Efficient numerical methods for nonlinear Schrodinger equations
NASA Astrophysics Data System (ADS)
Liang, Xiao
The nonlinear Schrodinger equations are widely used to model a number of important physical phenomena, including solitary wave propagations in optical fibers, deep water turbulence, laser beam transmissions, and the Bose-Einstein condensation, just to mention a few. In the field of optics and photonics, the systems of nonlinear Schrodinger equations can be used to model multi-component solitons and the interaction of self-focusing laser beams. In three spatial dimensions, the nonlinear Schrodinger equation is known as the Gross-Pitaevskii equation, which models the soliton in a low-cost graded-index fiber. Recently, research on nonlinear space fractional Schrodinger equations, which capture the self-similarity in the fractional environment, has become prevalent. Our study includes the systems of multi-dimensional nonlinear space fractional Schrodinger equations. To solve the systems of multi-dimensional nonlinear Schrodinger equations efficiently, several novel numerical methods are presented. The central difference and quartic spline approximation based exponential time differencing Crank-Nicolson method is introduced for solving systems of one- and two-dimensional nonlinear Schrodinger equations. A local extrapolation is employed to achieve fourth-order accuracy in time. The numerical examples include the transmission of a self-focusing laser beam. The local discontinuous Galerkin methods combined with the fourth-order exponential time differencing Runge-Kutta time discretization are studied for solving the systems of nonlinear Schrodinger equations with hyperbolic terms, which are critical in modeling optical solitons in the birefringent fibers. The local discontinuous Galerkin method is able to achieve any order of accuracy in space, thanks to the usage of piecewise polynomial spaces. The exponential time differencing methods are employed to deal with the coupled nonlinearities for the reason that there is no need to solve nonlinear systems at every time step
Efficient Numerical Methods for Stable Distributions
2007-11-02
0 and cutoffs c1 = −128 and c2 = +127 are used, corresponding to the common values used in digital signal processing. Five new functions for discrete...variables using the Chambers- Mallows - Stuck method, rounding them to the nearest integer, and then cutting off if the value is too high or too low...within the common matlab environment they use. We comment briefly on the commercialization of this in the last section. 3 -100 -50 0 50 100 0. 0 0. 01 0
An efficient numerical method for orbit computations
NASA Astrophysics Data System (ADS)
Palacios, M.; Abad, A.; Elipe, A.
1992-08-01
A nonstandard formulation of perturbed Keplerian motion is set forth based on the analysis by Deprit (1975) and incorporating quaternions to integrate the equations of motion. The properties of quaternions are discussed and applied to the portion of the equations of motion describing the rotations between the space frame and the departure frame. Angular momentum is assumed to be constant, and a redundant set of variables is introduced to test the equations of motion for different step sizes. The method is analyzed for the cases of artificial satellites in Keplerian circular orbits, Keplerian elliptical orbits, and zonal harmonics. The present formulation is shown to adequately represent the dynamical behavior while avoiding small inclinations. The rotations described by quaternions require less arithmetic operations and therefore save computation time, and the accuracy of the solutions are improved by at least two significant digits.
Efficient numerical methods for entropy-linear programming problems
NASA Astrophysics Data System (ADS)
Gasnikov, A. V.; Gasnikova, E. B.; Nesterov, Yu. E.; Chernov, A. V.
2016-04-01
Entropy-linear programming (ELP) problems arise in various applications. They are usually written as the maximization of entropy (minimization of minus entropy) under affine constraints. In this work, new numerical methods for solving ELP problems are proposed. Sharp estimates for the convergence rates of the proposed methods are established. The approach described applies to a broader class of minimization problems for strongly convex functionals with affine constraints.
An efficient numerical simulation method for a thin film SOI RESURF structure
NASA Astrophysics Data System (ADS)
Liu, Zhan; Gan, Jun-Ying; Gu, Xiao-Feng; Yu, Zong-guang; Yang, Lei
2009-02-01
In this paper, an efficient numerical simulation method, which combines the spline alternating direction implicit (SADI) method and the high-order compact (HOC) finite difference method, is presented to simulate the potential and electric field distributions along the semiconductor surface of thin film silicon-on-insulator (TFSOI) reduced surface field (RESURF) devices. The relative merit of HOC-SADI is compared with three other popular numerical simulation methods, Newton, Gummel and CGS. The numerical results obtained from the proposed scheme are compared to the simulator MEDICI. HOC-SADI is a faster algorithm than Newton, Gummel and CGS as is evident from the CPU times and the number of iterations.
Efficient numerical method for analyzing optical bistability in photonic crystal microcavities.
Yuan, Lijun; Lu, Ya Yan
2013-05-20
Nonlinear optical effects can be enhanced by photonic crystal microcavities and be used to develop practical ultra-compact optical devices with low power requirements. The finite-difference time-domain method is the standard numerical method for simulating nonlinear optical devices, but it has limitations in terms of accuracy and efficiency. In this paper, a rigorous and efficient frequency-domain numerical method is developed for analyzing nonlinear optical devices where the nonlinear effect is concentrated in the microcavities. The method replaces the linear problem outside the microcavities by a rigorous and numerically computed boundary condition, then solves the nonlinear problem iteratively in a small region around the microcavities. Convergence of the iterative method is much easier to achieve since the size of the problem is significantly reduced. The method is presented for a specific two-dimensional photonic crystal waveguide-cavity system with a Kerr nonlinearity, using numerical methods that can take advantage of the geometric features of the structure. The method is able to calculate multiple solutions exhibiting the optical bistability phenomenon in the strongly nonlinear regime.
Efficiency and Accuracy Verification of the Explicit Numerical Manifold Method for Dynamic Problems
NASA Astrophysics Data System (ADS)
Qu, X. L.; Wang, Y.; Fu, G. Y.; Ma, G. W.
2015-05-01
The original numerical manifold method (NMM) employs an implicit time integration scheme to achieve higher computational accuracy, but its efficiency is relatively low, especially when the open-close iterations of contact are involved. To improve its computational efficiency, a modified version of the NMM based on an explicit time integration algorithm is proposed in this study. The lumped mass matrix, internal force and damping vectors are derived for the proposed explicit scheme. A calibration study on P-wave propagation along a rock bar is conducted to investigate the efficiency and accuracy of the developed explicit numerical manifold method (ENMM) for wave propagation problems. Various considerations in the numerical simulations are discussed, and parametric studies are carried out to obtain an insight into the influencing factors on the efficiency and accuracy of wave propagation. To further verify the capability of the proposed ENMM, dynamic stability assessment for a fractured rock slope under seismic effect is analysed. It is shown that, compared to the original NMM, the computational efficiency of the proposed ENMM can be significantly improved.
AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L2 OPTIMAL MASS TRANSFER PROBLEM*
Haber, Eldad; Rehman, Tauseef; Tannenbaum, Allen
2010-01-01
In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L2 mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61–97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data. PMID:21278828
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
1984-01-01
The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.
Efficient and accurate numerical methods for the Klein-Gordon-Schroedinger equations
Bao, Weizhu . E-mail: bao@math.nus.edu.sg; Yang, Li . E-mail: yangli@nus.edu.sg
2007-08-10
In this paper, we present efficient, unconditionally stable and accurate numerical methods for approximations of the Klein-Gordon-Schroedinger (KGS) equations with/without damping terms. The key features of our methods are based on: (i) the application of a time-splitting spectral discretization for a Schroedinger-type equation in KGS (ii) the utilization of Fourier pseudospectral discretization for spatial derivatives in the Klein-Gordon equation in KGS (iii) the adoption of solving the ordinary differential equations (ODEs) in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying Crank-Nicolson/leap-frog for linear/nonlinear terms for time derivatives. The numerical methods are either explicit or implicit but can be solved explicitly, unconditionally stable, and of spectral accuracy in space and second-order accuracy in time. Moreover, they are time reversible and time transverse invariant when there is no damping terms in KGS, conserve (or keep the same decay rate of) the wave energy as that in KGS without (or with a linear) damping term, keep the same dynamics of the mean value of the meson field, and give exact results for the plane-wave solution. Extensive numerical tests are presented to confirm the above properties of our numerical methods for KGS. Finally, the methods are applied to study solitary-wave collisions in one dimension (1D), as well as dynamics of a 2D problem in KGS.
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
1984-01-01
A comparison of the efficiency of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations is presented. The methods examined include two general-purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.
Numerical multistep methods for the efficient solution of quantum mechanics and related problems
NASA Astrophysics Data System (ADS)
Anastassi, Z. A.; Simos, T. E.
2009-10-01
In this paper we present the recent development in the numerical integration of the Schrödinger equation and related systems of ordinary differential equations with oscillatory solutions, such as the N-body problem. We examine several types of multistep methods (explicit, implicit, predictor-corrector, hybrid) and several properties (P-stability, trigonometric fitting of various orders, phase fitting, high phase-lag order, algebraic order). We analyze the local truncation error and the stability of the methods. The error for the Schrödinger equation is also presented, which reveals the relation of the error to the energy. The efficiency of the methods is evaluated through the integration of five problems. Figures are presented and analyzed and some general conclusions are made. Code written in Maple is given for the development of all methods analyzed in this paper. Also the subroutines written in Matlab, that concern the integration of the methods, are presented.
An efficient numerical method for predicting the performance of valveless micropump
NASA Astrophysics Data System (ADS)
Braineard Eladi, Paul; Chatterjee, Dhiman; DasGupta, Amitava
2012-11-01
Numerical characterization of valveless micropumps involves fluid-structure interaction (FSI) between a membrane and the working fluid. FSI being computationally difficult, efforts have been mainly restricted to analyzing a given micropump performance. Designing an optimum micropump involves understanding the role of different geometric parameters and this forms the focus of the present work. It is shown that membrane displacement information extracted from a two-way coupled FSI simulation at a given frequency can be reliably used to carry out fluid flow simulations over a wide range of geometrical and operating parameters. The maximum variation between this approach and FSI is within 4% while there is a drastic reduction in computational time and resource. A micropump structure suitable for MEMS technology is considered in this work. An optimum micropump geometry, having a pump chamber height of 50 μm, diffuser length of 280 μm, throat width of 100 μm and separation distance between nozzle and diffuser openings of 2.5 mm, is recommended. The numerical prediction of flowrate at 200 Hz (68 μl min-1) for this pyramidal valveless micropump matches well with the experimental data (60 μl min-1) of the micropump fabricated using MEMS-based silicon micromachining. Thus an efficient numerical method to design valveless micropumps is proposed and validated through rigorous characterization.
An Efficient numerical method to calculate the conductivity tensor for disordered topological matter
NASA Astrophysics Data System (ADS)
Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.
2015-03-01
We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.
Devasenapathy, Deepa; Kannan, Kathiravan
2015-01-01
The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN) is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate. PMID:25793221
Devasenapathy, Deepa; Kannan, Kathiravan
2015-01-01
The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN) is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate.
NASA Astrophysics Data System (ADS)
Butet, J.; Bernasconi, G. D.; Yang, K.-Y.; Martin, O. J. F.
2016-09-01
During the last decade, important attention has been devoted to the observation of nonlinear optical processes in plasmonic nanosystems, giving rise to a new field of research called nonlinear plasmonics. The cornerstone of nonlinear plasmonics is the use of the large field enhancement associated with the excitation of localized surface plasmon resonances to reach high nonlinear conversion yields. Among all the nonlinear optical processes, second harmonic generation (SHG), the process whereby two photons at the fundamental frequency are converted into one photon at the second harmonic frequency, is undoubtedly the most studied one due to the relative simplicity of its experimental observation. However, the physical origin of SHG from plasmonic nanostructures hides a lot of subtleties, which are mainly related to its particular behavior upon inversion symmetry. In order to catch all the peculiarities of SHG, it is mandatory to develop dedicated numerical methods able to accurately describe all the underlying physical processes and the influence of the initial assumptions needs to be well-characterized. In this presentation, we discuss and compare different methods (namely full-wave computations based on the surface integral equations method, mode analysis, the Miller's rule, and the effective nonlinear susceptibility method) proposed for the evaluation of the SHG from plasmonic nanoparticles emphasizing their limitations and advantages. In particular, the design of double resonant antennas for efficient nonlinear conversion at the nanoscale is addressed in detail.
The development of efficient numerical time-domain modeling methods for geophysical wave propagation
NASA Astrophysics Data System (ADS)
Zhu, Lieyuan
This Ph.D. dissertation focuses on the numerical simulation of geophysical wave propagation in the time domain including elastic waves in solid media, the acoustic waves in fluid media, and the electromagnetic waves in dielectric media. This thesis shows that a linear system model can describe accurately the physical processes of those geophysical waves' propagation and can be used as a sound basis for modeling geophysical wave propagation phenomena. The generalized stability condition for numerical modeling of wave propagation is therefore discussed in the context of linear system theory. The efficiency of a series of different numerical algorithms in the time-domain for modeling geophysical wave propagation are discussed and compared. These algorithms include the finite-difference time-domain method, pseudospectral time domain method, alternating directional implicit (ADI) finite-difference time domain method. The advantages and disadvantages of these numerical methods are discussed and the specific stability condition for each modeling scheme is carefully derived in the context of the linear system theory. Based on the review and discussion of these existing approaches, the split step, ADI pseudospectral time domain (SS-ADI-PSTD) method is developed and tested for several cases. Moreover, the state-of-the-art stretched-coordinate perfect matched layer (SCPML) has also been implemented in SS-ADI-PSTD algorithm as the absorbing boundary condition for truncating the computational domain and absorbing the artificial reflection from the domain boundaries. After algorithmic development, a few case studies serve as the real-world examples to verify the capacities of the numerical algorithms and understand the capabilities and limitations of geophysical methods for detection of subsurface contamination. The first case is a study using ground penetrating radar (GPR) amplitude variation with offset (AVO) for subsurface non-aqueous-liquid (NAPL) contamination. The
An efficient numerical method for solving inverse conduction problem in a hollow cylinder
NASA Astrophysics Data System (ADS)
Mehta, R. C.
