clustering algorithms. The simulation results show that good classification performance can be achieved using the proposed MFC scheme with moderate time complexity. Proof-of-concept experiments are finally implemented to demonstrate MFC among PM-QPSK/16QAM/64QAM signals, which confirm the feasibility of our proposed MFC scheme.

Adaptive iterated function systems filter for images highly corrupted with fixed - Value impulse noise

NASA Astrophysics Data System (ADS)

Shanmugavadivu, P.; Eliahim Jeevaraj, P. S.

2014-06-01

The Adaptive Iterated Functions Systems (AIFS) Filter presented in this paper has an outstanding potential to attenuate the fixed-value impulse noise in images. This filter has two distinct phases namely noise detection and noise correction which uses Measure of Statistics and Iterated Function Systems (IFS) respectively. The performance of AIFS filter is assessed by three metrics namely, Peak Signal-to-Noise Ratio (PSNR), Mean Structural Similarity Index Matrix (MSSIM) and Human Visual Perception (HVP). The quantitative measures PSNR and MSSIM endorse the merit of this filter in terms of degree of noise suppression and details/edge preservation respectively, in comparison with the high performing filters reported in the recent literature. The qualitative measure HVP confirms the noise suppression ability of the devised filter. This computationally simple noise filter broadly finds application wherein the images are highly degraded by fixed-value impulse noise.

Decentralized control of sound radiation using iterative loop recovery.

PubMed

Schiller, Noah H; Cabell, Randolph H; Fuller, Chris R

2010-10-01

A decentralized model-based control strategy is designed to reduce low-frequency sound radiation from periodically stiffened panels. While decentralized control systems tend to be scalable, performance can be limited due to modeling error introduced by the unmodeled interaction between neighboring control units. Since bounds on modeling error are not known in advance, it is difficult to ensure the decentralized control system will be robust without making the controller overly conservative. Therefore an iterative approach is suggested, which utilizes frequency-shaped loop recovery. The approach accounts for modeling error introduced by neighboring control loops, requires no communication between subsystems, and is relatively simple. The control strategy is evaluated numerically using a model of a stiffened aluminum panel that is representative of the sidewall of an aircraft. Simulations demonstrate that the iterative approach can achieve significant reductions in radiated sound power from the stiffened panel without destabilizing neighboring control units.

Decentralized Control of Sound Radiation Using Iterative Loop Recovery

NASA Technical Reports Server (NTRS)

Schiller, Noah H.; Cabell, Randolph H.; Fuller, Chris R.

2009-01-01

A decentralized model-based control strategy is designed to reduce low-frequency sound radiation from periodically stiffened panels. While decentralized control systems tend to be scalable, performance can be limited due to modeling error introduced by the unmodeled interaction between neighboring control units. Since bounds on modeling error are not known in advance, it is difficult to ensure the decentralized control system will be robust without making the controller overly conservative. Therefore an iterative approach is suggested, which utilizes frequency-shaped loop recovery. The approach accounts for modeling error introduced by neighboring control loops, requires no communication between subsystems, and is relatively simple. The control strategy is evaluated numerically using a model of a stiffened aluminum panel that is representative of the sidewall of an aircraft. Simulations demonstrate that the iterative approach can achieve significant reductions in radiated sound power from the stiffened panel without destabilizing neighboring control units.

A strategy with novel evolutionary features for the iterated prisoner's dilemma.

PubMed

Li, Jiawei; Kendall, Graham

2009-01-01

In recent iterated prisoner's dilemma tournaments, the most successful strategies were those that had identification mechanisms. By playing a predetermined sequence of moves and learning from their opponents' responses, these strategies managed to identify their opponents. We believe that these identification mechanisms may be very useful in evolutionary games. In this paper one such strategy, which we call collective strategy, is analyzed. Collective strategies apply a simple but efficient identification mechanism (that just distinguishes themselves from other strategies), and this mechanism allows them to only cooperate with their group members and defect against any others. In this way, collective strategies are able to maintain a stable population in evolutionary iterated prisoner's dilemma. By means of an invasion barrier, this strategy is compared with other strategies in evolutionary dynamics in order to demonstrate its evolutionary features. We also find that this collective behavior assists the evolution of cooperation in specific evolutionary environments.

Accelerated Path-following Iterative Shrinkage Thresholding Algorithm with Application to Semiparametric Graph Estimation

PubMed Central

Zhao, Tuo; Liu, Han

2016-01-01

We propose an accelerated path-following iterative shrinkage thresholding algorithm (APISTA) for solving high dimensional sparse nonconvex learning problems. The main difference between APISTA and the path-following iterative shrinkage thresholding algorithm (PISTA) is that APISTA exploits an additional coordinate descent subroutine to boost the computational performance. Such a modification, though simple, has profound impact: APISTA not only enjoys the same theoretical guarantee as that of PISTA, i.e., APISTA attains a linear rate of convergence to a unique sparse local optimum with good statistical properties, but also significantly outperforms PISTA in empirical benchmarks. As an application, we apply APISTA to solve a family of nonconvex optimization problems motivated by estimating sparse semiparametric graphical models. APISTA allows us to obtain new statistical recovery results which do not exist in the existing literature. Thorough numerical results are provided to back up our theory. PMID:28133430

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

Turner, A.; Davis, A.; University of Wisconsin-Madison, Madison, WI 53706

CCFE perform Monte-Carlo transport simulations on large and complex tokamak models such as ITER. Such simulations are challenging since streaming and deep penetration effects are equally important. In order to make such simulations tractable, both variance reduction (VR) techniques and parallel computing are used. It has been found that the application of VR techniques in such models significantly reduces the efficiency of parallel computation due to 'long histories'. VR in MCNP can be accomplished using energy-dependent weight windows. The weight window represents an 'average behaviour' of particles, and large deviations in the arriving weight of a particle give rise tomore » extreme amounts of splitting being performed and a long history. When running on parallel clusters, a long history can have a detrimental effect on the parallel efficiency - if one process is computing the long history, the other CPUs complete their batch of histories and wait idle. Furthermore some long histories have been found to be effectively intractable. To combat this effect, CCFE has developed an adaptation of MCNP which dynamically adjusts the WW where a large weight deviation is encountered. The method effectively 'de-optimises' the WW, reducing the VR performance but this is offset by a significant increase in parallel efficiency. Testing with a simple geometry has shown the method does not bias the result. This 'long history method' has enabled CCFE to significantly improve the performance of MCNP calculations for ITER on parallel clusters, and will be beneficial for any geometry combining streaming and deep penetration effects. (authors)« less

Learning normalized inputs for iterative estimation in medical image segmentation.

PubMed

Drozdzal, Michal; Chartrand, Gabriel; Vorontsov, Eugene; Shakeri, Mahsa; Di Jorio, Lisa; Tang, An; Romero, Adriana; Bengio, Yoshua; Pal, Chris; Kadoury, Samuel

2018-02-01

In this paper, we introduce a simple, yet powerful pipeline for medical image segmentation that combines Fully Convolutional Networks (FCNs) with Fully Convolutional Residual Networks (FC-ResNets). We propose and examine a design that takes particular advantage of recent advances in the understanding of both Convolutional Neural Networks as well as ResNets. Our approach focuses upon the importance of a trainable pre-processing when using FC-ResNets and we show that a low-capacity FCN model can serve as a pre-processor to normalize medical input data. In our image segmentation pipeline, we use FCNs to obtain normalized images, which are then iteratively refined by means of a FC-ResNet to generate a segmentation prediction. As in other fully convolutional approaches, our pipeline can be used off-the-shelf on different image modalities. We show that using this pipeline, we exhibit state-of-the-art performance on the challenging Electron Microscopy benchmark, when compared to other 2D methods. We improve segmentation results on CT images of liver lesions, when contrasting with standard FCN methods. Moreover, when applying our 2D pipeline on a challenging 3D MRI prostate segmentation challenge we reach results that are competitive even when compared to 3D methods. The obtained results illustrate the strong potential and versatility of the pipeline by achieving accurate segmentations on a variety of image modalities and different anatomical regions. Copyright © 2017 Elsevier B.V. All rights reserved.

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

ULTRA-SHARP nonoscillatory convection schemes for high-speed steady multidimensional flow

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Mokhtari, Simin

1990-01-01

For convection-dominated flows, classical second-order methods are notoriously oscillatory and often unstable. For this reason, many computational fluid dynamicists have adopted various forms of (inherently stable) first-order upwinding over the past few decades. Although it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high convection conditions, these methods continue to enjoy widespread popularity for numerical heat transfer calculations, apparently due to a perceived lack of viable high accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as is shown, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high order accuracy, while requiring only a simple tridiagonal ADI line-solver, as used in the majority of general purpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high resolution nonoscillatory multidimensional steady state high speed convective modelling.

On a new method for calculating the potential flow past a body of revolution

NASA Technical Reports Server (NTRS)

Kaplan, Carl

1943-01-01

A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian profile itself. The use of this type of coordinate system yields a simple expression of the boundary condition at the surface of the solid and leads to a rational process of iteration for the solution of the differential equation for the velocity potential. It is shown that the velocity potential for an arbitrary body of revolution may be expressed in terms of universal functions which, although not normal, are obtainable by means of simple quadratures. The general results are applied to a body of revolution obtained by revolving a symmetrical Joukowski profile about its axis of symmetry. A numerical example further serves to illustrate the theory.

A multiscale method for modeling high-aspect-ratio micro/nano flows

NASA Astrophysics Data System (ADS)

Lockerby, Duncan; Borg, Matthew; Reese, Jason

2012-11-01

In this paper we present a new multiscale scheme for simulating micro/nano flows of high aspect ratio in the flow direction, e.g. within long ducts, tubes, or channels, of varying section. The scheme consists of applying a simple hydrodynamic description over the entire domain, and allocating micro sub-domains in very small ``slices'' of the channel. Every micro element is a molecular dynamics simulation (or other appropriate model, e.g., a direct simulation Monte Carlo method for micro-channel gas flows) over the local height of the channel/tube. The number of micro elements as well as their streamwise position is chosen to resolve the geometrical features of the macro channel. While there is no direct communication between individual micro elements, coupling occurs via an iterative imposition of mass and momentum-flux conservation on the macro scale. The greater the streamwise scale of the geometry, the more significant is the computational speed-up when compared to a full MD simulation. We test our new multiscale method on the case of a converging/diverging nanochannel conveying a simple Lennard-Jones liquid. We validate the results from our simulations by comparing them to a full MD simulation of the same test case. Supported by EPSRC Programme Grant, EP/I011927/1.