1984-06-01
A simple numerical scheme for solving the inverse conduction problem in a hollow cylinder is presented using transient temperature data for estimating the unknown surface conditions. A general digital program is discussed that can treat a variety of boundary conditions using a single set of equations. As an example, the method is applied to estimate the wall heat flux, surface temperature, convective heat transfer coefficient, and combustion gas temperature for a typical divergent rocket nozzle made of mild steel, and the results are compared with experimentally measured outer surface temperature data.
Efficient numerical method for computation of thermohydrodynamics of laminar lubricating films
NASA Technical Reports Server (NTRS)
Elrod, Harold G.
1989-01-01
The purpose of this paper is to describe an accurate, yet economical, method for computing temperature effects in laminar lubricating films in two dimensions. The procedure presented here is a sequel to one presented in Leeds in 1986 that was carried out for the one-dimensional case. Because of the marked dependence of lubricant viscosity on temperature, the effect of viscosity variation both across and along a lubricating film can dwarf other deviations from ideal constant-property lubrication. In practice, a thermohydrodynamics program will involve simultaneous solution of the film lubrication problem, together with heat conduction in a solid, complex structure. The extent of computation required makes economy in numerical processing of utmost importance. In pursuit of such economy, we here use techniques similar to those for Gaussian quadrature. We show that, for many purposes, the use of just two properly positioned temperatures (Lobatto points) characterizes well the transverse temperature distribution.
Miyabe, Kanji; Guiochon, Georges
2011-01-01
It is probably impossible to prepare high-performance liquid chromatography (HPLC) columns that have a completely homogeneous packing structure. Many reports in the literature show that the radial distributions of the mobile phase flow velocity and the local column efficiency are not flat, even in columns considered as good. A degree of radial heterogeneity seems to be a common property of all HPLC columns and an important source of peak tailing, which prevents the derivation of accurate information on chromatographic behavior from a straightforward analysis of elution peak profiles. This work reports on a numerical method developed to derive from recorded peak profiles the column efficiency at the column center, the degree of column radial heterogeneity, and the polynomial function that best represents the radial distributions of the flow velocity and the column efficiency. This numerical method was applied to two concrete examples of tailing peak profiles previously described. It was demonstrated that this numerical method is effective to estimate important parameters characterizing the radial heterogeneity of chromatographic columns.
NASA Astrophysics Data System (ADS)
Nagai, Yuki; Shinohara, Yasushi; Futamura, Yasunori; Sakurai, Tetsuya
2017-01-01
We propose the reduced-shifted conjugate-gradient (RSCG) method, which is numerically efficient to calculate a matrix element of a Green's function defined as a resolvent of a Hamiltonian operator, by solving linear equations with a desired accuracy. This method does not calculate solution vectors of linear equations but does directly calculate a matrix element of the resolvent. The matrix elements with different frequencies are simultaneously obtained. Thus, it is easy to calculate the exception value expressed as a Matsubara summation of these elements. To illustrate a power of our method, we choose a nano-structured superconducting system with a mean-field Bogoliubov-de Gennes (BdG) approach. This method allows us to treat with the system with the fabrication potential, where one cannot effectively use the kernel-polynomial-based method. We consider the d-wave nano-island superconductor by simultaneously solving the linear equations with a large number (˜50000) of Matsubara frequencies.
NASA Astrophysics Data System (ADS)
Gaudreault, Stéphane; Pudykiewicz, Janusz A.
2016-10-01
The exponential propagation methods were applied in the past for accurate integration of the shallow water equations on the sphere. Despite obvious advantages related to the exact solution of the linear part of the system, their use for the solution of practical problems in geophysics has been limited because efficiency of the traditional algorithm for evaluating the exponential of Jacobian matrix is inadequate. In order to circumvent this limitation, we modify the existing scheme by using the Incomplete Orthogonalization Method instead of the Arnoldi iteration. We also propose a simple strategy to determine the initial size of the Krylov space using information from previous time instants. This strategy is ideally suited for the integration of fluid equations where the structure of the system Jacobian does not change rapidly between the subsequent time steps. A series of standard numerical tests performed with the shallow water model on a geodesic icosahedral grid shows that the new scheme achieves efficiency comparable to the semi-implicit methods. This fact, combined with the accuracy and the mass conservation of the exponential propagation scheme, makes the presented method a good candidate for solving many practical problems, including numerical weather prediction.
Serang, Oliver
2015-08-01
Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in log-transformed form and denoted as "infimal convolution," "min-convolution," or "convolution on the tropical semiring"), for which no O(k log(k)) method is currently known. Presented here is an O(k log(k)) numerical method for estimating the max-convolution of two nonnegative vectors (e.g., two probability mass functions), where k is the length of the larger vector. This numerical max-convolution method is then demonstrated by performing fast max-product inference on a convolution tree, a data structure for performing fast inference given information on the sum of n discrete random variables in O(nk log(nk)log(n)) steps (where each random variable has an arbitrary prior distribution on k contiguous possible states). The numerical max-convolution method can be applied to specialized classes of hidden Markov models to reduce the runtime of computing the Viterbi path from nk(2) to nk log(k), and has potential application to the all-pairs shortest paths problem.
El-Lakkani, A; Mahran, H
2015-01-01
A new two-dimensional graphical representation of protein sequences is introduced. Twenty concentric evenly spaced circles divided by n radial lines into equal divisions are selected to represent any protein sequence of length n. Each circle represents one of the different 20 amino acids, and each radial line represents a single amino acid of the protein sequence. An efficient numerical method based on the graph is proposed to measure the similarity between two protein sequences. To prove the accuracy of our approach, the method is applied to NADH dehydrogenase subunit 5 (ND5) proteins of nine different species and 24 transferrin sequences from vertebrates. High values of correlation coefficient between our results and the results of ClustalW are obtained (approximately perfect correlations). These values are higher than the values obtained in many other related works.
NASA Astrophysics Data System (ADS)
Blum, Volker
This talk describes recent advances of a general, efficient, accurate all-electron electronic theory approach based on numeric atom-centered orbitals; emphasis is placed on developments related to materials for energy conversion and their discovery. For total energies and electron band structures, we show that the overall accuracy is on par with the best benchmark quality codes for materials, but scalable to large system sizes (1,000s of atoms) and amenable to both periodic and non-periodic simulations. A recent localized resolution-of-identity approach for the Coulomb operator enables O (N) hybrid functional based descriptions of the electronic structure of non-periodic and periodic systems, shown for supercell sizes up to 1,000 atoms; the same approach yields accurate results for many-body perturbation theory as well. For molecular systems, we also show how many-body perturbation theory for charged and neutral quasiparticle excitation energies can be efficiently yet accurately applied using basis sets of computationally manageable size. Finally, the talk highlights applications to the electronic structure of hybrid organic-inorganic perovskite materials, as well as to graphene-based substrates for possible future transition metal compound based electrocatalyst materials. All methods described here are part of the FHI-aims code. VB gratefully acknowledges contributions by numerous collaborators at Duke University, Fritz Haber Institute Berlin, TU Munich, USTC Hefei, Aalto University, and many others around the globe.
Efficient numerical method for computation of the thermohydrodynamics of laminar lubricating films
NASA Technical Reports Server (NTRS)
Elrod, H. G.
1991-01-01
The purpose of this paper is to describe an accurate, yet economical, method for computing temperature effects in laminar lubricating films in two dimensions. Because of the marked dependence of lubricant viscosity on temperature, the effect of viscosity variation both across and along a lubricating film can dwarf other deviations from ideal constant-property lubrication. In practice, a thermohydrodynamics program will involve simultaneous solution of the film lubrication problem, together with heat conduction in a solid, complex structure. In pursuit of computational economy, techniques similar to those for Gaussian quadrature are used; it is shown that, for many purposes, the use of just two properly positioned temperatures (Lobatto points) characterizes the transverse temperature distribution.
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
Introduction to Numerical Methods
Schoonover, Joseph A.
2016-06-14
These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.
NASA Technical Reports Server (NTRS)
Bardina, J. E.
1994-01-01
A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in
NASA Astrophysics Data System (ADS)
Tang, Qinglin; Zhang, Yong; Mauser, Norbert J.
2017-10-01
We present a robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose-Einstein condensates (BEC). Using the rotating Lagrangian coordinates transform (Bao et al., 2013), we reformulate the original coupled Gross-Pitaevskii equations (CGPE) into new equations where the rotating term vanishes and the potential becomes time-dependent. A time-splitting Fourier pseudospectral method is proposed to numerically solve the new equations where the nonlocal Dipole-Dipole Interactions (DDI) are computed by a newly-developed Gaussian-sum (GauSum) solver (Exl et al., 2016) which helps achieve spectral accuracy in space within O(N log N) operations (N is the total number of grid points). The new method is spectrally accurate in space and second order accurate in time - these accuracies are confirmed numerically. Dynamical properties of some physical quantities, including the total mass, energy, center of mass and angular momentum expectation, are presented and confirmed numerically. Interesting dynamical phenomena that are peculiar to the rotating two-component dipolar BECs, such as dynamics of center of mass, quantized vortex lattices dynamics and the collapse dynamics in 3D, are presented.
Numerical methods for molecular dynamics
Skeel, R.D.
1991-01-01
This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.
NASA Astrophysics Data System (ADS)
Mehrmann, Volker; Xu, Hongguo
2000-11-01
We study classical control problems like pole assignment, stabilization, linear quadratic control and H[infinity] control from a numerical analysis point of view. We present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework. We also discuss some new algorithmic approaches.
Numerical methods in acoustics
NASA Astrophysics Data System (ADS)
Candel, S. M.
This paper presents a survey of some computational techniques applicable to acoustic wave problems. Recent advances in wave extrapolation methods, spectral methods and boundary integral methods are discussed and illustrated by specific calculations.
Jauberteau, J L; Jauberteau, I
2007-04-01
The method proposed to determine the electron energy distribution is based on the numerical simulation of the effect induced by a sinusoidal perturbation superimposed to the direct current voltage applied to the probe. The simulation is generating a multiple harmonic components signal over the rough experimental data. Each harmonic component can be isolated by means of finite impulse response filters. Then, the second derivative is deduced from the second harmonic component using the Taylor expansion. The efficiency of the method is proved first on simple cases and second on typical Langmuir probes characteristics recorded in the expansion of a microwave plasma containing argon or nitrogen-hydrogen gas mixture. Results obtained using this method are compared to those, which are determined using a classical Savitzsky-Golay filter.
Jauberteau, J. L.; Jauberteau, I.
2007-04-15
The method proposed to determine the electron energy distribution is based on the numerical simulation of the effect induced by a sinusoidal perturbation superimposed to the direct current voltage applied to the probe. The simulation is generating a multiple harmonic components signal over the rough experimental data. Each harmonic component can be isolated by means of finite impulse response filters. Then, the second derivative is deduced from the second harmonic component using the Taylor expansion. The efficiency of the method is proved first on simple cases and second on typical Langmuir probes characteristics recorded in the expansion of a microwave plasma containing argon or nitrogen-hydrogen gas mixture. Results obtained using this method are compared to those, which are determined using a classical Savitzsky-Golay filter.
Efficient numerical evaluation of Feynman integrals
NASA Astrophysics Data System (ADS)
Li, Zhao; Wang, Jian; Yan, Qi-Shu; Zhao, Xiaoran
2016-03-01
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass. Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)
Determination of geopotential coefficients by efficient numerical integration techniques
NASA Astrophysics Data System (ADS)
Hansen, R. A.
An efficient, high accuracy, double integration method which evaluates the iterated form of the surface integral representations of the geopotential coefficients is presented. The efficiency and high accuracy of this method is obtained by the utilization of the Romberg numerical integration scheme. Additional efficiency is obtained by computing the inner integral which is common to many different coefficients only once. This method was tested using a test case earth which represented the basic features of the earth's potential field.
NASA Astrophysics Data System (ADS)
Encinas, A. H.; Gayoso-Martínez, V.; Martín Del Rey, A.; Martín-Vaquero, J.; Queiruga-Dios, A.
2016-03-01
In this paper, we discuss the problem of solving nonlinear Klein-Gordon equations (KGEs), which are especially useful to model nonlinear phenomena. In order to obtain more exact solutions, we have derived different fourth- and sixth-order, stable explicit and implicit finite difference schemes for some of the best known nonlinear KGEs. These new higher-order methods allow a reduction in the number of nodes, which is necessary to solve multi-dimensional KGEs. Moreover, we describe how higher-order stable algorithms can be constructed in a similar way following the proposed procedures. For the considered equations, the stability and consistency of the proposed schemes are studied under certain smoothness conditions of the solutions. In addition to that, we present experimental results obtained from numerical methods that illustrate the efficiency of the new algorithms, their stability, and their convergence rate.
Numerical Methods for Initial Value Problems.
1980-07-01
of general multistep methods for ordinary differential equations a4 to implement an efficient algorithm for the solution of stiff equations . Still...integral equations II. Roundoff error for variants of Gaussian elimination III. Multistep methods for ordinary differential equations IV. Multi-grid...62 -! Paige III. NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS ....... 63 1. Equivalent Forms of Multistep
A numerical method of regenerator
NASA Astrophysics Data System (ADS)
Zhu, Shaowei; Matsubara, Yoichi
2004-02-01
A numerical method for regenerators is introduced in this paper. It is not only suitable for the regenerators in cryocoolers and Stirling engines, but also suitable for the stacks in acoustic engines and the pulse tubes in pulse tube refrigerators. The numerical model is one dimensional periodic unsteady flow model. The numerical method is based on the control volume concept with the implicitly solve method. The iteration acceleration method, which considers the one-dimensional periodic unsteady problem as the steady two-dimensional problem, is used for decreasing the calculation time. By this method, the regenerator in an inertance tube pulse tube refrigerator was simulated. The result is useful for understanding how the inefficiency of the regenerator changes with the inertance effect.
An efficient algorithm for numerical airfoil optimization
NASA Technical Reports Server (NTRS)
Vanderplaats, G. N.
1979-01-01
A new optimization algorithm is presented. The method is based on sequential application of a second-order Taylor's series approximation to the airfoil characteristics. Compared to previous methods, design efficiency improvements of more than a factor of 2 are demonstrated. If multiple optimizations are performed, the efficiency improvements are more dramatic due to the ability of the technique to utilize existing data. The method is demonstrated by application to subsonic and transonic airfoil design but is a general optimization technique and is not limited to a particular application or aerodynamic analysis.
Numerical relativity and spectral methods
NASA Astrophysics Data System (ADS)
Grandclement, P.
2016-12-01
The term numerical relativity denotes the various techniques that aim at solving Einstein's equations using computers. Those computations can be divided into two families: temporal evolutions on the one hand and stationary or periodic solutions on the other one. After a brief presentation of those two classes of problems, I will introduce a numerical tool designed to solve Einstein's equations: the KADATH library. It is based on the the use of spectral methods that can reach high accuracy with moderate computational resources. I will present some applications about quasicircular orbits of black holes and boson star configurations.
Numerical methods for turbulent flow
NASA Technical Reports Server (NTRS)
Turner, James C., Jr.
1988-01-01
It has generally become accepted that the Navier-Strokes equations predict the dynamic behavior of turbulent as well as laminar flows of a fluid at a point in space away form a discontinuity such as a shock wave. Turbulence is also closely related to the phenomena of non-uniqueness of solutions of the Navier-Strokes equations. These second order, nonlinear partial differential equations can be solved analytically for only a few simple flows. Turbulent flow fields are much to complex to lend themselves to these few analytical methods. Numerical methods, therefore, offer the only possibility of achieving a solution of turbulent flow equations. In spite of recent advances in computer technology, the direct solution, by discrete methods, of the Navier-Strokes equations for turbulent flow fields is today, and in the foreseeable future, impossible. Thus the only economically feasible way to solve practical turbulent flow problems numerically is to use statistically averaged equations governing mean-flow quantities. The objective is to study some recent developments relating to the use of numerical methods to study turbulent flow.
Numerical prediction of Pelton turbine efficiency
NASA Astrophysics Data System (ADS)
Jošt, D.; Mežnar, P.; Lipej, A.
2010-08-01
This paper presents a numerical analysis of flow in a 2 jet Pelton turbine with horizontal axis. The analysis was done for the model at several operating points in different operating regimes. The results were compared to the results of a test of the model. Analysis was performed using ANSYS CFX-12.1 computer code. A k-ω SST turbulent model was used. Free surface flow was modelled by two-phase homogeneous model. At first, a steady state analysis of flow in the distributor with two injectors was performed for several needle strokes. This provided us with data on flow energy losses in the distributor and the shape and velocity of jets. The second step was an unsteady analysis of the runner with jets. Torque on the shaft was then calculated from pressure distribution data. Averaged torque values are smaller than measured ones. Consequently, calculated turbine efficiency is also smaller than the measured values, the difference is about 4 %. The shape of the efficiency diagram conforms well to the measurements.
An efficient numerical algorithm for transverse impact problems
NASA Technical Reports Server (NTRS)
Sankar, B. V.; Sun, C. T.
1985-01-01
Transverse impact problems in which the elastic and plastic indentation effects are considered, involve a nonlinear integral equation for the contact force, which, in practice, is usually solved by an iterative scheme with small increments in time. In this paper, a numerical method is proposed wherein the iterations of the nonlinear problem are separated from the structural response computations. This makes the numerical procedures much simpler and also efficient. The proposed method is applied to some impact problems for which solutions are available, and they are found to be in good agreement. The effect of the magnitude of time increment on the results is also discussed.
Numerical methods for multibody systems
NASA Technical Reports Server (NTRS)
Glowinski, Roland; Nasser, Mahmoud G.
1994-01-01
This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1989-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1989-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.
Numerical methods in heat transfer
Lewis, R.W.; Morgan, K.; Schrefler, B.A.
1983-01-01
Topics discussed in this book include modelling the effects of fire, ablation, heat flow in porous rock, thermal stress and dissolving coal. Alternative energy sources such as geothermal reservoirs and solar radiation are also discussed. Includes bibliographies at the end of the papers, a cited author index, and a subject index. Contents, abridged: Exact finite element solutions for linear steady state thermal problems. Steep gradient modelling in diffusion problems. Numerical solution of coupled conduction-convection problems using lumped-parameter methods. The prediction of turbulent heat transfer by the finite element methods. The influence of creep and transformation plasticity in the analysis of stresses due to heat treatment. Heat and moisture movement in wood composite materials during the pressing operation-a simplified model. Index.
Efficient numerical solution to vacuum decay with many fields
NASA Astrophysics Data System (ADS)
Masoumi, Ali; Olum, Ken D.; Shlaer, Benjamin
2017-01-01
Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in around a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here.
NASA Astrophysics Data System (ADS)
Mehta, Bhavyang
This study describes the system integration and operation of Southern Methodist University (SMU) - University of Texas at Dallas (UTD) anechoic chamber; far-field measurements of antenna parameters such as radiation efficiency, radiation patterns, directivity, and gain; and methodologies to improve measurement results. Also, it provides a brief explanation of the different methods used to make near-field measurements. This study primarily focuses on the ways to improve chamber's performance for far-field measurements. First, a methodology to improve the measurement results for broad-beam antennas such as Dipole is proposed. A few experiments were performed to identify the source of scattering, and accordingly, the mounting structure for the antenna under test (AUT) was changed to improve the results for the AUT's radiation pattern. Second, a method to compute the radiation efficiency of the antenna with broad beam is introduced. In this method, the total radiated power of Standard Gain Horn (SGH) antenna is compared with that of the AUT to evaluate the radiation efficiency of the AUT with the least possible uncertainties.
Numerical study of particle capture efficiency in fibrous filter
NASA Astrophysics Data System (ADS)
Fan, Jianhua; Lominé, Franck; Hellou, Mustapha
2017-06-01
Numerical simulations are performed for transport and deposition of particles over a fixed obstacle in a fluid flow. The effect of particle size and Stokes number on the particle capture efficiency is investigated using two methods. The first one is one-way coupling combining Lattice Boltzmann (LB) method with Lagrangian point-like approach. The second one is two-way coupling based on the coupling between Lattice Boltzmann method and discrete element (DE) method, which consider the particle influence on the fluid. Then the single fiber collection efficiency characterized by Stokes number (St) are simulated by LB-DE methods. Results show that two-way coupling method is more appropriate in our case for particles larger than 8 μm. A good agreement has also been observed between our simulation results and existing correlations for single fiber collection efficiency. The numerical simulations presented in this work are useful to understand the particle transport and deposition and to predict the capture efficiency.
Incompatible numerical manifold method for fracture problems
NASA Astrophysics Data System (ADS)
Wei, Gaofeng; Li, Kaitai; Jiang, Haihui
2010-05-01
The incompatible numerical manifold method (INMM) is based on the finite cover approximation theory, which provides a unified framework for problems dealing with continuum and discontinuities. The incompatible numerical manifold method employs two cover systems as follows. The mathematical cover system provides the nodes for forming finite covers of the solution domain and the weighted functions, and the physical cover system describes geometry of the domain and the discontinuous surfaces therein. In INMM, the mathematical finite cover approximation theory is used to model cracks that lead to interior discontinuities in the process of displacement. Therefore, the discontinuity is treated mathematically instead of empirically by the existing methods. However, one cover of a node is divided into two irregular sub-covers when the INMM is used to model the discontinuity. As a result, the method sometimes causes numerical errors at the tip of a crack. To improve the precision of the INMM, the analytical solution is used at the tip of a crack, and thus the cover displacement functions are extended with higher precision and computational efficiency. Some numerical examples are given.
Spectral Methods for Numerical Relativity.
Grandclément, Philippe; Novak, Jérôme
2009-01-01
Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole-binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole-binary mergers.
Numerical methods used in fusion science numerical modeling
NASA Astrophysics Data System (ADS)
Yagi, M.
2015-04-01
The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.
NASA Astrophysics Data System (ADS)
Gharti, H. N.; Austermann, J.; Komatitsch, D.; Lau, H. C.; Mitrovica, J. X.; Peter, D. B.; Tromp, J.; Xie, Z.; Zampini, S.
2013-12-01
The complete set of governing equations for global dynamic and quasistatic problems --such as post-seismic and post-glacial rebound, tidal loading, and long-period seismology-- involves a coupling between the conservation laws of continuum mechanics and Poisson/Laplace's equation. For dynamic problems, such as seismic wave propagation and the free oscillations of the Earth, it is possible to decouple Poisson's equation using an explicit time marching scheme so that it can be solved independently. For quasistatic problems, such as glacial isostatic adjustment and tidal loading, inertia is neglected, requiring an implicit time marching scheme. In the latter case, Poisson's equation cannot be decoupled. Although an explicit time scheme with an independent Poisson's solver is generally fast, such an approach is limited by conditional stability, such that a very large number of time steps is often necessary. On the other hand, an implicit time scheme coupled with Poisson's equation is generally slow but unconditionally stable. In both cases, the unbounded and large-scale nature of the problem poses numerical challenges, particularly for 3D Earth models. Most of the existing methods use spherical harmonics to solve the unbounded Poisson/Laplace's equation. Such methods are often limited to spherically-symmetric models or have to rely on iterative procedures. In view of these challenges, we develop a parallel software package based on the spectral-element method combined with a mapped infinite-element approach. While the spectral-element method is used within the Earth model, the infinite-element approach is employed in the outer region. In the infinite element approach, a so-called infinite-element layer is used to mimic all of space. The outermost edges of an element in the infinite-element layer are mapped to infinity in order to reproduce the behavior of gravitational potential outside the domain of interest, such that the potential decays to zero at infinity. Gauss
Linearized Implicit Numerical Method for Burgers' Equation
NASA Astrophysics Data System (ADS)
Mukundan, Vijitha; Awasthi, Ashish
2016-12-01
In this work, a novel numerical scheme based on method of lines (MOL) is proposed to solve the nonlinear time dependent Burgers' equation. The Burgers' equation is semi discretized in spatial direction by using MOL to yield system of nonlinear ordinary differential equations in time. The resulting system of nonlinear differential equations is integrated by an implicit finite difference method. We have not used Cole-Hopf transformation which gives less accurate solution for very small values of kinematic viscosity. Also, we have not considered nonlinear solvers that are computationally costlier and take more running time.In the proposed scheme nonlinearity is tackled by Taylor series and the use of fully discretized scheme is easy and practical. The proposed method is unconditionally stable in the linear sense. Furthermore, efficiency of the proposed scheme is demonstrated using three test problems.
Numerical methods for molecular dynamics. Progress report
Skeel, R.D.
1991-12-31
This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.
Fytas, Nikolaos G; Martín-Mayor, Víctor
2016-06-01
It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.
Numerical methods for problems in computational aeroacoustics
NASA Astrophysics Data System (ADS)
Mead, Jodi Lorraine
1998-12-01
A goal of computational aeroacoustics is the accurate calculation of noise from a jet in the far field. This work concerns the numerical aspects of accurately calculating acoustic waves over large distances and long time. More specifically, the stability, efficiency, accuracy, dispersion and dissipation in spatial discretizations, time stepping schemes, and absorbing boundaries for the direct solution of wave propagation problems are determined. Efficient finite difference methods developed by Tam and Webb, which minimize dispersion and dissipation, are commonly used for the spatial and temporal discretization. Alternatively, high order pseudospectral methods can be made more efficient by using the grid transformation introduced by Kosloff and Tal-Ezer. Work in this dissertation confirms that the grid transformation introduced by Kosloff and Tal-Ezer is not spectrally accurate because, in the limit, the grid transformation forces zero derivatives at the boundaries. If a small number of grid points are used, it is shown that approximations with the Chebyshev pseudospectral method with the Kosloff and Tal-Ezer grid transformation are as accurate as with the Chebyshev pseudospectral method. This result is based on the analysis of the phase and amplitude errors of these methods, and their use for the solution of a benchmark problem in computational aeroacoustics. For the grid transformed Chebyshev method with a small number of grid points it is, however, more appropriate to compare its accuracy with that of high- order finite difference methods. This comparison, for an order of accuracy 10-3 for a benchmark problem in computational aeroacoustics, is performed for the grid transformed Chebyshev method and the fourth order finite difference method of Tam. Solutions with the finite difference method are as accurate. and the finite difference method is more efficient than, the Chebyshev pseudospectral method with the grid transformation. The efficiency of the Chebyshev
Flow Structures and Efficiency of Swimming Fish school: Numerical Study
NASA Astrophysics Data System (ADS)
Yatagai, Yuzuru; Hattori, Yuji
2013-11-01
The flow structure and energy-saving mechanism in fish school is numerically investigated by using the volume penalization method. We calculate the various patterns of configuration of fishes and investigate the relation between spatial arrangement and the performance of fish. It is found that the down-stream fish gains a hydrodynamic advantage from the upstream wake shed by the upstream fish. The most efficient configuration is that the downstream fish is placed in the wake. It reduces the drag force of the downstream fish in comparison with that in solo swimming.