Measurement of surface tension by sessile drop tensiometer with superoleophobic surface

NASA Astrophysics Data System (ADS)

Kwak, Wonshik; Park, Jun Kwon; Yoon, Jinsung; Lee, Sanghyun; Hwang, Woonbong

2018-03-01

A sessile drop tensiometer provides a simple and efficient method of determining the surface tension of various liquids. The technique involves obtaining the shape of an axisymmetric liquid droplet and iterative fitting of the Young-Laplace equation, which balances the gravitational deformation of the drop. Since the advent of high quality digital cameras and desktop computers, this process has been automated with precision. However, despite its appealing simplicity, there are complications and limitations in a sessile drop tensiometer, i.e., it must dispense spherical droplets with low surface tension. We propose a method of measuring surface tension using a sessile drop tensiometer with a superoleophobic surface fabricated by acidic etching and anodization for liquids with low surface tension and investigate the accuracy of the measurement by changing the wettability of the measuring plate surface.

Computational method for the correction of proximity effect in electron-beam lithography (Poster Paper)

NASA Astrophysics Data System (ADS)

Chang, Chih-Yuan; Owen, Gerry; Pease, Roger Fabian W.; Kailath, Thomas

1992-07-01

Dose correction is commonly used to compensate for the proximity effect in electron lithography. The computation of the required dose modulation is usually carried out using 'self-consistent' algorithms that work by solving a large number of simultaneous linear equations. However, there are two major drawbacks: the resulting correction is not exact, and the computation time is excessively long. A computational scheme, as shown in Figure 1, has been devised to eliminate this problem by the deconvolution of the point spread function in the pattern domain. The method is iterative, based on a steepest descent algorithm. The scheme has been successfully tested on a simple pattern with a minimum feature size 0.5 micrometers , exposed on a MEBES tool at 10 KeV in 0.2 micrometers of PMMA resist on a silicon substrate.

Observations of the Geometry of Horizon-Based Optical Navigation

NASA Technical Reports Server (NTRS)

Christian, John; Robinson, Shane

2016-01-01

NASA's Orion Project has sparked a renewed interest in horizon-based optical navigation(OPNAV) techniques for spacecraft in the Earth-Moon system. Some approaches have begun to explore the geometry of horizon-based OPNAV and exploit the fact that it is a conic section problem. Therefore, the present paper focuses more deeply on understanding and leveraging the various geometric interpretations of horizon-based OPNAV. These results provide valuable insight into the fundamental workings of OPNAV solution methods, their convergence properties, and associated estimate covariance. Most importantly, the geometry and transformations uncovered in this paper lead to a simple and non-iterative solution to the generic horizon-based OPNAV problem. This represents a significant theoretical advancement over existing methods. Thus, we find that a clear understanding of geometric relationships is central to the prudent design, use, and operation of horizon-based OPNAV techniques.

Numerical study of read scheme in one-selector one-resistor crossbar array

NASA Astrophysics Data System (ADS)

Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin

2015-12-01

A comprehensive numerical circuit analysis of read schemes of a one selector-one resistance change memory (1S1R) crossbar array is carried out. Three schemes-the ground, V/2, and V/3 schemes-are compared with each other in terms of sensing margin and power consumption. Without the aid of a complex analytical approach or SPICE-based simulation, a simple numerical iteration method is developed to simulate entire current flows and node voltages within a crossbar array. Understanding such phenomena is essential in successfully evaluating the electrical specifications of selectors for suppressing intrinsic drawbacks of crossbar arrays, such as sneaky current paths and series line resistance problems. This method provides a quantitative tool for the accurate analysis of crossbar arrays and provides guidelines for developing an optimal read scheme, array configuration, and selector device specifications.

Deep Learning Nuclei Detection in Digitized Histology Images by Superpixels.

PubMed

Sornapudi, Sudhir; Stanley, Ronald Joe; Stoecker, William V; Almubarak, Haidar; Long, Rodney; Antani, Sameer; Thoma, George; Zuna, Rosemary; Frazier, Shelliane R

2018-01-01

Advances in image analysis and computational techniques have facilitated automatic detection of critical features in histopathology images. Detection of nuclei is critical for squamous epithelium cervical intraepithelial neoplasia (CIN) classification into normal, CIN1, CIN2, and CIN3 grades. In this study, a deep learning (DL)-based nuclei segmentation approach is investigated based on gathering localized information through the generation of superpixels using a simple linear iterative clustering algorithm and training with a convolutional neural network. The proposed approach was evaluated on a dataset of 133 digitized histology images and achieved an overall nuclei detection (object-based) accuracy of 95.97%, with demonstrated improvement over imaging-based and clustering-based benchmark techniques. The proposed DL-based nuclei segmentation Method with superpixel analysis has shown improved segmentation results in comparison to state-of-the-art methods.

Basic features of boron isotope separation by SILARC method in the two-step iterative static model

NASA Astrophysics Data System (ADS)

Lyakhov, K. A.; Lee, H. J.

2013-05-01

In this paper we develop a new static model for boron isotope separation by the laser assisted retardation of condensation method (SILARC) on the basis of model proposed by Jeff Eerkens. Our model is thought to be adequate to so-called two-step iterative scheme for isotope separation. This rather simple model helps to understand combined action on boron separation by SILARC method of all important parameters and relations between them. These parameters include carrier gas, molar fraction of BCl3 molecules in carrier gas, laser pulse intensity, gas pulse duration, gas pressure and temperature in reservoir and irradiation cells, optimal irradiation cell and skimmer chamber volumes, and optimal nozzle throughput. A method for finding optimal values of these parameters based on some objective function global minimum search was suggested. It turns out that minimum of this objective function is directly related to the minimum of total energy consumed, and total setup volume. Relations between nozzle throat area, IC volume, laser intensity, number of nozzles, number of vacuum pumps, and required isotope production rate were derived. Two types of industrial scale irradiation cells are compared. The first one has one large throughput slit nozzle, while the second one has numerous small nozzles arranged in parallel arrays for better overlap with laser beam. It is shown that the last one outperforms the former one significantly. It is argued that NO2 is the best carrier gas for boron isotope separation from the point of view of energy efficiency and Ar from the point of view of setup compactness.

Global Contrast Based Salient Region Detection.

PubMed

Cheng, Ming-Ming; Mitra, Niloy J; Huang, Xiaolei; Torr, Philip H S; Hu, Shi-Min

2015-03-01

Automatic estimation of salient object regions across images, without any prior assumption or knowledge of the contents of the corresponding scenes, enhances many computer vision and computer graphics applications. We introduce a regional contrast based salient object detection algorithm, which simultaneously evaluates global contrast differences and spatial weighted coherence scores. The proposed algorithm is simple, efficient, naturally multi-scale, and produces full-resolution, high-quality saliency maps. These saliency maps are further used to initialize a novel iterative version of GrabCut, namely SaliencyCut, for high quality unsupervised salient object segmentation. We extensively evaluated our algorithm using traditional salient object detection datasets, as well as a more challenging Internet image dataset. Our experimental results demonstrate that our algorithm consistently outperforms 15 existing salient object detection and segmentation methods, yielding higher precision and better recall rates. We also show that our algorithm can be used to efficiently extract salient object masks from Internet images, enabling effective sketch-based image retrieval (SBIR) via simple shape comparisons. Despite such noisy internet images, where the saliency regions are ambiguous, our saliency guided image retrieval achieves a superior retrieval rate compared with state-of-the-art SBIR methods, and additionally provides important target object region information.

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

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.

Real-time MRI-guided hyperthermia treatment using a fast adaptive algorithm

NASA Astrophysics Data System (ADS)

Stakhursky, Vadim L.; Arabe, Omar; Cheng, Kung-Shan; MacFall, James; Maccarini, Paolo; Craciunescu, Oana; Dewhirst, Mark; Stauffer, Paul; Das, Shiva K.

2009-04-01

Magnetic resonance (MR) imaging is promising for monitoring and guiding hyperthermia treatments. The goal of this work is to investigate the stability of an algorithm for online MR thermal image guided steering and focusing of heat into the target volume. The control platform comprised a four-antenna mini-annular phased array (MAPA) applicator operating at 140 MHz (used for extremity sarcoma heating) and a GE Signa Excite 1.5 T MR system, both of which were driven by a control workstation. MR proton resonance frequency shift images acquired during heating were used to iteratively update a model of the heated object, starting with an initial finite element computed model estimate. At each iterative step, the current model was used to compute a focusing vector, which was then used to drive the next iteration, until convergence. Perturbation of the driving vector was used to prevent the process from stalling away from the desired focus. Experimental validation of the performance of the automatic treatment platform was conducted with two cylindrical phantom studies, one homogeneous and one muscle equivalent with tumor tissue (conductivity 50% higher) inserted, with initial focal spots being intentionally rotated 90° and 50° away from the desired focus, mimicking initial setup errors in applicator rotation. The integrated MR-HT treatment platform steered the focus of heating into the desired target volume in two quite different phantom tissue loads which model expected patient treatment configurations. For the homogeneous phantom test where the target was intentionally offset by 90° rotation of the applicator, convergence to the proper phase focus in the target occurred after 16 iterations of the algorithm. For the more realistic test with a muscle equivalent phantom with tumor inserted with 50° applicator displacement, only two iterations were necessary to steer the focus into the tumor target. Convergence improved the heating efficacy (the ratio of integral temperature in the tumor to integral temperature in normal tissue) by up to six-fold, compared to the first iteration. The integrated MR-HT treatment algorithm successfully steered the focus of heating into the desired target volume for both the simple homogeneous and the more challenging muscle equivalent phantom with tumor insert models of human extremity sarcomas after 16 and 2 iterations, correspondingly. The adaptive method for MR thermal image guided focal steering shows promise when tested in phantom experiments on a four-antenna phased array applicator.

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.

Database searching and accounting of multiplexed precursor and product ion spectra from the data independent analysis of simple and complex peptide mixtures.