A stable and efficient numerical algorithm for unconfined aquifer analysis.
Keating, Elizabeth; Zyvoloski, George
2009-01-01
The nonlinearity of equations governing flow in unconfined aquifers poses challenges for numerical models, particularly in field-scale applications. Existing methods are often unstable, do not converge, or require extremely fine grids and small time steps. Standard modeling procedures such as automated model calibration and Monte Carlo uncertainty analysis typically require thousands of model runs. Stable and efficient model performance is essential to these analyses. We propose a new method that offers improvements in stability and efficiency and is relatively tolerant of coarse grids. It applies a strategy similar to that in the MODFLOW code to the solution of Richard's equation with a grid-dependent pressure/saturation relationship. The method imposes a contrast between horizontal and vertical permeability in gridblocks containing the water table, does not require "dry" cells to convert to inactive cells, and allows recharge to flow through relatively dry cells to the water table. We establish the accuracy of the method by comparison to an analytical solution for radial flow to a well in an unconfined aquifer with delayed yield. Using a suite of test problems, we demonstrate the efficiencies gained in speed and accuracy over two-phase simulations, and improved stability when compared to MODFLOW. The advantages for applications to transient unconfined aquifer analysis are clearly demonstrated by our examples. We also demonstrate applicability to mixed vadose zone/saturated zone applications, including transport, and find that the method shows great promise for these types of problem as well.
A stable and efficient numerical algorithm for unconfined aquifer analysis
Keating, Elizabeth; Zyvoloski, George
2008-01-01
The non-linearity of equations governing flow in unconfined aquifers poses challenges for numerical models, particularly in field-scale applications. Existing methods are often unstable, do not converge, or require extremely fine grids and small time steps. Standard modeling procedures such as automated model calibration and Monte Carlo uncertainty analysis typically require thousands of forward model runs. Stable and efficient model performance is essential to these analyses. We propose a new method that offers improvements in stability and efficiency, and is relatively tolerant of coarse grids. It applies a strategy similar to that in the MODFLOW code to solution of Richard's Equation with a grid-dependent pressure/saturation relationship. The method imposes a contrast between horizontal and vertical permeability in gridblocks containing the water table. We establish the accuracy of the method by comparison to an analytical solution for radial flow to a well in an unconfined aquifer with delayed yield. Using a suite of test problems, we demonstrate the efficiencies gained in speed and accuracy over two-phase simulations, and improved stability when compared to MODFLOW. The advantages for applications to transient unconfined aquifer analysis are clearly demonstrated by our examples. We also demonstrate applicability to mixed vadose zone/saturated zone applications, including transport, and find that the method shows great promise for these types of problem, as well.
Numerical methods for engine-airframe integration
Murthy, S.N.B.; Paynter, G.C.
1986-01-01
Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison of full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment.
A simple, reliable and efficient scheme for automatic numerical integration
NASA Astrophysics Data System (ADS)
Pérez-Jordá, JoséM.; San-Fabián, Emilio; Moscardó, Federico
1992-06-01
A scheme for automatic numerical integration is presented. It uses the change of variable x=1+( {2}/{π}){[1+ {2}/{3}(1-z 2)]z√1-z 2 - arccosz} to transform the integral to be computed, ∫ 1-1f( x) d x, into ( {16}/{3π})∫ 1-1f(x)(1-z 2)√1-z 2dz , which is approximated by successive n-points Gauss-Chebyshev quadrature formulas of the second kind ( In). Due to the special nature of their abscissas and weights, a sequence of formulas I 1, I 3, I 7,…, I {(n-1)}/{2}, I n, I 2n+1 may be generated, such that I2 n+1 may be computed with only n + 1 new integrand evaluations, using the previous value of In. An error estimation is proposed for I2 n+1 , which only needs two previous values of the sequence ( In and I {(n+1)}/{2}). The algorithm may be implemented by a very short program (a FORTRAN 77 version is included) that spends practically all its running time in integrand evaluations. It is compared with other methods for automatic numerical integration (trapezoidal rule, Simpson's rule, Romberg's method, an adaptive Gauss-Kronrod rule and Clenshaw-Curtis method) over a broad set of 20 functions. We conclude that the present method is very simple and reliable and is the most efficient among the methods tested here. Possible applications in density functional theory are explored.
An Efficient Numerical Approach for Nonlinear Fokker-Planck equations
NASA Astrophysics Data System (ADS)
Otten, Dustin; Vedula, Prakash
2009-03-01
Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.
Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals
NASA Technical Reports Server (NTRS)
Fink, Patrick W.; Wilton, Donald R.; Khayat, Michael A.
2007-01-01
Recently, significant progress has been made in the handling of singular and nearly-singular potential integrals that commonly arise in the Boundary Element Method (BEM). To facilitate object-oriented programming and handling of higher order basis functions, cancellation techniques are favored over techniques involving singularity subtraction. However, gradients of the Newton-type potentials, which produce hypersingular kernels, are also frequently required in BEM formulations. As is the case with the potentials, treatment of the near-hypersingular integrals has proven more challenging than treating the limiting case in which the observation point approaches the surface. Historically, numerical evaluation of these near-hypersingularities has often involved a two-step procedure: a singularity subtraction to reduce the order of the singularity, followed by a boundary contour integral evaluation of the extracted part. Since this evaluation necessarily links basis function, Green s function, and the integration domain (element shape), the approach ill fits object-oriented programming concepts. Thus, there is a need for cancellation-type techniques for efficient numerical evaluation of the gradient of the potential. Progress in the development of efficient cancellation-type procedures for the gradient potentials was recently presented. To the extent possible, a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. However, since the gradient kernel involves singularities of different orders, we also require that the transformation leaves remaining terms that are analytic. The terms "normal" and "tangential" are used herein with reference to the source element. Also, since computational formulations often involve the numerical evaluation of both potentials and their gradients, it is highly desirable that a single integration procedure efficiently handles both.
Excel spreadsheet in teaching numerical methods
NASA Astrophysics Data System (ADS)
Djamila, Harimi
2017-09-01
One of the important objectives in teaching numerical methods for undergraduates’ students is to bring into the comprehension of numerical methods algorithms. Although, manual calculation is important in understanding the procedure, it is time consuming and prone to error. This is specifically the case when considering the iteration procedure used in many numerical methods. Currently, many commercial programs are useful in teaching numerical methods such as Matlab, Maple, and Mathematica. These are usually not user-friendly by the uninitiated. Excel spreadsheet offers an initial level of programming, which it can be used either in or off campus. The students will not be distracted with writing codes. It must be emphasized that general commercial software is required to be introduced later to more elaborated questions. This article aims to report on a teaching numerical methods strategy for undergraduates engineering programs. It is directed to students, lecturers and researchers in engineering field.
A hierarchical energy efficiency evaluation model of numerical control workshop
NASA Astrophysics Data System (ADS)
Xu, Binzi; Wang, Yan; Ji, Zhicheng
2017-07-01
Energy consumption of numerical control (NC) workshop has lots of characteristics, such as hierarchy, multi-sources and time-varying. These characteristics make the modeling and evaluation of energy consumption in NC workshop very difficult. In this paper, a novel hierarchical model of the energy consumption in NC workshop is presented. Then, the calculation methods of energy efficiency in each layer are given. Furthermore, the acquisition method of the energy consumption data which is easily implemented is put forward and an experiment in NC workshop was made to illustrate the effectiveness of the proposed energy consumption model. The experimental results showed that the model cannot only describe the energy consumption effectively but also provide a way to identify the bottleneck of energy consumption in the workshop.
Dynamic optimization of bioprocesses: efficient and robust numerical strategies.
Banga, Julio R; Balsa-Canto, Eva; Moles, Carmen G; Alonso, Antonio A
2005-06-29
The dynamic optimization (open loop optimal control) of non-linear bioprocesses is considered in this contribution. These processes can be described by sets of non-linear differential and algebraic equations (DAEs), usually subject to constraints in the state and control variables. A review of the available solution techniques for this class of problems is presented, highlighting the numerical difficulties arising from the non-linear, constrained and often discontinuous nature of these systems. In order to surmount these difficulties, we present several alternative stochastic and hybrid techniques based on the control vector parameterization (CVP) approach. The CVP approach is a direct method which transforms the original problem into a non-linear programming (NLP) problem, which must be solved by a suitable (efficient and robust) solver. In particular, a hybrid technique uses a first global optimization phase followed by a fast second phase based on a local deterministic method, so it can handle the nonconvexity of many of these NLPs. The efficiency and robustness of these techniques is illustrated by solving several challenging case studies regarding the optimal control of fed-batch bioreactors and other bioprocesses. In order to fairly evaluate their advantages, a careful and critical comparison with several other direct approaches is provided. The results indicate that the two-phase hybrid approach presents the best compromise between robustness and efficiency.
Implicit Numerical Methods in Meteorology
NASA Technical Reports Server (NTRS)
Augenbaum, J.
1984-01-01
The development of a fully implicit finite-difference model, whose time step is chosen solely to resolve accurately the physical flow of interest is discussed. The method is based on an operator factorization which reduces the dimensionality of the implicit approach: at each time step only (spatially) one-dimensional block-tridiagonal linear systems must be solved. The scheme uses two time levels and is second-order accurate in time. Compact implicit spatial differences are used, yielding fourth-order accuracy both vertically and horizontally. In addition, the development of a fully interactive computer code is discussed. With this code the user will have a choice of models, with various levels of accuracy and sophistication, which are imbedded, as subsets of the fully implicit 3D code.
Numerical Methods For Chemically Reacting Flows
NASA Technical Reports Server (NTRS)
Leveque, R. J.; Yee, H. C.
1990-01-01
Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.
Perception of numerical methods in rarefied gasdynamics
NASA Technical Reports Server (NTRS)
Bird, G. A.
1989-01-01
The relationships between various numerical methods applied to problems in rarefied gasdynamics are discussed, with emphasis on conflicting viewpoints and computational requirements associated with physical simulation versus the numerical solution of the Boltzmann equation. The basic differences between the molecular dynamics and direct simulation methods are shown to affect their applicability to dense and rarefied flows. Methods for the probabilistic selection of representative collision in the direct simulation Monte Carlo method are reviewed. A method combining the most desirable features of the earlier methods is presented.
New Methods of Energy Efficient Radon Mitigation
Fisk, W.J.; Prill, R.J.; Wooley, J.; Bonnefous, Y.C.; Gadgil, A.J.; Riley, W.J.
1994-05-01
Two new radon mitigation techniques are introduced and their evaluation in a field study complemented by numerical model predictions is described. Based on numerical predictions, installation of a sub gravel membrane at the study site resulted in a factor of two reduction in indoor radon concentrations. Experimental data indicated that installation of 'short-circuit' pipes extending between the subslab gravel and outdoors, caused an additional factor of two decrease in the radon concentration. Consequently, the combination of these two passive radon mitigation features, called the membrane and short-circuit (MASC) technique, was associated with a factor of four reduction in indoor radon concentration. The energy-efficient active radon mitigation method, called efficient active subslab pressurization (EASP), required only 20% of the fan energy of conventional active subslab depressurization and reduced the indoor radon concentration by approximately a factor of 15, including the numerically-predicted impact of the sub-gravel membrane.
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
Klein, R I; Stone, J M
2007-11-20
We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.
Numerical Methods for Nonlinear Hillslope Transport Laws
NASA Astrophysics Data System (ADS)
Perron, J. T.
2008-12-01
The numerical methods used to solve nonlinear sediment transport equations often set restrictive limits on the stability and accuracy of landscape evolution models. This is especially true for hillslope transport laws in which sediment flux increases nonlinearly as the surface slope approaches a limiting value. Standard explicit finite difference methods applied to such laws are subject to fundamental limits on numerical stability that require time steps much shorter than the timescales over which landscapes evolve, creating a heavy computational burden. Methods that rely on cell-to-cell sediment routing schemes can introduce significant errors that may not be obvious unless the numerical solution is compared with a known solution. I present a new, implicit method for nonlinear hillslope transport that builds on a previously proposed approach to modeling alluvial sediment transport but avoids the use of a cell-to-cell sediment routing scheme. Comparisons of numerical solutions with analytic solutions in one and two dimensions show that the new method retains the accuracy of the explicit method while allowing timesteps several orders of magnitude longer than the maximum timesteps permitted by the explicit method. The method can be adapted to any transport law in which the expression for sediment flux is differentiable, including coupled systems in which sediment flux is a function of quantities such as soil depth.
Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals
NASA Technical Reports Server (NTRS)
Fink, Patricia W.; Wilton, D. R.; Khayat, Michael A.
2007-01-01
Simple and efficient numerical procedures for evaluating the gradient of Newton-type potentials are presented. Convergences of both normal and tangential components of the gradient are examined. The convergence of the vector potential is also examined, and it is shown that the scheme for handling near-hypersingular integrals also is effective for the nearly singular potential terms.
Numerical Processing Efficiency Improved in Experienced Mental Abacus Children
ERIC Educational Resources Information Center
Wang, Yunqi; Geng, Fengji; Hu, Yuzheng; Du, Fenglei; Chen, Feiyan
2013-01-01
Experienced mental abacus (MA) users are able to perform mental arithmetic calculations with unusual speed and accuracy. However, it remains unclear whether their extraordinary gains in mental arithmetic ability are accompanied by an improvement in numerical processing efficiency. To address this question, the present study, using a numerical…
Numerical Processing Efficiency Improved in Experienced Mental Abacus Children
ERIC Educational Resources Information Center
Wang, Yunqi; Geng, Fengji; Hu, Yuzheng; Du, Fenglei; Chen, Feiyan
2013-01-01
Experienced mental abacus (MA) users are able to perform mental arithmetic calculations with unusual speed and accuracy. However, it remains unclear whether their extraordinary gains in mental arithmetic ability are accompanied by an improvement in numerical processing efficiency. To address this question, the present study, using a numerical…
Numerical Algorithms for Precise and Efficient Orbit Propagation and Positioning
NASA Astrophysics Data System (ADS)
Bradley, Ben K.
Motivated by the growing space catalog and the demands for precise orbit determination with shorter latency for science and reconnaissance missions, this research improves the computational performance of orbit propagation through more efficient and precise numerical integration and frame transformation implementations. Propagation of satellite orbits is required for astrodynamics applications including mission design, orbit determination in support of operations and payload data analysis, and conjunction assessment. Each of these applications has somewhat different requirements in terms of accuracy, precision, latency, and computational load. This dissertation develops procedures to achieve various levels of accuracy while minimizing computational cost for diverse orbit determination applications. This is done by addressing two aspects of orbit determination: (1) numerical integration used for orbit propagation and (2) precise frame transformations necessary for force model evaluation and station coordinate rotations. This dissertation describes a recently developed method for numerical integration, dubbed Bandlimited Collocation Implicit Runge-Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. It requires significantly fewer force function evaluations than explicit Runge-Kutta schemes and approaches the efficiency of the 8th-order Gauss-Jackson multistep method. Converting between the Geocentric Celestial Reference System (GCRS) and International Terrestrial Reference System (ITRS) is necessary for many applications in astrodynamics, such as orbit propagation, orbit determination, and analyzing geoscience data from satellite missions. This dissertation provides simplifications to the Celestial Intermediate Origin (CIO) transformation scheme and Earth orientation parameter (EOP) storage for use in positioning and
A numerical method for phase-change problems
NASA Technical Reports Server (NTRS)
Kim, Charn-Jung; Kaviany, Massoud
1990-01-01
A highly accurate and efficient finite-difference method for phase-change problems with multiple moving boundaries of irregular shape is developed by employing a coordinate transformation that immobilizes moving boundaries and preserves the conservative forms of the original governing equations. The numerical method is first presented for one-dimensional phase-change problems (involving large density variation between phases, heat generation, and multiple moving boundaries) and then extended to solve two-dimensional problems (without change of densities between phases). Numerical solutions are obtained non-iteratively using an explicit treatment of the interfacial mass and energy balances and an implicit treatment of the temperature field equations. The accuracy and flexibility of the present numerical method are verified by solving some phase-change problems and comparing the results with existing analytical, semi-analytical and numerical solutions. Results indicate that one- and two-dimensional phase-change problems can be handled easily with excellent accuracies.
A numerical method for phase-change problems
NASA Technical Reports Server (NTRS)
Kim, Charn-Jung; Kaviany, Massoud
1990-01-01
A highly accurate and efficient finite-difference method for phase-change problems with multiple moving boundaries of irregular shape is developed by employing a coordinate transformation that immobilizes moving boundaries and preserves the conservative forms of the original governing equations. The numerical method is first presented for one-dimensional phase-change problems (involving large density variation between phases, heat generation, and multiple moving boundaries) and then extended to solve two-dimensional problems (without change of densities between phases). Numerical solutions are obtained non-iteratively using an explicit treatment of the interfacial mass and energy balances and an implicit treatment of the temperature field equations. The accuracy and flexibility of the present numerical method are verified by solving some phase-change problems and comparing the results with existing analytical, semi-analytical and numerical solutions. Results indicate that one- and two-dimensional phase-change problems can be handled easily with excellent accuracies.
Numerical methods for nonlinear hillslope transport laws
NASA Astrophysics Data System (ADS)
Perron, J. Taylor
2011-06-01
The numerical methods used to solve nonlinear sediment transport equations often set very restrictive limits on the stability and accuracy of landscape evolution models. This is especially true for hillslope transport laws in which sediment flux increases nonlinearly as the surface slope approaches a limiting value. Explicit-time finite difference methods applied to such laws are subject to fundamental limits on numerical stability that require time steps much shorter than the timescales over which landscapes evolve, creating a heavy computational burden. I present an implicit method for nonlinear hillslope transport that builds on a previously proposed approach to modeling alluvial sediment transport and improves stability and accuracy by avoiding the direct calculation of sediment flux. This method can be adapted to any transport law in which the expression for sediment flux is differentiable. Comparisons of numerical solutions with analytic solutions in one and two dimensions show that the implicit method retains the accuracy of a standard explicit method while permitting time steps several orders of magnitude longer than the maximum stable time step for the explicit method. The ability to take long time steps affords a substantial savings in overall computation time, despite the implicit method's higher per-iteration computational cost. Implicit models for hillslope evolution also offer a distinct advantage when modeling the response of hillslopes to incising channels.
Numerical comparison between DHF and RHF methods
NASA Astrophysics Data System (ADS)
Kobus, J.; Jaskolski, W.
1987-10-01
A detailed numerical comparison of the Dirac-Hartree-Fock method and the relativistic Hartree-Fock (RHF) method of Cowan and Griffith (1976) is presented, considering the total energy, the orbital energies, and the one-electron and two-electron integrals. The RHF method is found to yield accurate values of the relativistic transition energies. Using accurate values of the correlation corrections for p-electron and d-electron systems, the usefulness of the RHF method in obtaining relativistic corrections to the differential term energies is demonstrated. Advantages of the method for positron scattering on heavy systems are also pointed out.
Numerical Methods through Open-Ended Projects
ERIC Educational Resources Information Center
Cline, Kelly S.
2005-01-01
We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible…
A numerical method of detecting singularity
NASA Technical Reports Server (NTRS)
Laporte, M.; Vignes, J.
1978-01-01
A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.
NASA Technical Reports Server (NTRS)
Friedmann, P.; Hammond, C. E.; Woo, T.-H.
1977-01-01
Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.
Numerical Methods for Explosion Plume Predictions
1993-03-12
AD-A262 343 6 NAVSWC TR 91-718 A -22~4..v~w•T ,,-., I II It ill/111111 ti(. NUMERICAL METHODS FOR EXPLOSION PLUME PREDICTIONS BY W.G. SZYMCZAK AND A...METHODS FOR EXPLOSION PLUME PREDICTIONS BY W. G. SZYMCZAK AND A. B. WARDLAW RESEARCH AND TECHNOLOGY DEPARTMENT 12 MARCH 1993 Approved for public release...2 TABLES Table Page 3-1 SHALLOW DEPTH EXPLOSION BUBBLE INITIAL DATA
A hybrid numerical method for orbit correction
White, G.; Himel, T.; Shoaee, H.
1997-09-01
The authors describe a simple hybrid numerical method for beam orbit correction in particle accelerators. The method overcomes both degeneracy in the linear system being solved and respects boundaries on the solution. It uses the Singular Value Decomposition (SVD) to find and remove the null-space in the system, followed by a bounded Linear Least Squares analysis of the remaining recast problem. It was developed for correcting orbit and dispersion in the B-factory rings.
Numerical solutions of the GEW equation using MLS collocation method
NASA Astrophysics Data System (ADS)
Kaplan, Ayşe Gül; Dereli, Yılmaz
In this paper, the generalized equal width wave (GEW) equation is solved by using moving least squares collocation (MLSC) method. To test the accuracy of the method some numerical experiments are presented. The motion of single solitary waves, the interaction of two solitary waves and the Maxwellian initial condition problems are chosen as test problems. For the single solitary wave motion whose analytical solution was known L2, L∞ error norms and pointwise rates of convergence were calculated. Also mass, energy and momentum invariants were calculated for every test problems. Obtained numerical results are compared with some earlier works. It is seen that the method is very efficient and reliable due to obtained numerical results are very satisfactorily. Stability analysis of difference equation was done by applying the moving least squares collocation method for GEW equation.
Hyperbolic conservation laws and numerical methods
NASA Technical Reports Server (NTRS)
Leveque, Randall J.
1990-01-01
The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.
A numerical method to model excitable cells.
Joyner, R W; Westerfield, M; Moore, J W; Stockbridge, N
1978-01-01
We have extended a fast, stable, and accurate method for the numerical solution of cable equations to include changes in geometry and membrane properties in order to model a single excitable cell realistically. In addition, by including the provision that the radius may be a function of distance along an axis, we have achieved a general and powerful method for simulating a cell with any number of branched processes, any or all of which may be nonuniform in diameter, and with no restriction on the branching pattern. PMID:656539
An Efficient Numerical Solution of Nonlinear Hunter-Saxton Equation
NASA Astrophysics Data System (ADS)
Parand, Kourosh; Delkhosh, Mehdi
2017-05-01
In this paper, the nonlinear Hunter-Saxton equation, which is a famous partial differential equation, is solved by using a hybrid numerical method based on the quasilinearization method and the bivariate generalized fractional order of the Chebyshev functions (B-GFCF) collocation method. First, using the quasilinearization method, the equation is converted into a sequence of linear partial differential equations (LPD), and then these LPDs are solved using the B-GFCF collocation method. A very good approximation of solutions is obtained, and comparisons show that the obtained results are more accurate than the results of other researchers.
A novel gas-droplet numerical method for spray combustion
NASA Technical Reports Server (NTRS)
Chen, C. P.; Shang, H. M.; Jiang, Y.
1991-01-01
This paper presents a non-iterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully-interacting combination of Eulerian fluid and Lagrangian particle calculation. The interaction calculations between the two phases are formulated on a pressure-velocity coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell (PSIC) procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data, as well as efficiency assessments are given for some sprays typical of spray combustion applications.
Numerical determination of personal aerosol sampler aspiration efficiency.
Lo Savio, Simone; Paradisi, Paolo; Tampieri, Francesco; Belosi, Franco; Morigi, Maria Pia; Agostini, Sergio
2003-04-01
In this work the determination of the aspiration efficiency of personal aerosol samplers, commonly used in occupational exposure assessment, is investigated by means of CFD techniques. Specifically, it will be described a code to calculate the particle trajectories in a given flow field. At the present state the code considers only the effects of the mean flow field on the particle motion, whereas the turbulent diffusion effects are neglected. Comparisons with experimental measurements are also given in the framework of a research contract, supported by the European Community, with several experimental contributions from the participants. The main objective of the European research is to develop a new approach to experimentation with airborne particle flows, working on a reduced scale. This methodology has the advantage of allowing real-time aerosol determination and use of small wind tunnels, with a better experimental control. In this article we describe how the methodology has been verified using computational fluid dynamics. Experimental and numerical aspiration efficiencies have been compared and the influence of gravity and turbulence intensity in full and reduced scale has been investigated. The numerical techniques described here are in agreement with previous similar research and allow at least qualitative predictions of aspiration efficiency for real samplers, taking care of orientation from the incoming air flow. The major discrepancies among predicted and experimental results may be a consequence of bounce effects, which are very difficult to eliminate also by greasing the sampler surface.
An efficient numerical procedure for thermohydrodynamic analysis of cavitating bearings
NASA Technical Reports Server (NTRS)
Vijayaraghavan, D.
1995-01-01
An efficient and accurate numerical procedure to determine the thermo-hydrodynamic performance of cavitating bearings is described. This procedure is based on the earlier development of Elrod for lubricating films, in which the properties across the film thickness are determined at Lobatto points and their distributions are expressed by collocated polynomials. The cavitated regions and their boundaries are rigorously treated. Thermal boundary conditions at the surfaces, including heat dissipation through the metal to the ambient, are incorporated. Numerical examples are presented comparing the predictions using this procedure with earlier theoretical predictions and experimental data. With a few points across the film thickness and across the journal and the bearing in the radial direction, the temperature profile is very well predicted.
Simple numerical method for predicting steady compressible flows
NASA Technical Reports Server (NTRS)
Vonlavante, Ernst; Nelson, N. Duane
1986-01-01
A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.
RELAP-7 Numerical Stabilization: Entropy Viscosity Method
R. A. Berry; M. O. Delchini; J. Ragusa
2014-06-01
The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.