PubMed

Li, Guo-Zhong; Vissers, Johannes P C; Silva, Jeffrey C; Golick, Dan; Gorenstein, Marc V; Geromanos, Scott J

2009-03-01

A novel database search algorithm is presented for the qualitative identification of proteins over a wide dynamic range, both in simple and complex biological samples. The algorithm has been designed for the analysis of data originating from data independent acquisitions, whereby multiple precursor ions are fragmented simultaneously. Measurements used by the algorithm include retention time, ion intensities, charge state, and accurate masses on both precursor and product ions from LC-MS data. The search algorithm uses an iterative process whereby each iteration incrementally increases the selectivity, specificity, and sensitivity of the overall strategy. Increased specificity is obtained by utilizing a subset database search approach, whereby for each subsequent stage of the search, only those peptides from securely identified proteins are queried. Tentative peptide and protein identifications are ranked and scored by their relative correlation to a number of models of known and empirically derived physicochemical attributes of proteins and peptides. In addition, the algorithm utilizes decoy database techniques for automatically determining the false positive identification rates. The search algorithm has been tested by comparing the search results from a four-protein mixture, the same four-protein mixture spiked into a complex biological background, and a variety of other "system" type protein digest mixtures. The method was validated independently by data dependent methods, while concurrently relying on replication and selectivity. Comparisons were also performed with other commercially and publicly available peptide fragmentation search algorithms. The presented results demonstrate the ability to correctly identify peptides and proteins from data independent acquisition strategies with high sensitivity and specificity. They also illustrate a more comprehensive analysis of the samples studied; providing approximately 20% more protein identifications, compared to a more conventional data directed approach using the same identification criteria, with a concurrent increase in both sequence coverage and the number of modified peptides.

Inspiring Examples in Rearrangements of Infinite Series

ERIC Educational Resources Information Center

Ramasinghe, W.

2002-01-01

Simple examples are really encouraging in the understanding of rearrangements of infinite series, since many texts and teachers provide only existence theorems. In the absence of examples, an existence theorem is just a statement and lends little confidence to understanding. Iterated sums of double series seem to have a similar spirit of…

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.

Reliability of Hull Girder Ultimate Strength of Steel Ships

NASA Astrophysics Data System (ADS)

Da-wei, Gao; Gui-jie, Shi

2018-03-01

Hull girder ultimate strength is an evaluation index reflecting the true safety margin or structural redundancy about container ships. Especially, after the hull girder fracture accident of the MOL COMFORT, the 8,000TEU class large container ship, on June 17 2013, larger container ship safety has been paid on much more attention. In this paper, different methods of calculating hull girder ultimate strength are firstly discussed and compared with. The bending ultimate strength can be analyzed by nonlinear finite element method (NFEM) and increment-iterative method, and also the shear ultimate strength can be analyzed by NFEM and simple equations. Then, the probability distribution of hull girder wave loads and still water loads of container ship are summarized. At last, the reliability of hull girder ultimate strength under bending moment and shear forces for three container ships is analyzed by using a first order method. The conclusions can be applied to give guidance for ship design and safety evaluation.

Global Patch Matching

NASA Astrophysics Data System (ADS)

Huang, X.; Hu, K.; Ling, X.; Zhang, Y.; Lu, Z.; Zhou, G.

2017-09-01

This paper introduces a novel global patch matching method that focuses on how to remove fronto-parallel bias and obtain continuous smooth surfaces with assuming that the scenes covered by stereos are piecewise continuous. Firstly, simple linear iterative cluster method (SLIC) is used to segment the base image into a series of patches. Then, a global energy function, which consists of a data term and a smoothness term, is built on the patches. The data term is the second-order Taylor expansion of correlation coefficients, and the smoothness term is built by combing connectivity constraints and the coplanarity constraints are combined to construct the smoothness term. Finally, the global energy function can be built by combining the data term and the smoothness term. We rewrite the global energy function in a quadratic matrix function, and use least square methods to obtain the optimal solution. Experiments on Adirondack stereo and Motorcycle stereo of Middlebury benchmark show that the proposed method can remove fronto-parallel bias effectively, and produce continuous smooth surfaces.

Calibration of stereo rigs based on the backward projection process

NASA Astrophysics Data System (ADS)

Gu, Feifei; Zhao, Hong; Ma, Yueyang; Bu, Penghui; Zhao, Zixin

2016-08-01

High-accuracy 3D measurement based on binocular vision system is heavily dependent on the accurate calibration of two rigidly-fixed cameras. In most traditional calibration methods, stereo parameters are iteratively optimized through the forward imaging process (FIP). However, the results can only guarantee the minimal 2D pixel errors, but not the minimal 3D reconstruction errors. To address this problem, a simple method to calibrate a stereo rig based on the backward projection process (BPP) is proposed. The position of a spatial point can be determined separately from each camera by planar constraints provided by the planar pattern target. Then combined with pre-defined spatial points, intrinsic and extrinsic parameters of the stereo-rig can be optimized by minimizing the total 3D errors of both left and right cameras. An extensive performance study for the method in the presence of image noise and lens distortions is implemented. Experiments conducted on synthetic and real data demonstrate the accuracy and robustness of the proposed method.

A new parametric method to smooth time-series data of metabolites in metabolic networks.

PubMed

Miyawaki, Atsuko; Sriyudthsak, Kansuporn; Hirai, Masami Yokota; Shiraishi, Fumihide

2016-12-01

Mathematical modeling of large-scale metabolic networks usually requires smoothing of metabolite time-series data to account for measurement or biological errors. Accordingly, the accuracy of smoothing curves strongly affects the subsequent estimation of model parameters. Here, an efficient parametric method is proposed for smoothing metabolite time-series data, and its performance is evaluated. To simplify parameter estimation, the method uses S-system-type equations with simple power law-type efflux terms. Iterative calculation using this method was found to readily converge, because parameters are estimated stepwise. Importantly, smoothing curves are determined so that metabolite concentrations satisfy mass balances. Furthermore, the slopes of smoothing curves are useful in estimating parameters, because they are probably close to their true behaviors regardless of errors that may be present in the actual data. Finally, calculations for each differential equation were found to converge in much less than one second if initial parameters are set at appropriate (guessed) values. Copyright © 2016 Elsevier Inc. All rights reserved.

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

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.

A new multistage groundwater transport inverse method: presentation, evaluation, and implications

USGS Publications Warehouse

Anderman, Evan R.; Hill, Mary C.

1999-01-01

More computationally efficient methods of using concentration data are needed to estimate groundwater flow and transport parameters. This work introduces and evaluates a three‐stage nonlinear‐regression‐based iterative procedure in which trial advective‐front locations link decoupled flow and transport models. Method accuracy and efficiency are evaluated by comparing results to those obtained when flow‐ and transport‐model parameters are estimated simultaneously. The new method is evaluated as conclusively as possible by using a simple test case that includes distinct flow and transport parameters, but does not include any approximations that are problem dependent. The test case is analytical; the only flow parameter is a constant velocity, and the transport parameters are longitudinal and transverse dispersivity. Any difficulties detected using the new method in this ideal situation are likely to be exacerbated in practical problems. Monte‐Carlo analysis of observation error ensures that no specific error realization obscures the results. Results indicate that, while this, and probably other, multistage methods do not always produce optimal parameter estimates, the computational advantage may make them useful in some circumstances, perhaps as a precursor to using a simultaneous method.

General method of solving the Schroedinger equation of atoms and molecules

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

Nakatsuji, Hiroshi

2005-12-15

We propose a general method of solving the Schroedinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schroedinger equation and related principles, we can avoid the singularity problem of atoms and molecules and formulate a general method of calculating the exact wave functions in an analytical expansion form. We choose initial function {psi}{sub 0} and scaling g function, and then the ICI method automatically generates the wave function that hasmore » the exact structure by using the Hamiltonian of the system. The Hamiltonian contains all the information of the system. The free ICI method provides a flexible and variationally favorable procedure of constructing the exact wave function. We explain the computational procedure of the analytical ICI method routinely performed in our laboratory. Simple examples are given using hydrogen atom for the nuclear singularity case, the Hooke's atom for the electron singularity case, and the helium atom for both cases.« less

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.

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

Locations of Sampling Stations for Water Quality Monitoring in Water Distribution Networks.

PubMed

Rathi, Shweta; Gupta, Rajesh

2014-04-01

Water quality is required to be monitored in the water distribution networks (WDNs) at salient locations to assure the safe quality of water supplied to the consumers. Such monitoring stations (MSs) provide warning against any accidental contaminations. Various objectives like demand coverage, time for detection, volume of water contaminated before detection, extent of contamination, expected population affected prior to detection, detection likelihood and others, have been independently or jointly considered in determining optimal number and location of MSs in WDNs. "Demand coverage" defined as the percentage of network demand monitored by a particular monitoring station is a simple measure to locate MSs. Several methods based on formulation of coverage matrix using pre-specified coverage criteria and optimization have been suggested. Coverage criteria is defined as some minimum percentage of total flow received at the monitoring stations that passed through any upstream node included then as covered node of the monitoring station. Number of monitoring stations increases with the increase in the value of coverage criteria. Thus, the design of monitoring station becomes subjective. A simple methodology is proposed herein which priority wise iteratively selects MSs to achieve targeted demand coverage. The proposed methodology provided the same number and location of MSs for illustrative network as an optimization method did. Further, the proposed method is simple and avoids subjectivity that could arise from the consideration of coverage criteria. The application of methodology is also shown on a WDN of Dharampeth zone (Nagpur city WDN in Maharashtra, India) having 285 nodes and 367 pipes.

Calculation of three-dimensional (3-D) internal flow by means of the velocity-vorticity formulation on a staggered grid

NASA Technical Reports Server (NTRS)

Stremel, Paul M.

1995-01-01

A method has been developed to accurately compute the viscous flow in three-dimensional (3-D) enclosures. This method is the 3-D extension of a two-dimensional (2-D) method developed for the calculation of flow over airfoils. The 2-D method has been tested extensively and has been shown to accurately reproduce experimental results. As in the 2-D method, the 3-D method provides for the non-iterative solution of the incompressible Navier-Stokes equations by means of a fully coupled implicit technique. The solution is calculated on a body fitted computational mesh incorporating a staggered grid methodology. In the staggered grid method, the three components of vorticity are defined at the centers of the computational cell sides, while the velocity components are defined as normal vectors at the centers of the computational cell faces. The staggered grid orientation provides for the accurate definition of the vorticity components at the vorticity locations, the divergence of vorticity at the mesh cell nodes and the conservation of mass at the mesh cell centers. The solution is obtained by utilizing a fractional step solution technique in the three coordinate directions. The boundary conditions for the vorticity and velocity are calculated implicitly as part of the solution. The method provides for the non-iterative solution of the flow field and satisfies the conservation of mass and divergence of vorticity to machine zero at each time step. To test the method, the calculation of simple driven cavity flows have been computed. The driven cavity flow is defined as the flow in an enclosure driven by a moving upper plate at the top of the enclosure. To demonstrate the ability of the method to predict the flow in arbitrary cavities, results will he shown for both cubic and curved cavities.

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.

Digital image classification with the help of artificial neural network by simple histogram

PubMed Central

Dey, Pranab; Banerjee, Nirmalya; Kaur, Rajwant

2016-01-01

Background: Visual image classification is a great challenge to the cytopathologist in routine day-to-day work. Artificial neural network (ANN) may be helpful in this matter. Aims and Objectives: In this study, we have tried to classify digital images of malignant and benign cells in effusion cytology smear with the help of simple histogram data and ANN. Materials and Methods: A total of 404 digital images consisting of 168 benign cells and 236 malignant cells were selected for this study. The simple histogram data was extracted from these digital images and an ANN was constructed with the help of Neurointelligence software [Alyuda Neurointelligence 2.2 (577), Cupertino, California, USA]. The network architecture was 6-3-1. The images were classified as training set (281), validation set (63), and test set (60). The on-line backpropagation training algorithm was used for this study. Result: A total of 10,000 iterations were done to train the ANN system with the speed of 609.81/s. After the adequate training of this ANN model, the system was able to identify all 34 malignant cell images and 24 out of 26 benign cells. Conclusion: The ANN model can be used for the identification of the individual malignant cells with the help of simple histogram data. This study will be helpful in the future to identify malignant cells in unknown situations. PMID:27279679

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

Sparse-view proton computed tomography using modulated proton beams.

PubMed

Lee, Jiseoc; Kim, Changhwan; Min, Byungjun; Kwak, Jungwon; Park, Seyjoon; Lee, Se Byeong; Park, Sungyong; Cho, Seungryong

2015-02-01

Proton imaging that uses a modulated proton beam and an intensity detector allows a relatively fast image acquisition compared to the imaging approach based on a trajectory tracking detector. In addition, it requires a relatively simple implementation in a conventional proton therapy equipment. The model of geometric straight ray assumed in conventional computed tomography (CT) image reconstruction is however challenged by multiple-Coulomb scattering and energy straggling in the proton imaging. Radiation dose to the patient is another important issue that has to be taken care of for practical applications. In this work, the authors have investigated iterative image reconstructions after a deconvolution of the sparsely view-sampled data to address these issues in proton CT. Proton projection images were acquired using the modulated proton beams and the EBT2 film as an intensity detector. Four electron-density cylinders representing normal soft tissues and bone were used as imaged object and scanned at 40 views that are equally separated over 360°. Digitized film images were converted to water-equivalent thickness by use of an empirically derived conversion curve. For improving the image quality, a deconvolution-based image deblurring with an empirically acquired point spread function was employed. They have implemented iterative image reconstruction algorithms such as adaptive steepest descent-projection onto convex sets (ASD-POCS), superiorization method-projection onto convex sets (SM-POCS), superiorization method-expectation maximization (SM-EM), and expectation maximization-total variation minimization (EM-TV). Performance of the four image reconstruction algorithms was analyzed and compared quantitatively via contrast-to-noise ratio (CNR) and root-mean-square-error (RMSE). Objects of higher electron density have been reconstructed more accurately than those of lower density objects. The bone, for example, has been reconstructed within 1% error. EM-based algorithms produced an increased image noise and RMSE as the iteration reaches about 20, while the POCS-based algorithms showed a monotonic convergence with iterations. The ASD-POCS algorithm outperformed the others in terms of CNR, RMSE, and the accuracy of the reconstructed relative stopping power in the region of lung and soft tissues. The four iterative algorithms, i.e., ASD-POCS, SM-POCS, SM-EM, and EM-TV, have been developed and applied for proton CT image reconstruction. Although it still seems that the images need to be improved for practical applications to the treatment planning, proton CT imaging by use of the modulated beams in sparse-view sampling has demonstrated its feasibility.

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.

Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for Lp-Regularization Using the Multiple Sub-Dictionary Representation

PubMed Central

Zhang, Jie; Fan, Shangang; Xiong, Jian; Cheng, Xiefeng; Sari, Hikmet; Adachi, Fumiyuki

2017-01-01

Both L1/2 and L2/3 are two typical non-convex regularizations of Lp (0

Autocratic strategies for iterated games with arbitrary action spaces.

PubMed

McAvoy, Alex; Hauert, Christoph

2016-03-29

The recent discovery of zero-determinant strategies for the iterated prisoner's dilemma sparked a surge of interest in the surprising fact that a player can exert unilateral control over iterated interactions. These remarkable strategies, however, are known to exist only in games in which players choose between two alternative actions such as "cooperate" and "defect." Here we introduce a broader class of autocratic strategies by extending zero-determinant strategies to iterated games with more general action spaces. We use the continuous donation game as an example, which represents an instance of the prisoner's dilemma that intuitively extends to a continuous range of cooperation levels. Surprisingly, despite the fact that the opponent has infinitely many donation levels from which to choose, a player can devise an autocratic strategy to enforce a linear relationship between his or her payoff and that of the opponent even when restricting his or her actions to merely two discrete levels of cooperation. In particular, a player can use such a strategy to extort an unfair share of the payoffs from the opponent. Therefore, although the action space of the continuous donation game dwarfs that of the classic prisoner's dilemma, players can still devise relatively simple autocratic and, in particular, extortionate strategies.

Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for Lp-Regularization Using the Multiple Sub-Dictionary Representation.

PubMed

Li, Yunyi; Zhang, Jie; Fan, Shangang; Yang, Jie; Xiong, Jian; Cheng, Xiefeng; Sari, Hikmet; Adachi, Fumiyuki; Gui, Guan

2017-12-15

Both L 1/2 and L 2/3 are two typical non-convex regularizations of L p (0

CALCULATION OF GAMMA SPECTRA IN A PLASTIC SCINTILLATOR FOR ENERGY CALIBRATIONAND DOSE COMPUTATION.

PubMed

Kim, Chankyu; Yoo, Hyunjun; Kim, Yewon; Moon, Myungkook; Kim, Jong Yul; Kang, Dong Uk; Lee, Daehee; Kim, Myung Soo; Cho, Minsik; Lee, Eunjoong; Cho, Gyuseong

2016-09-01

Plastic scintillation detectors have practical advantages in the field of dosimetry. Energy calibration of measured gamma spectra is important for dose computation, but it is not simple in the plastic scintillators because of their different characteristics and a finite resolution. In this study, the gamma spectra in a polystyrene scintillator were calculated for the energy calibration and dose computation. Based on the relationship between the energy resolution and estimated energy broadening effect in the calculated spectra, the gamma spectra were simply calculated without many iterations. The calculated spectra were in agreement with the calculation by an existing method and measurements. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

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.

Comparison of some optimal control methods for the design of turbine blades

NASA Technical Reports Server (NTRS)

Desilva, B. M. E.; Grant, G. N. C.

1977-01-01

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Program VSAERO theory document: A computer program for calculating nonlinear aerodynamic characteristics of arbitrary configurations

NASA Technical Reports Server (NTRS)

Maskew, Brian

1987-01-01

The VSAERO low order panel method formulation is described for the calculation of subsonic aerodynamic characteristics of general configurations. The method is based on piecewise constant doublet and source singularities. Two forms of the internal Dirichlet boundary condition are discussed and the source distribution is determined by the external Neumann boundary condition. A number of basic test cases are examined. Calculations are compared with higher order solutions for a number of cases. It is demonstrated that for comparable density of control points where the boundary conditions are satisfied, the low order method gives comparable accuracy to the higher order solutions. It is also shown that problems associated with some earlier low order panel methods, e.g., leakage in internal flows and junctions and also poor trailing edge solutions, do not appear for the present method. Further, the application of the Kutta conditions is extremely simple; no extra equation or trailing edge velocity point is required. The method has very low computing costs and this has made it practical for application to nonlinear problems requiring iterative solutions for wake shape and surface boundary layer effects.

A new ghost-node method for linking different models and initial investigations of heterogeneity and nonmatching grids

USGS Publications Warehouse

Dickinson, J.E.; James, S.C.; Mehl, S.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Faunt, C.C.; Eddebbarh, A.-A.

2007-01-01

A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly heterogeneous systems. ?? 2007 Elsevier Ltd. All rights reserved.

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

Intelligent model-based OPC

NASA Astrophysics Data System (ADS)

Huang, W. C.; Lai, C. M.; Luo, B.; Tsai, C. K.; Chih, M. H.; Lai, C. W.; Kuo, C. C.; Liu, R. G.; Lin, H. T.

2006-03-01

Optical proximity correction is the technique of pre-distorting mask layouts so that the printed patterns are as close to the desired shapes as possible. For model-based optical proximity correction, a lithographic model to predict the edge position (contour) of patterns on the wafer after lithographic processing is needed. Generally, segmentation of edges is performed prior to the correction. Pattern edges are dissected into several small segments with corresponding target points. During the correction, the edges are moved back and forth from the initial drawn position, assisted by the lithographic model, to finally settle on the proper positions. When the correction converges, the intensity predicted by the model in every target points hits the model-specific threshold value. Several iterations are required to achieve the convergence and the computation time increases with the increase of the required iterations. An artificial neural network is an information-processing paradigm inspired by biological nervous systems, such as how the brain processes information. It is composed of a large number of highly interconnected processing elements (neurons) working in unison to solve specific problems. A neural network can be a powerful data-modeling tool that is able to capture and represent complex input/output relationships. The network can accurately predict the behavior of a system via the learning procedure. A radial basis function network, a variant of artificial neural network, is an efficient function approximator. In this paper, a radial basis function network was used to build a mapping from the segment characteristics to the edge shift from the drawn position. This network can provide a good initial guess for each segment that OPC has carried out. The good initial guess reduces the required iterations. Consequently, cycle time can be shortened effectively. The optimization of the radial basis function network for this system was practiced by genetic algorithm, which is an artificially intelligent optimization method with a high probability to obtain global optimization. From preliminary results, the required iterations were reduced from 5 to 2 for a simple dumbbell-shape layout.

Nonlinear random response prediction using MSC/NASTRAN

NASA Technical Reports Server (NTRS)

Robinson, J. H.; Chiang, C. K.; Rizzi, S. A.

1993-01-01

An equivalent linearization technique was incorporated into MSC/NASTRAN to predict the nonlinear random response of structures by means of Direct Matrix Abstract Programming (DMAP) modifications and inclusion of the nonlinear differential stiffness module inside the iteration loop. An iterative process was used to determine the rms displacements. Numerical results obtained for validation on simple plates and beams are in good agreement with existing solutions in both the linear and linearized regions. The versatility of the implementation will enable the analyst to determine the nonlinear random responses for complex structures under combined loads. The thermo-acoustic response of a hexagonal thermal protection system panel is used to highlight some of the features of the program.