Yao, Yuan; Du, Fenglei; Wang, Chunjie; Liu, Yuqiu; Weng, Jian; Chen, Feiyan
2015-01-01
This study examined whether long-term abacus-based mental calculation (AMC) training improved numerical processing efficiency and at what stage of information processing the effect appeard. Thirty-three children participated in the study and were randomly assigned to two groups at primary school entry, matched for age, gender and IQ. All children went through the same curriculum except that the abacus group received a 2-h/per week AMC training, while the control group did traditional numerical practice for a similar amount of time. After a 2-year training, they were tested with a numerical Stroop task. Electroencephalographic (EEG) and event related potential (ERP) recording techniques were used to monitor the temporal dynamics during the task. Children were required to determine the numerical magnitude (NC) (NC task) or the physical size (PC task) of two numbers presented simultaneously. In the NC task, the AMC group showed faster response times but similar accuracy compared to the control group. In the PC task, the two groups exhibited the same speed and accuracy. The saliency of numerical information relative to physical information was greater in AMC group. With regards to ERP results, the AMC group displayed congruity effects both in the earlier (N1) and later (N2 and LPC (late positive component) time domain, while the control group only displayed congruity effects for LPC. In the left parietal region, LPC amplitudes were larger for the AMC than the control group. Individual differences for LPC amplitudes over left parietal area showed a positive correlation with RTs in the NC task in both congruent and neutral conditions. After controlling for the N2 amplitude, this correlation also became significant in the incongruent condition. Our results suggest that AMC training can strengthen the relationship between symbolic representation and numerical magnitude so that numerical information processing becomes quicker and automatic in AMC children. PMID:26042012
Efficient Parallel Algorithm For Direct Numerical Simulation of Turbulent Flows
NASA Technical Reports Server (NTRS)
Moitra, Stuti; Gatski, Thomas B.
1997-01-01
A distributed algorithm for a high-order-accurate finite-difference approach to the direct numerical simulation (DNS) of transition and turbulence in compressible flows is described. This work has two major objectives. The first objective is to demonstrate that parallel and distributed-memory machines can be successfully and efficiently used to solve computationally intensive and input/output intensive algorithms of the DNS class. The second objective is to show that the computational complexity involved in solving the tridiagonal systems inherent in the DNS algorithm can be reduced by algorithm innovations that obviate the need to use a parallelized tridiagonal solver.
An efficient numerical model for hydrodynamic parameterization in 2D fractured dual-porosity media
NASA Astrophysics Data System (ADS)
Fahs, Hassane; Hayek, Mohamed; Fahs, Marwan; Younes, Anis
2014-01-01
This paper presents a robust and efficient numerical model for the parameterization of the hydrodynamic in fractured porous media. The developed model is based upon the refinement indicators algorithm for adaptive multi-scale parameterization. For each level of refinement, the Levenberg-Marquardt method is used to minimize the difference between the measured and predicted data that are obtained by solving the direct problem with the mixed finite element method. Sensitivities of state variables with respect to the parameters are calculated by the sensitivity method. The adjoint-state method is used to calculate the local gradients of the objective function necessary for the computation of the refinement indicators. Validity and efficiency of the proposed model are demonstrated by means of several numerical experiments. The developed numerical model provides encouraging results, even for noisy data and/or with a reduced number of measured heads.
Numerical analysis method for linear induction machines.
NASA Technical Reports Server (NTRS)
Elliott, D. G.
1972-01-01
A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.
Numerical methods for finding stationary gravitational solutions
NASA Astrophysics Data System (ADS)
Dias, Óscar J. C.; Santos, Jorge E.; Way, Benson
2016-07-01
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small rotating black holes in AdS{}5× {S}5. We also include several tools and tricks that have been useful throughout the literature.
Numerical analysis method for linear induction machines.
NASA Technical Reports Server (NTRS)
Elliott, D. G.
1972-01-01
A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.
Numerical solution methods for viscoelastic orthotropic materials
NASA Technical Reports Server (NTRS)
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1988-01-01
Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.
Efficient numerical simulation of heat storage in subsurface georeservoirs
NASA Astrophysics Data System (ADS)
Boockmeyer, A.; Bauer, S.
2015-12-01
The transition of the German energy market towards renewable energy sources, e.g. wind or solar power, requires energy storage technologies to compensate for their fluctuating production. Large amounts of energy could be stored in georeservoirs such as porous formations in the subsurface. One possibility here is to store heat with high temperatures of up to 90°C through borehole heat exchangers (BHEs) since more than 80 % of the total energy consumption in German households are used for heating and hot water supply. Within the ANGUS+ project potential environmental impacts of such heat storages are assessed and quantified. Numerical simulations are performed to predict storage capacities, storage cycle times, and induced effects. For simulation of these highly dynamic storage sites, detailed high-resolution models are required. We set up a model that accounts for all components of the BHE and verified it using experimental data. The model ensures accurate simulation results but also leads to large numerical meshes and thus high simulation times. In this work, we therefore present a numerical model for each type of BHE (single U, double U and coaxial) that reduces the number of elements and the simulation time significantly for use in larger scale simulations. The numerical model includes all BHE components and represents the temporal and spatial temperature distribution with an accuracy of less than 2% deviation from the fully discretized model. By changing the BHE geometry and using equivalent parameters, the simulation time is reduced by a factor of ~10 for single U-tube BHEs, ~20 for double U-tube BHEs and ~150 for coaxial BHEs. Results of a sensitivity study that quantify the effects of different design and storage formation parameters on temperature distribution and storage efficiency for heat storage using multiple BHEs are then shown. It is found that storage efficiency strongly depends on the number of BHEs composing the storage site, their distance and
Computational methods for aerodynamic design using numerical optimization
NASA Technical Reports Server (NTRS)
Peeters, M. F.
1983-01-01
Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.
Simple numerical method for solving the steady Euler equations
NASA Technical Reports Server (NTRS)
Von Lavante, E.; Melson, N. Duane
1987-01-01
A numerical method for solving the isenthalpic form of the governing equations for compressible inviscid flows is developed. The method is based on the concept of flux vector splitting in its implicit form and is tested on several demanding configurations. Time marching to steady state is accelerated by the implementation of the multigrid procedure which very effectively increases the rate of convergence. Steady-state results are obtained for various test cases. Only short computational times are required due to the relative efficiency of the basic method.
Application of numerical methods to elasticity imaging.
Castaneda, Benjamin; Ormachea, Juvenal; Rodríguez, Paul; Parker, Kevin J
2013-03-01
Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity.
Mathematica with a Numerical Methods Course
NASA Astrophysics Data System (ADS)
Varley, Rodney
2003-04-01
An interdisciplinary "Numerical Methods" course has been shared between physics, mathematics and computer science since 1992 at Hunter C. Recently, the lectures and workshops for this course have become formalized and placed on the internet at http://www.ph.hunter.cuny.edu (follow the links "Course Listings and Websites" >> "PHYS385 (Numerical Methods)". Mathematica notebooks for the lectures are available for automatic download (by "double clicking" the lecture icon) for student use in the classroom or at home. AOL (or Netscape/Explorer) can be used provided Mathematica (or the "free" MathReader) has been made a "helper application". Using Mathematica has the virtue that mathematical equations (no LaTex required) can easily be included with the text and Mathematica's graphing is easy to use. Computational cells can be included within the notebook and students may easily modify the calculation to see the result of "what if..." questions. Homework is sent as Mathematica notebooks to the instructor via the internet and the corrected workshops are returned in the same manner. Most exam questions require computational solutions.
NASA Astrophysics Data System (ADS)
Li, Tiexiang; Huang, Tsung-Ming; Lin, Wen-Wei; Wang, Jenn-Nan
2017-03-01
We propose an efficient eigensolver for computing densely distributed spectra of the two-dimensional transmission eigenvalue problem (TEP), which is derived from Maxwell’s equations with Tellegen media and the transverse magnetic mode. The governing equations, when discretized by the standard piecewise linear finite element method, give rise to a large-scale quadratic eigenvalue problem (QEP). Our numerical simulation shows that half of the positive eigenvalues of the QEP are densely distributed in some interval near the origin. The quadratic Jacobi-Davidson method with a so-called non-equivalence deflation technique is proposed to compute the dense spectrum of the QEP. Extensive numerical simulations show that our proposed method processes the convergence efficiently, even when it needs to compute more than 5000 desired eigenpairs. Numerical results also illustrate that the computed eigenvalue curves can be approximated by nonlinear functions, which can be applied to estimate the denseness of the eigenvalues for the TEP.
Homogenization and Numerical Methods for Hyperbolic Equations
NASA Astrophysics Data System (ADS)
Liu, Jian-Guo
1990-01-01
This dissertation studies three aspects of analysis and numerical methods for partial differential equations with oscillatory solutions. 1. Homogenization theory for certain linear hyperbolic equations is developed. We derive the homogenized convection equations for linear convection problems with rapidly varying velocity in space and time. We find that the oscillatory solutions are very sensitive to the arithmetic properties of certain parameters, such as the corresponding rotation number and the ratio between the components of the mean velocity field in linear convection. We also show that the oscillatory velocity field in two dimensional incompressible flow behaves like shear flows. 2. The homogenization of scalar nonlinear conservation laws in several space variables with oscillatory initial data is also discussed. We prove that the initial oscillations will be eliminated for any positive time when the equations are non-degenerate. This is also true for degenerate equations if there is enough mixing among the initial oscillations in the degenerate direction. Otherwise, the initial oscillation, for which the homogenized equation is obtained, will survive and be propagated. The large-time behavior of conservation laws with several space variables is studied. We show that, under a new nondegenerate condition (the second derivatives of the flux functions are linearly independent in any interval), a piecewise smooth periodic solution with converge strongly to the mean value of initial data. This generalizes Glimm and Lax's result for the one dimensional problem (3). 3. Numerical simulations of the oscillatory solutions are also carried out. We give some error estimate for varepsilon-h resonance ( varepsilon: oscillation wave length, h: numerical step) and prove essential convergence (24) of order alpha < 1 for some numerical schemes. These include upwind schemes and particle methods for linear hyperbolic equations with oscillatory coefficients. A stochastic analysis
Optimization methods and silicon solar cell numerical models
NASA Technical Reports Server (NTRS)
Girardini, K.; Jacobsen, S. E.
1986-01-01
An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.
The Improvement of Efficiency in the Numerical Computation of Orbit Trajectories
NASA Technical Reports Server (NTRS)
Dyer, J.; Danchick, R.; Pierce, S.; Haney, R.
1972-01-01
An analysis, system design, programming, and evaluation of results are described for numerical computation of orbit trajectories. Evaluation of generalized methods, interaction of different formulations for satellite motion, transformation of equations of motion and integrator loads, and development of efficient integrators are also considered.
Numerical method for gas dynamics combining characteristic and conservation concepts
NASA Technical Reports Server (NTRS)
Coakley, T. J.
1981-01-01
An efficient implicit numerical method that solves the compressible Navier-Stokes equations in arbitrary curvilinear coordinates by the finite-volume technique is presented. An intrinsically dissipative difference scheme and a fully implicit treatment of boundary conditions, based on characteristic and conservation concepts, are used to improve stability and accuracy. Efficiency is achieved by using a diagonal form of the implicit algorithm and spatially varying time-steps. Comparisons of various schemes and methods are presented for one- and two-dimensional flows, including transonic separated flow past a thick circular-arc airfoil in a channel. The new method is equal to or better than a version of MacCormack's hybrid method in accuracy and it converges to a steady state up to an order of magnitude faster.
Numerical method for gas dynamics combining characteristic and conservation concepts
NASA Technical Reports Server (NTRS)
Coakley, T. J.
1981-01-01
An efficient implicit numerical method that solves the compressible Navier-Stokes equations in arbitrary curvilinear coordinates by the finite-volume technique is presented. An intrinsically dissipative difference scheme and a fully implicit treatment of boundary conditions, based on characteristic and conservation concepts, are used to improve stability and accuracy. Efficiency is achieved by using a diagonal form of the implicit algorithm and spatially varying time-steps. Comparisons of various schemes and methods are presented for one- and two-dimensional flows, including transonic separated flow past a thick circular-arc airfoil in a channel. The new method is equal to or better than a version of MacCormack's hybrid method in accuracy and it converges to a steady state up to an order of magnitude faster.
High accuracy mantle convection simulation through modern numerical methods
NASA Astrophysics Data System (ADS)
Kronbichler, Martin; Heister, Timo; Bangerth, Wolfgang
2012-10-01
Numerical simulation of the processes in the Earth's mantle is a key piece in understanding its dynamics, composition, history and interaction with the lithosphere and the Earth's core. However, doing so presents many practical difficulties related to the numerical methods that can accurately represent these processes at relevant scales. This paper presents an overview of the state of the art in algorithms for high-Rayleigh number flows such as those in the Earth's mantle, and discusses their implementation in the Open Source code ASPECT (Advanced Solver for Problems in Earth's ConvecTion). Specifically, we show how an interconnected set of methods for adaptive mesh refinement (AMR), higher order spatial and temporal discretizations, advection stabilization and efficient linear solvers can provide high accuracy at a numerical cost unachievable with traditional methods, and how these methods can be designed in a way so that they scale to large numbers of processors on compute clusters. ASPECT relies on the numerical software packages DEAL.II and TRILINOS, enabling us to focus on high level code and keeping our implementation compact. We present results from validation tests using widely used benchmarks for our code, as well as scaling results from parallel runs.
Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems
Cai, Wei
2014-05-15
Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equations such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.
Efficient numerical simulation of electron states in quantum wires
NASA Technical Reports Server (NTRS)
Kerkhoven, Thomas; Galick, Albert T.; Ravaioli, Umberto; Arends, John H.; Saad, Youcef
1990-01-01
A new algorithm is presented for the numerical simulation of electrons in a quantum wire as described by a two-dimensional eigenvalue problem for Schroedinger's equation coupled with Poisson's equation. Initially, the algorithm employs an underrelaxed fixed point iteration to generate an approximation which is reasonably close to the solution. Subsequently, this approximate solution is employed as an initial guess for a Jacobian-free implementation of an approximate Newton method. In this manner the nonlinearity in the model is dealt with effectively. The effectiveness of this approach is demonstrated in a set of numerical experiments which study the electron states on the cross section of a quantum wire structure based on III-V semiconductors at 4.2 and 77 K.