Computer Simulation and Experiments on the Quasi-Static Mechanics and Transport Properties of Granular Materials

DTIC Science & Technology

1993-10-01

ismalzO cif(iprepk.eq.2)istp=1 c--anumber of cyclic shearings for packing or steps for simple shear do 598 istaistold+1,istold+istp 3 icheck =0 iter3O0...lowstrn=0 highstrna=0 nostop=O I692 i~tr.e3adnso~qOte icheck ~ icheck +1 call rmatx-.copy(3,3,struO,stru)I else if(lowstrn.it .2)then icheck ~ icheck +1 do...690 i=1,3 do 690 j=1,3 strn(i,j)=strn(i,j)/2.0 690 continueI lowstrn=lowstrn+l iter3O0 if(nostop. eq. 1)nostop=0 if (highutrn. eq. 0)then icheck

Iterative categorization (IC): a systematic technique for analysing qualitative data

PubMed Central

2016-01-01

Abstract The processes of analysing qualitative data, particularly the stage between coding and publication, are often vague and/or poorly explained within addiction science and research more broadly. A simple but rigorous and transparent technique for analysing qualitative textual data, developed within the field of addiction, is described. The technique, iterative categorization (IC), is suitable for use with inductive and deductive codes and can support a range of common analytical approaches, e.g. thematic analysis, Framework, constant comparison, analytical induction, content analysis, conversational analysis, discourse analysis, interpretative phenomenological analysis and narrative analysis. Once the data have been coded, the only software required is a standard word processing package. Worked examples are provided. PMID:26806155

Fast inverse scattering solutions using the distorted Born iterative method and the multilevel fast multipole algorithm

PubMed Central

Hesford, Andrew J.; Chew, Weng C.

2010-01-01

The distorted Born iterative method (DBIM) computes iterative solutions to nonlinear inverse scattering problems through successive linear approximations. By decomposing the scattered field into a superposition of scattering by an inhomogeneous background and by a material perturbation, large or high-contrast variations in medium properties can be imaged through iterations that are each subject to the distorted Born approximation. However, the need to repeatedly compute forward solutions still imposes a very heavy computational burden. To ameliorate this problem, the multilevel fast multipole algorithm (MLFMA) has been applied as a forward solver within the DBIM. The MLFMA computes forward solutions in linear time for volumetric scatterers. The typically regular distribution and shape of scattering elements in the inverse scattering problem allow the method to take advantage of data redundancy and reduce the computational demands of the normally expensive MLFMA setup. Additional benefits are gained by employing Kaczmarz-like iterations, where partial measurements are used to accelerate convergence. Numerical results demonstrate both the efficiency of the forward solver and the successful application of the inverse method to imaging problems with dimensions in the neighborhood of ten wavelengths. PMID:20707438

An Efficient, Non-iterative Method of Identifying the Cost-Effectiveness Frontier

PubMed Central

Suen, Sze-chuan; Goldhaber-Fiebert, Jeremy D.

2015-01-01

Cost-effectiveness analysis aims to identify treatments and policies that maximize benefits subject to resource constraints. However, the conventional process of identifying the efficient frontier (i.e., the set of potentially cost-effective options) can be algorithmically inefficient, especially when considering a policy problem with many alternative options or when performing an extensive suite of sensitivity analyses for which the efficient frontier must be found for each. Here, we describe an alternative one-pass algorithm that is conceptually simple, easier to implement, and potentially faster for situations that challenge the conventional approach. Our algorithm accomplishes this by exploiting the relationship between the net monetary benefit and the cost-effectiveness plane. To facilitate further evaluation and use of this approach, we additionally provide scripts in R and Matlab that implement our method and can be used to identify efficient frontiers for any decision problem. PMID:25926282

Extended estimator approach for 2×2 games and its mapping to the Ising Hamiltonian

NASA Astrophysics Data System (ADS)

Ariosa, D.; Fort, H.

2005-01-01

We consider a system of adaptive self-interested agents interacting by playing an iterated pairwise prisoner’s dilemma (PD) game. Each player has two options: either cooperate (C) or defect (D). Agents have no (long term) memory to reciprocate nor identifying tags to distinguish C from D. We show how their 16 possible elementary Markovian (one-step memory) strategies can be cast in a simple general formalism in terms of an estimator of expected utilities Δ* . This formalism is helpful to map a subset of these strategies into an Ising Hamiltonian in a straightforward way. This connection in turn serves to shed light on the evolution of the iterated games played by agents, which can represent a broad variety of individuals from firms of a market to species coexisting in an ecosystem. Additionally, this magnetic description may be useful to introduce noise in a natural and simple way. The equilibrium states reached by the system depend strongly on whether the dynamics are synchronous or asynchronous and also on the system connectivity.

Quasi-perfect FIFO: Synchronous or asynchronous with application in controller design for the UNICON laser memory. [digital memory and buffer storage

NASA Technical Reports Server (NTRS)

Lim, R. S.

1974-01-01

The first-in-first-out memory buffer (FIFO), is an elastic digital memory whose main application is in data buffering between devices operating at different rates. Data written into the top is moved autonomously down toward the bottom of the FIFO to the lowest unoccupied location, and data read from the bottom of the FIFO will cause data from the top to move autonomously down toward the bottom. The FIFO is available in MOS LSI asynchronous form with data rate in the 1 MHz region. The FIFO described yields a simple high-speed iterative implementation, either synchronous of asynchronous. Because of this simple iterative structure, the FIFO is expandable in both number of words and bits per word, and it is attractive from the viewpoint of integrated-circuit production. For the synchronous FIFO, a model was built and successfully used in the controller for the UNICON laser memory. For the asynchronous FIFO, a model was built and also successfully used in a high-performance magnetic tape controller.

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…

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

Techniques and Software for Monolithic Preconditioning of Moderately-sized Geodynamic Stokes Flow Problems

NASA Astrophysics Data System (ADS)

Sanan, Patrick; May, Dave A.; Schenk, Olaf; Bollhöffer, Matthias

2017-04-01

Geodynamics simulations typically involve the repeated solution of saddle-point systems arising from the Stokes equations. These computations often dominate the time to solution. Direct solvers are known for their robustness and ``black box'' properties, yet exhibit superlinear memory requirements and time to solution. More complex multilevel-preconditioned iterative solvers have been very successful for large problems, yet their use can require more effort from the practitioner in terms of setting up a solver and choosing its parameters. We champion an intermediate approach, based on leveraging the power of modern incomplete factorization techniques for indefinite symmetric matrices. These provide an interesting alternative in situations in between the regimes where direct solvers are an obvious choice and those where complex, scalable, iterative solvers are an obvious choice. That is, much like their relatives for definite systems, ILU/ICC-preconditioned Krylov methods and ILU/ICC-smoothed multigrid methods, the approaches demonstrated here provide a useful addition to the solver toolkit. We present results with a simple, PETSc-based, open-source Q2-Q1 (Taylor-Hood) finite element discretization, in 2 and 3 dimensions, with the Stokes and Lamé (linear elasticity) saddle point systems. Attention is paid to cases in which full-operator incomplete factorization gives an improvement in time to solution over direct solution methods (which may not even be feasible due to memory limitations), without the complication of more complex (or at least, less-automatic) preconditioners or smoothers. As an important factor in the relevance of these tools is their availability in portable software, we also describe open-source PETSc interfaces to the factorization routines.

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.

Effective Iterated Greedy Algorithm for Flow-Shop Scheduling Problems with Time lags

NASA Astrophysics Data System (ADS)

ZHAO, Ning; YE, Song; LI, Kaidian; CHEN, Siyu

2017-05-01

Flow shop scheduling problem with time lags is a practical scheduling problem and attracts many studies. Permutation problem(PFSP with time lags) is concentrated but non-permutation problem(non-PFSP with time lags) seems to be neglected. With the aim to minimize the makespan and satisfy time lag constraints, efficient algorithms corresponding to PFSP and non-PFSP problems are proposed, which consist of iterated greedy algorithm for permutation(IGTLP) and iterated greedy algorithm for non-permutation (IGTLNP). The proposed algorithms are verified using well-known simple and complex instances of permutation and non-permutation problems with various time lag ranges. The permutation results indicate that the proposed IGTLP can reach near optimal solution within nearly 11% computational time of traditional GA approach. The non-permutation results indicate that the proposed IG can reach nearly same solution within less than 1% computational time compared with traditional GA approach. The proposed research combines PFSP and non-PFSP together with minimal and maximal time lag consideration, which provides an interesting viewpoint for industrial implementation.

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

A coloured oil level indicator detection method based on simple linear iterative clustering

NASA Astrophysics Data System (ADS)

Liu, Tianli; Li, Dongsong; Jiao, Zhiming; Liang, Tao; Zhou, Hao; Yang, Guoqing

2017-12-01

A detection method of coloured oil level indicator is put forward. The method is applied to inspection robot in substation, which realized the automatic inspection and recognition of oil level indicator. Firstly, the detected image of the oil level indicator is collected, and the detected image is clustered and segmented to obtain the label matrix of the image. Secondly, the detection image is processed by colour space transformation, and the feature matrix of the image is obtained. Finally, the label matrix and feature matrix are used to locate and segment the detected image, and the upper edge of the recognized region is obtained. If the upper limb line exceeds the preset oil level threshold, the alarm will alert the station staff. Through the above-mentioned image processing, the inspection robot can independently recognize the oil level of the oil level indicator, and instead of manual inspection. It embodies the automatic and intelligent level of unattended operation.

a Cloud Boundary Detection Scheme Combined with Aslic and Cnn Using ZY-3, GF-1/2 Satellite Imagery

NASA Astrophysics Data System (ADS)

Guo, Z.; Li, C.; Wang, Z.; Kwok, E.; Wei, X.

2018-04-01

Remote sensing optical image cloud detection is one of the most important problems in remote sensing data processing. Aiming at the information loss caused by cloud cover, a cloud detection method based on convolution neural network (CNN) is presented in this paper. Firstly, a deep CNN network is used to extract the multi-level feature generation model of cloud from the training samples. Secondly, the adaptive simple linear iterative clustering (ASLIC) method is used to divide the detected images into superpixels. Finally, the probability of each superpixel belonging to the cloud region is predicted by the trained network model, thereby generating a cloud probability map. The typical region of GF-1/2 and ZY-3 were selected to carry out the cloud detection test, and compared with the traditional SLIC method. The experiment results show that the average accuracy of cloud detection is increased by more than 5 %, and it can detected thin-thick cloud and the whole cloud boundary well on different imaging platforms.

Mission and system optimization of nuclear electric propulsion vehicles for lunar and Mars missions

NASA Technical Reports Server (NTRS)

Gilland, James H.

1991-01-01

The detailed mission and system optimization of low thrust electric propulsion missions is a complex, iterative process involving interaction between orbital mechanics and system performance. Through the use of appropriate approximations, initial system optimization and analysis can be performed for a range of missions. The intent of these calculations is to provide system and mission designers with simple methods to assess system design without requiring access or detailed knowledge of numerical calculus of variations optimizations codes and methods. Approximations for the mission/system optimization of Earth orbital transfer and Mars mission have been derived. Analyses include the variation of thruster efficiency with specific impulse. Optimum specific impulse, payload fraction, and power/payload ratios are calculated. The accuracy of these methods is tested and found to be reasonable for initial scoping studies. Results of optimization for Space Exploration Initiative lunar cargo and Mars missions are presented for a range of power system and thruster options.

Stochastic Spectral Descent for Discrete Graphical Models

DOE PAGES

Carlson, David; Hsieh, Ya-Ping; Collins, Edo; ...

2015-12-14

Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted asmore » gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.« 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.

Simplified multiple headspace extraction gas chromatographic technique for determination of monomer solubility in water.

PubMed

Chai, X S; Schork, F J; DeCinque, Anthony

2005-04-08

This paper reports an improved headspace gas chromatographic (GC) technique for determination of monomer solubilities in water. The method is based on a multiple headspace extraction GC technique developed previously [X.S. Chai, Q.X. Hou, F.J. Schork, J. Appl. Polym. Sci., in press], but with the major modification in the method calibration technique. As a result, only a few iterations of headspace extraction and GC measurement are required, which avoids the "exhaustive" headspace extraction, and thus the experimental time for each analysis. For highly insoluble monomers, effort must be made to minimize adsorption in the headspace sampling channel, transportation conduit and capillary column by using higher operating temperature and a short capillary column in the headspace sampler and GC system. For highly water soluble monomers, a new calibration method is proposed. The combinations of these technique modifications results in a method that is simple, rapid and automated. While the current focus of the authors is on the determination of monomer solubility in aqueous solutions, the method should be applicable to determination of solubility of any organic in water.

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.

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.

A wave superposition method formulated in digital acoustic space

NASA Astrophysics Data System (ADS)

Hwang, Yong-Sin

In this thesis, a new formulation of the Wave Superposition method is proposed wherein the conventional mesh approach is replaced by a simple 3-D digital work space that easily accommodates shape optimization for minimizing or maximizing radiation efficiency. As sound quality is in demand in almost all product designs and also because of fierce competition between product manufacturers, faster and accurate computational method for shape optimization is always desired. Because the conventional Wave Superposition method relies solely on mesh geometry, it cannot accommodate fast shape changes in the design stage of a consumer product or machinery, where many iterations of shape changes are required. Since the use of a mesh hinders easy shape changes, a new approach for representing geometry is introduced by constructing a uniform lattice in a 3-D digital work space. A voxel (a portmanteau, a new word made from combining the sound and meaning, of the words, volumetric and pixel) is essentially a volume element defined by the uniform lattice, and does not require separate connectivity information as a mesh element does. In the presented method, geometry is represented with voxels that can easily adapt to shape changes, therefore it is more suitable for shape optimization. The new method was validated by computing radiated sound power of structures of simple and complex geometries and complex mode shapes. It was shown that matching volume velocity is a key component to an accurate analysis. A sensitivity study showed that it required at least 6 elements per acoustic wavelength, and a complexity study showed a minimal reduction in computational time.

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

When Homoplasy Is Not Homoplasy: Dissecting Trait Evolution by Contrasting Composite and Reductive Coding.

PubMed

Torres-Montúfar, Alejandro; Borsch, Thomas; Ochoterena, Helga

2018-05-01

The conceptualization and coding of characters is a difficult issue in phylogenetic systematics, no matter which inference method is used when reconstructing phylogenetic trees or if the characters are just mapped onto a specific tree. Complex characters are groups of features that can be divided into simpler hierarchical characters (reductive coding), although the implied hierarchical relational information may change depending on the type of coding (composite vs. reductive). Up to now, there is no common agreement to either code characters as complex or simple. Phylogeneticists have discussed which coding method is best but have not incorporated the heuristic process of reciprocal illumination to evaluate the coding. Composite coding allows to test whether 1) several characters were linked resulting in a structure described as a complex character or trait or 2) independently evolving characters resulted in the configuration incorrectly interpreted as a complex character. We propose that complex characters or character states should be decomposed iteratively into simpler characters when the original homology hypothesis is not corroborated by a phylogenetic analysis, and the character or character state is retrieved as homoplastic. We tested this approach using the case of fruit types within subfamily Cinchonoideae (Rubiaceae). The iterative reductive coding of characters associated with drupes allowed us to unthread fruit evolution within Cinchonoideae. Our results show that drupes and berries are not homologous. As a consequence, a more precise ontology for the Cinchonoideae drupes is required.

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.

A novel technique for real-time estimation of edge pedestal density gradients via reflectometer time delay data

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

Zeng, L., E-mail: zeng@fusion.gat.com; Doyle, E. J.; Rhodes, T. L.

2016-11-15

A new model-based technique for fast estimation of the pedestal electron density gradient has been developed. The technique uses ordinary mode polarization profile reflectometer time delay data and does not require direct profile inversion. Because of its simple data processing, the technique can be readily implemented via a Field-Programmable Gate Array, so as to provide a real-time density gradient estimate, suitable for use in plasma control systems such as envisioned for ITER, and possibly for DIII-D and Experimental Advanced Superconducting Tokamak. The method is based on a simple edge plasma model with a linear pedestal density gradient and low scrape-off-layermore » density. By measuring reflectometer time delays for three adjacent frequencies, the pedestal density gradient can be estimated analytically via the new approach. Using existing DIII-D profile reflectometer data, the estimated density gradients obtained from the new technique are found to be in good agreement with the actual density gradients for a number of dynamic DIII-D plasma conditions.« less

Mining Peripheral Arterial Disease Cases from Narrative Clinical Notes Using Natural Language Processing

PubMed Central

Afzal, Naveed; Sohn, Sunghwan; Abram, Sara; Scott, Christopher G.; Chaudhry, Rajeev; Liu, Hongfang; Kullo, Iftikhar J.; Arruda-Olson, Adelaide M.

2016-01-01

Objective Lower extremity peripheral arterial disease (PAD) is highly prevalent and affects millions of individuals worldwide. We developed a natural language processing (NLP) system for automated ascertainment of PAD cases from clinical narrative notes and compared the performance of the NLP algorithm to billing code algorithms, using ankle-brachial index (ABI) test results as the gold standard. Methods We compared the performance of the NLP algorithm to 1) results of gold standard ABI; 2) previously validated algorithms based on relevant ICD-9 diagnostic codes (simple model) and 3) a combination of ICD-9 codes with procedural codes (full model). A dataset of 1,569 PAD patients and controls was randomly divided into training (n= 935) and testing (n= 634) subsets. Results We iteratively refined the NLP algorithm in the training set including narrative note sections, note types and service types, to maximize its accuracy. In the testing dataset, when compared with both simple and full models, the NLP algorithm had better accuracy (NLP: 91.8%, full model: 81.8%, simple model: 83%, P<.001), PPV (NLP: 92.9%, full model: 74.3%, simple model: 79.9%, P<.001), and specificity (NLP: 92.5%, full model: 64.2%, simple model: 75.9%, P<.001). Conclusions A knowledge-driven NLP algorithm for automatic ascertainment of PAD cases from clinical notes had greater accuracy than billing code algorithms. Our findings highlight the potential of NLP tools for rapid and efficient ascertainment of PAD cases from electronic health records to facilitate clinical investigation and eventually improve care by clinical decision support. PMID:28189359

A novel approach to solve nonlinear Fredholm integral equations of the second kind.

PubMed

Li, Hu; Huang, Jin

2016-01-01

In this paper, we present a novel approach to solve nonlinear Fredholm integral equations of the second kind. This algorithm is constructed by the integral mean value theorem and Newton iteration. Convergence and error analysis of the numerical solutions are given. Moreover, Numerical examples show the algorithm is very effective and simple.

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

DART system analysis.

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

Boggs, Paul T.; Althsuler, Alan; Larzelere, Alex R.

2005-08-01

The Design-through-Analysis Realization Team (DART) is chartered with reducing the time Sandia analysts require to complete the engineering analysis process. The DART system analysis team studied the engineering analysis processes employed by analysts in Centers 9100 and 8700 at Sandia to identify opportunities for reducing overall design-through-analysis process time. The team created and implemented a rigorous analysis methodology based on a generic process flow model parameterized by information obtained from analysts. They also collected data from analysis department managers to quantify the problem type and complexity distribution throughout Sandia's analyst community. They then used this information to develop a communitymore » model, which enables a simple characterization of processes that span the analyst community. The results indicate that equal opportunity for reducing analysis process time is available both by reducing the ''once-through'' time required to complete a process step and by reducing the probability of backward iteration. In addition, reducing the rework fraction (i.e., improving the engineering efficiency of subsequent iterations) offers approximately 40% to 80% of the benefit of reducing the ''once-through'' time or iteration probability, depending upon the process step being considered. Further, the results indicate that geometry manipulation and meshing is the largest portion of an analyst's effort, especially for structural problems, and offers significant opportunity for overall time reduction. Iteration loops initiated late in the process are more costly than others because they increase ''inner loop'' iterations. Identifying and correcting problems as early as possible in the process offers significant opportunity for time savings.« less

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.

Autocratic strategies for iterated games with arbitrary action spaces

PubMed Central

2016-01-01

The recent discovery of zero-determinant strategies for the iterated prisoner’s dilemma sparked a surge of interest in the surprising fact that a player can exert unilateral control over iterated interactions. These remarkable strategies, however, are known to exist only in games in which players choose between two alternative actions such as “cooperate” and “defect.” Here we introduce a broader class of autocratic strategies by extending zero-determinant strategies to iterated games with more general action spaces. We use the continuous donation game as an example, which represents an instance of the prisoner’s dilemma that intuitively extends to a continuous range of cooperation levels. Surprisingly, despite the fact that the opponent has infinitely many donation levels from which to choose, a player can devise an autocratic strategy to enforce a linear relationship between his or her payoff and that of the opponent even when restricting his or her actions to merely two discrete levels of cooperation. In particular, a player can use such a strategy to extort an unfair share of the payoffs from the opponent. Therefore, although the action space of the continuous donation game dwarfs that of the classic prisoner’s dilemma, players can still devise relatively simple autocratic and, in particular, extortionate strategies. PMID:26976578

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.

A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian assisted with an ancillary qubit system

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Lee, Seung-Woo; Lee, Chang-Woo; Jeong, Hyunseok

2015-01-01

We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied to the initial state assisted with an ancillary qubit. The fraction of the lowest eigenstate in the initial state is then amplified up to 1. We prove that our algorithm can faithfully work for any arbitrary Hamiltonian in the theoretical analysis. Numerical analyses are also carried out. We firstly provide a numerical proof-of-principle demonstration with a simple Hamiltonian in order to compare our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently proposed in Xu (Nat Photonics 8:113, 2014). The result shows a good agreement with our theoretical analysis, exhibiting the comparable behavior to the best `cooling' with the DLAC method. We then consider a random Hamiltonian model for further analysis of our algorithm. By numerical simulations, we show that the total number of iterations is proportional to , where is the difference between the two lowest eigenvalues and is an error defined as the probability that the finally obtained system state is in an unexpected (i.e., not the lowest) eigenstate.

Surface emissivity and temperature retrieval for a hyperspectral sensor

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

Borel, C.C.

1998-12-01

With the growing use of hyper-spectral imagers, e.g., AVIRIS in the visible and short-wave infrared there is hope of using such instruments in the mid-wave and thermal IR (TIR) some day. The author believes that this will enable him to get around using the present temperature-emissivity separation algorithms using methods which take advantage of the many channels available in hyper-spectral imagers. A simple fact used in coming up with a novel algorithm is that a typical surface emissivity spectrum are rather smooth compared to spectral features introduced by the atmosphere. Thus, a iterative solution technique can be devised which retrievesmore » emissivity spectra based on spectral smoothness. To make the emissivities realistic, atmospheric parameters are varied using approximations, look-up tables derived from a radiative transfer code and spectral libraries. One such iterative algorithm solves the radiative transfer equation for the radiance at the sensor for the unknown emissivity and uses the blackbody temperature computed in an atmospheric window to get a guess for the unknown surface temperature. By varying the surface temperature over a small range a series of emissivity spectra are calculated. The one with the smoothest characteristic is chosen. The algorithm was tested on synthetic data using MODTRAN and the Salisbury emissivity database.« less

Active Player Modeling in the Iterated Prisoner's Dilemma

PubMed Central

Park, Hyunsoo; Kim, Kyung-Joong

2016-01-01

The iterated prisoner's dilemma (IPD) is well known within the domain of game theory. Although it is relatively simple, it can also elucidate important problems related to cooperation and trust. Generally, players can predict their opponents' actions when they are able to build a precise model of their behavior based on their game playing experience. However, it is difficult to make such predictions based on a limited number of games. The creation of a precise model requires the use of not only an appropriate learning algorithm and framework but also a good dataset. Active learning approaches have recently been introduced to machine learning communities. The approach can usually produce informative datasets with relatively little effort. Therefore, we have proposed an active modeling technique to predict the behavior of IPD players. The proposed method can model the opponent player's behavior while taking advantage of interactive game environments. This experiment used twelve representative types of players as opponents, and an observer used an active modeling algorithm to model these opponents. This observer actively collected data and modeled the opponent's behavior online. Most of our data showed that the observer was able to build, through direct actions, a more accurate model of an opponent's behavior than when the data were collected through random actions. PMID:26989405

Active Player Modeling in the Iterated Prisoner's Dilemma.

PubMed

Park, Hyunsoo; Kim, Kyung-Joong

2016-01-01

The iterated prisoner's dilemma (IPD) is well known within the domain of game theory. Although it is relatively simple, it can also elucidate important problems related to cooperation and trust. Generally, players can predict their opponents' actions when they are able to build a precise model of their behavior based on their game playing experience. However, it is difficult to make such predictions based on a limited number of games. The creation of a precise model requires the use of not only an appropriate learning algorithm and framework but also a good dataset. Active learning approaches have recently been introduced to machine learning communities. The approach can usually produce informative datasets with relatively little effort. Therefore, we have proposed an active modeling technique to predict the behavior of IPD players. The proposed method can model the opponent player's behavior while taking advantage of interactive game environments. This experiment used twelve representative types of players as opponents, and an observer used an active modeling algorithm to model these opponents. This observer actively collected data and modeled the opponent's behavior online. Most of our data showed that the observer was able to build, through direct actions, a more accurate model of an opponent's behavior than when the data were collected through random actions.

Neighbourhood-consensus message passing and its potentials in image processing applications

NASA Astrophysics Data System (ADS)

Ružic, Tijana; Pižurica, Aleksandra; Philips, Wilfried

2011-03-01

In this paper, a novel algorithm for inference in Markov Random Fields (MRFs) is presented. Its goal is to find approximate maximum a posteriori estimates in a simple manner by combining neighbourhood influence of iterated conditional modes (ICM) and message passing of loopy belief propagation (LBP). We call the proposed method neighbourhood-consensus message passing because a single joint message is sent from the specified neighbourhood to the central node. The message, as a function of beliefs, represents the agreement of all nodes within the neighbourhood regarding the labels of the central node. This way we are able to overcome the disadvantages of reference algorithms, ICM and LBP. On one hand, more information is propagated in comparison with ICM, while on the other hand, the huge amount of pairwise interactions is avoided in comparison with LBP by working with neighbourhoods. The idea is related to the previously developed iterated conditional expectations algorithm. Here we revisit it and redefine it in a message passing framework in a more general form. The results on three different benchmarks demonstrate that the proposed technique can perform well both for binary and multi-label MRFs without any limitations on the model definition. Furthermore, it manifests improved performance over related techniques either in terms of quality and/or speed.

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.

Inversion of Attributes and Full Waveforms of Ground Penetrating Radar Data Using PEST

NASA Astrophysics Data System (ADS)

Jazayeri, S.; Kruse, S.; Esmaeili, S.

2015-12-01

We seek to establish a method, based on freely available software, for inverting GPR signals for the underlying physical properties (electrical permittivity, magnetic permeability, target geometries). Such a procedure should be useful for classroom instruction and for analyzing surface GPR surveys over simple targets. We explore the applicability of the PEST parameter estimation software package for GPR inversion (www.pesthomepage.org). PEST is designed to invert data sets with large numbers of parameters, and offers a variety of inversion methods. Although primarily used in hydrogeology, the code has been applied to a wide variety of physical problems. The PEST code requires forward model input; the forward model of the GPR signal is done with the GPRMax package (www.gprmax.com). The problem of extracting the physical characteristics of a subsurface anomaly from the GPR data is highly nonlinear. For synthetic models of simple targets in homogeneous backgrounds, we find PEST's nonlinear Gauss-Marquardt-Levenberg algorithm is preferred. This method requires an initial model, for which the weighted differences between model-generated data and those of the "true" synthetic model (the objective function) are calculated. In order to do this, the Jacobian matrix and the derivatives of the observation data in respect to the model parameters are computed using a finite differences method. Next, the iterative process of building new models by updating the initial values starts in order to minimize the objective function. Another measure of the goodness of the final acceptable model is the correlation coefficient which is calculated based on the method of Cooley and Naff. An accepted final model satisfies both of these conditions. Models to date show that physical properties of simple isolated targets against homogeneous backgrounds can be obtained from multiple traces from common-offset surface surveys. Ongoing work examines the inversion capabilities with more complex target geometries and heterogeneous soils.

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

Ultrathin metasurface with high absorptance for waterborne sound

NASA Astrophysics Data System (ADS)

Mei, Jun; Zhang, Xiujuan; Wu, Ying

2018-03-01

We present a design for an acoustic metasurface which can efficiently absorb low-frequency sound energy in water. The metasurface has a simple structure and consists of only two common materials: i.e., water and silicone rubber. The optimized material and geometrical parameters of the designed metasurface are determined by an analytic formula in conjunction with an iterative process based on the retrieval method. Although the metasurface is as thin as 0.15 of the wavelength, it can absorb 99.7% of the normally incident sound wave energy. Furthermore, the metasurface maintains a substantially high absorptance over a relatively broad bandwidth, and also works well for oblique incidence with an incident angle of up to 50°. Potential applications in the field of underwater sound isolation are expected.

DAVIS: A direct algorithm for velocity-map imaging system

NASA Astrophysics Data System (ADS)

Harrison, G. R.; Vaughan, J. C.; Hidle, B.; Laurent, G. M.

2018-05-01

In this work, we report a direct (non-iterative) algorithm to reconstruct the three-dimensional (3D) momentum-space picture of any charged particles collected with a velocity-map imaging system from the two-dimensional (2D) projected image captured by a position-sensitive detector. The method consists of fitting the measured image with the 2D projection of a model 3D velocity distribution defined by the physics of the light-matter interaction. The meaningful angle-correlated information is first extracted from the raw data by expanding the image with a complete set of Legendre polynomials. Both the particle's angular and energy distributions are then directly retrieved from the expansion coefficients. The algorithm is simple, easy to implement, fast, and explicitly takes into account the pixelization effect in the measurement.

Fast and robust estimation of ophthalmic wavefront aberrations

NASA Astrophysics Data System (ADS)

Dillon, Keith

2016-12-01

Rapidly rising levels of myopia, particularly in the developing world, have led to an increased need for inexpensive and automated approaches to optometry. A simple and robust technique is provided for estimating major ophthalmic aberrations using a gradient-based wavefront sensor. The approach is based on the use of numerical calculations to produce diverse combinations of phase components, followed by Fourier transforms to calculate the coefficients. The approach does not utilize phase unwrapping nor iterative solution of inverse problems. This makes the method very fast and tolerant to image artifacts, which do not need to be detected and masked or interpolated as is needed in other techniques. These features make it a promising algorithm on which to base low-cost devices for applications that may have limited access to expert maintenance and operation.

LIDAR TS for ITER core plasma. Part II: simultaneous two wavelength LIDAR TS

NASA Astrophysics Data System (ADS)

Gowers, C.; Nielsen, P.; Salzmann, H.

2017-12-01

We have shown recently, and in more detail at this conference (Salzmann et al) that the LIDAR approach to ITER core TS measurements requires only two mirrors in the inaccessible port plug area of the machine. This leads to simplified and robust alignment, lower risk of mirror damage by plasma contamination and much simpler calibration, compared with the awkward and vulnerable optical geometry of the conventional imaging TS approach, currently under development by ITER. In the present work we have extended the simulation code used previously to include the case of launching two laser pulses, of different wavelengths, simultaneously in LIDAR geometry. The aim of this approach is to broaden the choice of lasers available for the diagnostic. In the simulation code it is assumed that two short duration (300 ps) laser pulses of different wavelengths, from an Nd:YAG laser are launched through the plasma simultaneously. The temperature and density profiles are deduced in the usual way but from the resulting combined scattered signals in the different spectral channels of the single spectrometer. The spectral response and quantum efficiencies of the detectors used in the simulation are taken from catalogue data for commercially available Hamamatsu MCP-PMTs. The response times, gateability and tolerance to stray light levels of this type of photomultiplier have already been demonstrated in the JET LIDAR system and give sufficient spatial resolution to meet the ITER specification. Here we present the new simulation results from the code. They demonstrate that when the detectors are combined with this two laser, LIDAR approach, the full range of the specified ITER core plasma Te and ne can be measured with sufficient accuracy. So, with commercially available detectors and a simple modification of a Nd:YAG laser similar to that currently being used in the design of the conventional ITER core TS design mentioned above, the ITER requirements can be met.

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.

Identifying a set of influential spreaders in complex networks

NASA Astrophysics Data System (ADS)

Zhang, Jian-Xiong; Chen, Duan-Bing; Dong, Qiang; Zhao, Zhi-Dan

2016-06-01

Identifying a set of influential spreaders in complex networks plays a crucial role in effective information spreading. A simple strategy is to choose top-r ranked nodes as spreaders according to influence ranking method such as PageRank, ClusterRank and k-shell decomposition. Besides, some heuristic methods such as hill-climbing, SPIN, degree discount and independent set based are also proposed. However, these approaches suffer from a possibility that some spreaders are so close together that they overlap sphere of influence or time consuming. In this report, we present a simply yet effectively iterative method named VoteRank to identify a set of decentralized spreaders with the best spreading ability. In this approach, all nodes vote in a spreader in each turn, and the voting ability of neighbors of elected spreader will be decreased in subsequent turn. Experimental results on four real networks show that under Susceptible-Infected-Recovered (SIR) and Susceptible-Infected (SI) models, VoteRank outperforms the traditional benchmark methods on both spreading rate and final affected scale. What’s more, VoteRank has superior computational efficiency.

Boosted Multivariate Trees for Longitudinal Data

PubMed Central

Pande, Amol; Li, Liang; Rajeswaran, Jeevanantham; Ehrlinger, John; Kogalur, Udaya B.; Blackstone, Eugene H.; Ishwaran, Hemant

2017-01-01

Machine learning methods provide a powerful approach for analyzing longitudinal data in which repeated measurements are observed for a subject over time. We boost multivariate trees to fit a novel flexible semi-nonparametric marginal model for longitudinal data. In this model, features are assumed to be nonparametric, while feature-time interactions are modeled semi-nonparametrically utilizing P-splines with estimated smoothing parameter. In order to avoid overfitting, we describe a relatively simple in sample cross-validation method which can be used to estimate the optimal boosting iteration and which has the surprising added benefit of stabilizing certain parameter estimates. Our new multivariate tree boosting method is shown to be highly flexible, robust to covariance misspecification and unbalanced designs, and resistant to overfitting in high dimensions. Feature selection can be used to identify important features and feature-time interactions. An application to longitudinal data of forced 1-second lung expiratory volume (FEV1) for lung transplant patients identifies an important feature-time interaction and illustrates the ease with which our method can find complex relationships in longitudinal data. PMID:29249866

Method for data compression by associating complex numbers with files of data values

DOEpatents

Feo, J.T.; Hanks, D.C.; Kraay, T.A.

1998-02-10

A method for compressing data for storage or transmission is disclosed. Given a complex polynomial and a value assigned to each root, a root generated data file (RGDF) is created, one entry at a time. Each entry is mapped to a point in a complex plane. An iterative root finding technique is used to map the coordinates of the point to the coordinates of one of the roots of the polynomial. The value associated with that root is assigned to the entry. An equational data compression (EDC) method reverses this procedure. Given a target data file, the EDC method uses a search algorithm to calculate a set of m complex numbers and a value map that will generate the target data file. The error between a simple target data file and generated data file is typically less than 10%. Data files can be transmitted or stored without loss by transmitting the m complex numbers, their associated values, and an error file whose size is at most one-tenth of the size of the input data file. 4 figs.

Residential roof condition assessment system using deep learning

NASA Astrophysics Data System (ADS)

Wang, Fan; Kerekes, John P.; Xu, Zhuoyi; Wang, Yandong

2018-01-01

The emergence of high resolution (HR) and ultra high resolution (UHR) airborne remote sensing imagery is enabling humans to move beyond traditional land cover analysis applications to the detailed characterization of surface objects. A residential roof condition assessment method using techniques from deep learning is presented. The proposed method operates on individual roofs and divides the task into two stages: (1) roof segmentation, followed by (2) condition classification of the segmented roof regions. As the first step in this process, a self-tuning method is proposed to segment the images into small homogeneous areas. The segmentation is initialized with simple linear iterative clustering followed by deep learned feature extraction and region merging, with the optimal result selected by an unsupervised index, Q. After the segmentation, a pretrained residual network is fine-tuned on the augmented roof segments using a proposed k-pixel extension technique for classification. The effectiveness of the proposed algorithm was demonstrated on both HR and UHR imagery collected by EagleView over different study sites. The proposed algorithm has yielded promising results and has outperformed traditional machine learning methods using hand-crafted features.

Method for data compression by associating complex numbers with files of data values

DOEpatents

Feo, John Thomas; Hanks, David Carlton; Kraay, Thomas Arthur

1998-02-10

A method for compressing data for storage or transmission. Given a complex polynomial and a value assigned to each root, a root generated data file (RGDF) is created, one entry at a time. Each entry is mapped to a point in a complex plane. An iterative root finding technique is used to map the coordinates of the point to the coordinates of one of the roots of the polynomial. The value associated with that root is assigned to the entry. An equational data compression (EDC) method reverses this procedure. Given a target data file, the EDC method uses a search algorithm to calculate a set of m complex numbers and a value map that will generate the target data file. The error between a simple target data file and generated data file is typically less than 10%. Data files can be transmitted or stored without loss by transmitting the m complex numbers, their associated values, and an error file whose size is at most one-tenth of the size of the input data file.

Probe-specific mixed-model approach to detect copy number differences using multiplex ligation-dependent probe amplification (MLPA)

PubMed Central

González, Juan R; Carrasco, Josep L; Armengol, Lluís; Villatoro, Sergi; Jover, Lluís; Yasui, Yutaka; Estivill, Xavier

2008-01-01

Background MLPA method is a potentially useful semi-quantitative method to detect copy number alterations in targeted regions. In this paper, we propose a method for the normalization procedure based on a non-linear mixed-model, as well as a new approach for determining the statistical significance of altered probes based on linear mixed-model. This method establishes a threshold by using different tolerance intervals that accommodates the specific random error variability observed in each test sample. Results Through simulation studies we have shown that our proposed method outperforms two existing methods that are based on simple threshold rules or iterative regression. We have illustrated the method using a controlled MLPA assay in which targeted regions are variable in copy number in individuals suffering from different disorders such as Prader-Willi, DiGeorge or Autism showing the best performace. Conclusion Using the proposed mixed-model, we are able to determine thresholds to decide whether a region is altered. These threholds are specific for each individual, incorporating experimental variability, resulting in improved sensitivity and specificity as the examples with real data have revealed. PMID:18522760

Global convergence of inexact Newton methods for transonic flow

NASA Technical Reports Server (NTRS)

Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.

1990-01-01

In computational fluid dynamics, nonlinear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these nonlinear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modeled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.

Method development and qualification of capillary zone electrophoresis for investigation of therapeutic monoclonal antibody quality.

PubMed

Suba, Dávid; Urbányi, Zoltán; Salgó, András

2016-10-01

Capillary electrophoresis techniques are widely used in the analytical biotechnology. Different electrophoretic techniques are very adequate tools to monitor size-and charge heterogenities of protein drugs. Method descriptions and development studies of capillary zone electrophoresis (CZE) have been described in literature. Most of them are performed based on the classical one-factor-at-time (OFAT) approach. In this study a very simple method development approach is described for capillary zone electrophoresis: a "two-phase-four-step" approach is introduced which allows a rapid, iterative method development process and can be a good platform for CZE method. In every step the current analytical target profile and an appropriate control strategy were established to monitor the current stage of development. A very good platform was established to investigate intact and digested protein samples. Commercially available monoclonal antibody was chosen as model protein for the method development study. The CZE method was qualificated after the development process and the results were presented. The analytical system stability was represented by the calculated RSD% value of area percentage and migration time of the selected peaks (<0.8% and <5%) during the intermediate precision investigation. Copyright © 2016 Elsevier B.V. All rights reserved.

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 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

A Simple Classroom Simulation of Heat Energy Diffusing through a Metal Bar

ERIC Educational Resources Information Center

Kinsler, Mark; Kinzel, Evelyn

2007-01-01

We present an iterative procedure that does not rely on calculus to model heat flow through a uniform bar of metal and thus avoids the use of the partial differential equation typically needed to describe heat diffusion. The procedure is based on first principles and can be done with students at the blackboard. It results in a plot that…

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.

3D near-to-surface conductivity reconstruction by inversion of VETEM data using the distorted Born iterative method

USGS Publications Warehouse

Wang, G.L.; Chew, W.C.; Cui, T.J.; Aydiner, A.A.; Wright, D.L.; Smith, D.V.

2004-01-01

Three-dimensional (3D) subsurface imaging by using inversion of data obtained from the very early time electromagnetic system (VETEM) was discussed. The study was carried out by using the distorted Born iterative method to match the internal nonlinear property of the 3D inversion problem. The forward solver was based on the total-current formulation bi-conjugate gradient-fast Fourier transform (BCCG-FFT). It was found that the selection of regularization parameter follow a heuristic rule as used in the Levenberg-Marquardt algorithm so that the iteration is stable.