Optimization methods and silicon solar cell numerical models
NASA Technical Reports Server (NTRS)
Girardini, K.
1986-01-01
The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.
A numerical efficient way to minimize classical density functional theory.
Edelmann, Markus; Roth, Roland
2016-02-21
The minimization of the functional of the grand potential within the framework of classical density functional theory in three spatial dimensions can be numerically very demanding. The Picard iteration, that is often employed, is very simple and robust but can be rather slow. While a number of different algorithms for optimization problems have been suggested, there is still great need for additional strategies. Here, we present an approach based on the limited memory Broyden algorithm that is efficient and relatively simple to implement. We demonstrate the performance of this algorithm with the minimization of an inhomogeneous bulk structure of a fluid with competing interactions. For the problems we studied, we find that the presented algorithm improves performance by roughly a factor of three.
The instanton method and its numerical implementation in fluid mechanics
NASA Astrophysics Data System (ADS)
Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias
2015-08-01
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.
An efficient cuckoo search algorithm for numerical function optimization
NASA Astrophysics Data System (ADS)
Ong, Pauline; Zainuddin, Zarita
2013-04-01
Cuckoo search algorithm which reproduces the breeding strategy of the best known brood parasitic bird, the cuckoos has demonstrated its superiority in obtaining the global solution for numerical optimization problems. However, the involvement of fixed step approach in its exploration and exploitation behavior might slow down the search process considerably. In this regards, an improved cuckoo search algorithm with adaptive step size adjustment is introduced and its feasibility on a variety of benchmarks is validated. The obtained results show that the proposed scheme outperforms the standard cuckoo search algorithm in terms of convergence characteristic while preserving the fascinating features of the original method.
An efficient numerical technique for the solution of nonlinear singular boundary value problems
NASA Astrophysics Data System (ADS)
Singh, Randhir; Kumar, Jitendra
2014-04-01
In this work, a new technique based on Green's function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The technique relies on constructing Green's function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed technique avoids solving a sequence of transcendental equations for the undetermined coefficients. It approximates the solution in the form of a series with easily computable components. Additionally, the convergence analysis and the error estimate of the proposed method are supplemented. The reliability and efficiency of the proposed method are demonstrated by several numerical examples. The numerical results reveal that the proposed method is very efficient and accurate.
Numerical methods for analyzing electromagnetic scattering
NASA Technical Reports Server (NTRS)
Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.
1985-01-01
Numerical methods to analyze electromagnetic scattering are presented. The dispersions and attenuations of the normal modes in a circular waveguide coated with lossy material were completely analyzed. The radar cross section (RCS) from a circular waveguide coated with lossy material was calculated. The following is observed: (1) the interior irradiation contributes to the RCS much more than does the rim diffraction; (2) at low frequency, the RCS from the circular waveguide terminated by a perfect electric conductor (PEC) can be reduced more than 13 dB down with a coating thickness less than 1% of the radius using the best lossy material available in a 6 radius-long cylinder; (3) at high frequency, a modal separation between the highly attenuated and the lowly attenuated modes is evident if the coating material is too lossy, however, a large RCS reduction can be achieved for a small incident angle with a thin layer of coating. It is found that the waveguide coated with a lossy magnetic material can be used as a substitute for a corrugated waveguide to produce a circularly polarized radiation yield.
An Efficient Method for Performing Partial Fraction Expansion.
1980-02-01
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Numerical simulation of boundary layers. Part 1: Weak formulation and numerical method
NASA Technical Reports Server (NTRS)
Spalart, P. R.
1986-01-01
A numerical method designed to solve the time-dependent, three-dimensional, incompressible Navier-Stokes equations in boundary layers is presented. The fluid domain is the half-space over a flat plate, and periodic conditions are applied in the horizontal directions. The discretization is spectral. The basis functions are divergence-free and a weak formulation of the momentum equation is used, which eliminates the pressure term. An exponential mapping and Jacobi polynomials are used in the semi-infinite direction, with the irrotational component receiving special treatment. Issues related to the accuracy, stability and efficiency of the method are discussed. Very fast convergence is demonstrated on some model problems with smooth solutions. The method has also been shown to accurately resolve the fine scales of transitional and turbulent boundary layers.
Performance analysis of a mirror by numerical iterative method.
Park, Kwijong; Cho, Myung; Lee, Dae-Hee; Moon, Bongkon
2014-12-29
Zernike polynomials are generally used to predict the optical performance of a mirror. However, it can also be done by a numerical iterative method. As piston, tip, tilt, and defocus (P.T.T.F) aberrations can be easily removed by optical alignment, we iteratively used a rotation transformation and a paraboloid graph subtraction for removal of the aberrations from a raw deformation of the optical surface through a Finite Element Method (FEM). The results of a 30 cm concave circular mirror corrected by the iterative method were almost the same as those yielded by Zernike polynomial fitting, and the computational time was fast. In addition, a concave square mirror whose surface area is π was analyzed in order to visualize the deformation maps of a general mirror aperture shape. The iterative method can be applicable efficiently because it does not depend on the mirror aperture shape.
[Numerical methods for multi-fluid flows]. Final progress report
Pozrikidis, C.
1998-07-21
The central objective of this research has been to develop efficient numerical methods for computing multi-fluid flows with large interfacial deformations, and apply these methods to study the rheology of suspensions of deformable particles with viscous and non-Newtonian interfacial behavior. The mathematical formulation employs boundary-integral, immersed-boundary, and related numerical methods. Particles of interest include liquid drops with constant surface tension and capsules whose interfaces exhibit viscoelastic and incompressible characteristics. In one family of problems, the author has considered the shear-driven and pressure-driven flow of a suspension of two-dimensional liquid drops with ordered and random structure. In a second series of investigations, the author carried out dynamic simulations of two-dimensional, unbounded, doubly-periodic shear flows with random structure. Another family of problems addresses the deformation of three-dimensional capsules whose interfaces exhibit isotropic surface tension, viscous, elastic, or incompressible behavior, in simple shear flow. The numerical results extend previous asymptotic theories for small deformations and illuminate the mechanism of membrane rupture.
Numerical methods for large eddy simulation of acoustic combustion instabilities
NASA Astrophysics Data System (ADS)
Wall, Clifton T.
Acoustic combustion instabilities occur when interaction between the combustion process and acoustic modes in a combustor results in periodic oscillations in pressure, velocity, and heat release. If sufficiently large in amplitude, these instabilities can cause operational difficulties or the failure of combustor hardware. In many situations, the dominant instability is the result of the interaction between a low frequency acoustic mode of the combustor and the large scale hydrodynamics. Large eddy simulation (LES), therefore, is a promising tool for the prediction of these instabilities, since both the low frequency acoustic modes and the large scale hydrodynamics are well resolved in LES. Problems with the tractability of such simulations arise, however, due to the difficulty of solving the compressible Navier-Stokes equations efficiently at low Mach number and due to the large number of acoustic periods that are often required for such instabilities to reach limit cycles. An implicit numerical method for the solution of the compressible Navier-Stokes equations has been developed which avoids the acoustic CFL restriction, allowing for significant efficiency gains at low Mach number, while still resolving the low frequency acoustic modes of interest. In the limit of a uniform grid the numerical method causes no artificial damping of acoustic waves. New, non-reflecting boundary conditions have also been developed for use with the characteristic-based approach of Poinsot and Lele (1992). The new boundary conditions are implemented in a manner which allows for significant reduction of the computational domain of an LES by eliminating the need to perform LES in regions where one-dimensional acoustics significantly affect the instability but details of the hydrodynamics do not. These new numerical techniques have been demonstrated in an LES of an experimental combustor. The new techniques are shown to be an efficient means of performing LES of acoustic combustion
Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies
Safta, Cosmin; Najm, Habib N.; Phipps, Eric Todd
2014-09-01
Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.
Efficient Cfd/csd Coupling Methods for Aeroelastic Applications
NASA Astrophysics Data System (ADS)
Chen, Long; Xu, Tianhao; Xie, Jing
2016-06-01
A fast aeroelastic numerical simulation method using CFD/CSD coupling are developed. Generally, aeroelastic numerical simulation costs much time and significant hardware resources with CFD/CSD coupling. In this paper, dynamic grid method, full implicit scheme, parallel technology and improved coupling method are researched for efficiency simulation. An improved Delaunay graph mapping method is proposed for efficient dynamic grid deform. Hybrid grid finite volume method is used to solve unsteady flow fields. The dual time stepping method based on parallel implicit scheme is used in temporal discretization for efficiency simulation. An approximate system of linear equations is solved by the GMRES algorithm with a LU-SGS preconditioner. This method leads to a significant increase in performance over the explicit and LU-SGS implicit methods. A modification of LU-SGS is proposed to improve the parallel performance. Parallel computing overs a very effective way to improve our productivity in doing CFD/CFD coupling analysis. Improved loose coupling method is an efficiency way over the loose coupling method and tight coupling method. 3D wing's aeroelastic phenomenon is simulated by solving Reynolds-averaged Navier-Stokes equations using improved loose coupling method. The flutter boundary is calculated and agrees well with experimental data. The transonic hole is very clear in numerical simulation results.
Advanced numerical methods in mesh generation and mesh adaptation
Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A
2010-01-01
Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge
Efficient numerical integration of neutrino oscillations in matter
NASA Astrophysics Data System (ADS)
Casas, F.; D'Olivo, J. C.; Oteo, J. A.
2016-12-01
A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a general numerical integrator, a fact that could smooth the way for massive numerical integration concomitant with experimental data analyses. Detailed illustrations about numerical procedure and computer time costs are provided.
The numerical methods for the fluid flow of UCMCWS
Zhang Wenfu; Li Hui; Zhu Shuquan; Wang Zuna
1997-12-31
As an alternative for diesel oil for internal combustion engines, the fluid flow state of Ultra Clean Micronized Coal-Water Slurry (UCMCWS) in mini pipe and nozzle of a diesel engine must be known. In the laboratory three kinds of UCMCWS have been made with coal containing less than 0.8% ash, viscosity less than 600 mPa.s and concentration between 50% and 56%. Because the UCMCWS is a non-Newtonian fluid, there are no analytical resolution for pipe flow, especially in inlet and outlet sections. In this case using the numerical methods to research the flow state of UCMCWS is a useful method. Using the method of finite element, the flow state of UCMCWS in inlet and outlet sections (similar to a nozzle) have been studied. The distribution of velocity at different pressures of UCMCWS in outlet and inlet sections have been obtained. The result of the numerical methods is the efficient base for the pipe and nozzle design.
Improved numerical methods for turbulent viscous recirculating flows
NASA Technical Reports Server (NTRS)
Vandoormaal, J. P.; Turan, A.; Raithby, G. D.
1986-01-01
The objective of the present study is to improve both the accuracy and computational efficiency of existing numerical techniques used to predict viscous recirculating flows in combustors. A review of the status of the study is presented along with some illustrative results. The effort to improve the numerical techniques consists of the following technical tasks: (1) selection of numerical techniques to be evaluated; (2) two dimensional evaluation of selected techniques; and (3) three dimensional evaluation of technique(s) recommended in Task 2.
Computationally Efficient Numerical Model for the Evolution of Directional Ocean Surface Waves
NASA Astrophysics Data System (ADS)
Malej, M.; Choi, W.; Goullet, A.
2011-12-01
The main focus of this work has been the asymptotic and numerical modeling of weakly nonlinear ocean surface wave fields. In particular, a development of an efficient numerical model for the evolution of nonlinear ocean waves, including extreme waves known as Rogue/Freak waves, is of direct interest. Due to their elusive and destructive nature, the media often portrays Rogue waves as unimaginatively huge and unpredictable monsters of the sea. To address some of these concerns, derivations of reduced phase-resolving numerical models, based on the small wave steepness assumption, are presented and their corresponding numerical simulations via Fourier pseudo-spectral methods are discussed. The simulations are initialized with a well-known JONSWAP wave spectrum and different angular distributions are employed. Both deterministic and Monte-Carlo ensemble average simulations were carried out. Furthermore, this work concerns the development of a new computationally efficient numerical model for the short term prediction of evolving weakly nonlinear ocean surface waves. The derivations are originally based on the work of West et al. (1987) and since the waves in the ocean tend to travel primarily in one direction, the aforementioned new numerical model is derived with an additional assumption of a weak transverse dependence. In turn, comparisons of the ensemble averaged randomly initialized spectra, as well as deterministic surface-to-surface correlations are presented. The new model is shown to behave well in various directional wave fields and can potentially be a candidate for computationally efficient prediction and propagation of extreme ocean surface waves - Rogue/Freak waves.
Zou, Ling; Zhao, Haihua; Kim, Seung Jun
2016-11-16
In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to themore » low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.« less
Zou, Ling; Zhao, Haihua; Kim, Seung Jun
2016-11-16
In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to the low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.
A numerical method for solving the Vlasov equation
NASA Technical Reports Server (NTRS)
Satofuka, N.
1982-01-01
A numerical procedure is derived for the solution of the Vlasov-Poisson system of equations in two phase-space variables. Derivatives with respect to the phase-space variables are approximated by a weighted sum of the values of the distribution function at property chosen neighboring points. The resulting set of ordinary differential equations is then solved by using an appropriate time intergration scheme. The accuracy of the proposed method is tested with some simple model problems. The results for the free streaming case, linear Landau damping, and nonlinear Landau damping are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient.
Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods
NASA Technical Reports Server (NTRS)
Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark
2002-01-01
Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.
Numerical method of characteristics for one-dimensional blood flow
NASA Astrophysics Data System (ADS)
Acosta, Sebastian; Puelz, Charles; Rivière, Béatrice; Penny, Daniel J.; Rusin, Craig G.
2015-08-01
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.
Numerical Method of Characteristics for One-Dimensional Blood Flow.
Acosta, Sebastian; Puelz, Charles; Riviére, Béatrice; Penny, Daniel J; Rusin, Craig G
2015-08-01
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.
Numerical Method of Characteristics for One–Dimensional Blood Flow
Puelz, Charles; Riviére, Béatrice; Penny, Daniel J.; Rusin, Craig G.
2015-01-01
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant. PMID:25931614
Numerical Simulation of Tubular Pumping Systems with Different Regulation Methods
NASA Astrophysics Data System (ADS)
Zhu, Honggeng; Zhang, Rentian; Deng, Dongsheng; Feng, Xusong; Yao, Linbi
2010-06-01
Since the flow in tubular pumping systems is basically along axial direction and passes symmetrically through the impeller, most satisfying the basic hypotheses in the design of impeller and having higher pumping system efficiency in comparison with vertical pumping system, they are being widely applied to low-head pumping engineering. In a pumping station, the fluctuation of water levels in the sump and discharge pool is most common and at most time the pumping system runs under off-design conditions. Hence, the operation of pump has to be flexibly regulated to meet the needs of flow rates, and the selection of regulation method is as important as that of pump to reduce operation cost and achieve economic operation. In this paper, the three dimensional time-averaged Navier-Stokes equations are closed by RNG κ-ɛ turbulent model, and two tubular pumping systems with different regulation methods, equipped with the same pump model but with different designed system structures, are numerically simulated respectively to predict the pumping system performances and analyze the influence of regulation device and help designers make final decision in the selection of design schemes. The computed results indicate that the pumping system with blade-adjusting device needs longer suction box, and the increased hydraulic loss will lower the pumping system efficiency in the order of 1.5%. The pumping system with permanent magnet motor, by means of variable speed regulation, obtains higher system efficiency partly for shorter suction box and partly for different structure design. Nowadays, the varied speed regulation is realized by varied frequency device, the energy consumption of which is about 3˜4% of output power of the motor. Hence, when the efficiency of variable frequency device is considered, the total pumping system efficiency will probably be lower.
Efficient implementation of the Lanczos method for magnetic systems
Schnack, Juergen Hage, Peter; Schmidt, Heinz-Juergen
2008-04-20
Numerically exact investigations of interacting spin systems provide a major tool for an understanding of their magnetic properties. For medium size systems the approximate Lanczos diagonalization is the most common method. In this article we suggest two improvements: efficient basis coding in subspaces and simple restructuring for openMP parallelization.
Numerical Methods for Partial Differential Equations.
1984-01-09
114). The pursuit of a linear-time solution led Brent and Luk to consider Jacobi methods . They have found an implementation using an n/2 xn/2 array...cyclic Jacobi method . It takes 0(n) time to perform a sweep of the method, and 0(log n) sweeps for the method to converge 1 1. Brent and Luk have...Hestenes algorithm that, in real arithmetic, is an exact analogue of their Jacobi method applied to the eigenproblem for ATA. The array requires 0(rnn
NASA Astrophysics Data System (ADS)
Li, Zheng; Wang, Hong; Yang, Danping
2017-10-01
We present a space-time fractional Allen-Cahn phase-field model that describes the transport of the fluid mixture of two immiscible fluid phases. The space and time fractional order parameters control the sharpness and the decay behavior of the interface via a seamless transition of the parameters. Although they are shown to provide more accurate description of anomalous diffusion processes and sharper interfaces than traditional integer-order phase-field models do, fractional models yield numerical methods with dense stiffness matrices. Consequently, the resulting numerical schemes have significantly increased computational work and memory requirement. We develop a lossless fast numerical method for the accurate and efficient numerical simulation of the space-time fractional phase-field model. Numerical experiments shows the utility of the fractional phase-field model and the corresponding fast numerical method.
Efficient finite element method for grating profile reconstruction
NASA Astrophysics Data System (ADS)
Zhang, Ruming; Sun, Jiguang
2015-12-01
This paper concerns the reconstruction of grating profiles from scattering data. The inverse problem is formulated as an optimization problem with a regularization term. We devise an efficient finite element method (FEM) and employ a quasi-Newton method to solve it. For the direct problems, the FEM stiff and mass matrices are assembled once at the beginning of the numerical procedure. Then only minor changes are made to the mass matrix at each iteration, which significantly saves the computation cost. Numerical examples show that the method is effective and robust.
Numerical methods in Markov chain modeling
NASA Technical Reports Server (NTRS)
Philippe, Bernard; Saad, Youcef; Stewart, William J.
1989-01-01
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
Interpolation Method Needed for Numerical Uncertainty
NASA Technical Reports Server (NTRS)
Groves, Curtis E.; Ilie, Marcel; Schallhorn, Paul A.
2014-01-01
Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.
Simple and Efficient Numerical Techniques for Treating Bodies of Revolution
1979-03-01
results computed with DBR are compared with those of Davis, which were obtained using a set of hybrid integral equations [ 14 ]. Davis apparently...INTRODUCTION 1 II. NUMERICAL SOLUTION PROCEDURE FOR A BODY OF REVOLU- 3 TION 2.1 Formulation of the Integral Equations 3 2.2 Numerical Results for the Body of...the ’ and 14 56 Integral Functions A.2 Singularity Analysis of the Integral 60 Function U 0 A.3 Singularity Analys s of the Integral 63 Functions U
A numerical method for the study of the circulation of the world ocean
Bryan, K.
1997-08-01
This paper describes a detail computational procedure involving a finite difference numerical schemes to study the circulation models of the world oceans. To obtain an efficient numerical method for low-frequency, large-scale current systems, surfaces gravity-inertial waves are filtered out by the rigid-lid approximation. Special features of the ocean circulation are resolved in the numerical model by allowing for a variable spacing in either the zonal or meridional direction. 20 refs., 5 figs., 1 tab.
Numerical analysis of the orthogonal descent method
Shokov, V.A.; Shchepakin, M.B.
1994-11-01
The author of the orthogonal descent method has been testing it since 1977. The results of these tests have only strengthened the need for further analysis and development of orthogonal descent algorithms for various classes of convex programming problems. Systematic testing of orthogonal descent algorithms and comparison of test results with other nondifferentiable optimization methods was conducted at TsEMI RAN in 1991-1992 using the results.
Numerical methods for reduction of topside ionograms
NASA Technical Reports Server (NTRS)
Mcculley, L.
1972-01-01
Several alternative methods for solving the group height equation are presented. Three of these are now in operation at Ames Research Center and use data contained in a single ionogram trace. From the data an electron density profile N(h) is computed. If the ionogram also exhibits other traces, reverse ionogram traces are computed, using the N(h) profile, for comparison with the redundant data. When agreement is poor, the initial data trace is reinterpreted, another N(h) profile computed, and the reverse traces generated once again. This process is repeated until a desired degree of consistency is achieved. To reduce the necessity for human intervention and eliminate decision making required in conjunction with the preceding methods, a method is proposed that accepts as input, all data from a single ionogram. In general, no electron density function will satisfy these data exactly, but a best N(h) profile can be computed. Finally, a method is described that eliminates the need to assume that the ionosphere is spherically stratified. Horizontal gradients in electron density are detected and accounted for by processing several ionograms from the same satellite pass simultaneously. This idea is derived as an extension of one of the basic methods.
Numerical study on the influence of boss cap fins on efficiency of controllable-pitch propeller
NASA Astrophysics Data System (ADS)
Xiong, Ying; Wang, Zhanzhi; Qi, Wanjiang
2013-03-01
Numerical simulation is investigated to disclose how propeller boss cap fins (PBCF) operate utilizing Reynolds-averaged Navier-Stokes (RANS) method. In addition, exploration of the influencing mechanism of PBCF on the open water efficiency of one controllable-pitch propeller is analyzed through the open water characteristic curves, blade surface pressure distribution and hub streamline distribution. On this basis, the influence of parameters including airfoil profile, diameter, axial position of installation and circumferential installation angle on the open water efficiency of the controllable-pitch propeller is investigated. Numerical results show: for the controllable-pitch propeller, the thrust generated is at the optimum when the radius of boss cap fins is 1.5 times of propeller hub with an optimal installation position in the axial direction, and its optimal circumferential installation position is the midpoint of the extension line of the front and back ends of two adjacent propeller roots in the front of fin root. Under these optimal parameters, the gain of open water efficiency of the controllable-pitch propeller with different advance velocity coefficients is greater than 0.01, which accounts for approximately an increase of 1%-5% of open water efficiency.
NASA Technical Reports Server (NTRS)
Maccormack, R. W.
1978-01-01
The calculation of flow fields past aircraft configuration at flight Reynolds numbers is considered. Progress in devising accurate and efficient numerical methods, in understanding and modeling the physics of turbulence, and in developing reliable and powerful computer hardware is discussed. Emphasis is placed on efficient solutions to the Navier-Stokes equations.
Numerical Methods Using B-Splines
NASA Technical Reports Server (NTRS)
Shariff, Karim; Merriam, Marshal (Technical Monitor)
1997-01-01
The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.
Modelling asteroid brightness variations. I - Numerical methods
NASA Technical Reports Server (NTRS)
Karttunen, H.
1989-01-01
A method for generating lightcurves of asteroid models is presented. The effects of the shape of the asteroid and the scattering law of a surface element are distinctly separable, being described by chosen functions that can easily be changed. The shape is specified by means of two functions that yield the length of the radius vector and the normal vector of the surface at a given point. The general shape must be convex, but spherical concavities producing macroscopic shadowing can also be modeled.
Numerical orbit integration efficiency of the Delaunay-Similar elements
NASA Technical Reports Server (NTRS)
Pierce, S.
1974-01-01
Orbit equations with a set of conservative and a set of nonconservative perturbing potentials were considered. Scheifele's DS formulation of these equations has dependent variables similar to Delaunay's orbital elements with the true anomaly as the independent variable. Efficiency curves of computing cost v.s. accuracy were constructed for Adams integrators of order of 2 through 15 with several correcting algorithms and for a Runga-Kutta integrator. Considering stability regions, choices were made for the optimally efficient integration modes for the DS elements. Integrating in these modes reduces computing costs for a specified accuracy.
Fast Numerical Methods for the Design of Layered Photonic Structures with Rough Interfaces
NASA Technical Reports Server (NTRS)
Komarevskiy, Nikolay; Braginsky, Leonid; Shklover, Valery; Hafner, Christian; Lawson, John
2011-01-01
Modified boundary conditions (MBC) and a multilayer approach (MA) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with arbitrary permittivity tensor. MBC and MA are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.
Two Different Methods for Numerical Solution of the Modified Burgers' Equation
Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi
2014-01-01
A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM. PMID:25162064
Two different methods for numerical solution of the modified Burgers' equation.
Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi
2014-01-01
A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM.
An efficient numerical model for multicomponent compressible flow in fractured porous media
NASA Astrophysics Data System (ADS)
Zidane, Ali; Firoozabadi, Abbas
2014-12-01
An efficient and accurate numerical model for multicomponent compressible single-phase flow in fractured media is presented. The discrete-fracture approach is used to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross flow equilibrium in the fractures. This will allow large matrix elements in the neighborhood of the fractures and considerable speed up of the algorithm. We use an implicit finite volume (FV) scheme to solve the species mass balance equation in the fractures. This step avoids the use of Courant-Freidricks-Levy (CFL) condition and contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix. Four numerical examples are presented to demonstrate the robustness and efficiency of the proposed model. We show that the combination of the fracture cross-flow equilibrium and the implicit composition calculation in the fractures increase the computational speed 20-130 times in 2D. In 3D, one may expect even a higher computational efficiency.
Adaptive Numerical Dissipation Controls for High Order Methods
NASA Technical Reports Server (NTRS)
Yee, Helen C.; Sjogreen, B.; Sandham, N. D.; Mansour, Nagi (Technical Monitor)
2001-01-01
A numerical scheme for direct numerical simulation of shock-turbulence interactions of high speed compressible flows would ideally not be significantly more expensive than the standard fourth or sixth-order compact or non-compact central differencing scheme. It should be possible to resolve all scales down to scales of order of the Kolmogorov scales of turbulence accurately and efficiently, while at the same time being able to capture steep gradients occurring at much smaller scales efficiently. The goal of this lecture is to review the progress and new development of the low dissipative high order shock-capturing schemes proposed by Yee et al. Comparison on the efficiency and accuracy of this class of schemes with spectral and the fifth-order WENO (weighted essentially nonoscillatory) scheme will be presented. A new approach to dynamically sense the appropriate amount of numerical dissipation to be added at each grid point using non-orthogonal wavelets will be discussed.
Ren, Qiang; Nagar, Jogender; Kang, Lei; Bian, Yusheng; Werner, Ping; Werner, Douglas H
2017-05-18
A highly efficient numerical approach for simulating the wideband optical response of nano-architectures comprised of Drude-Critical Points (DCP) media (e.g., gold and silver) is proposed and validated through comparing with commercial computational software. The kernel of this algorithm is the subdomain level discontinuous Galerkin time domain (DGTD) method, which can be viewed as a hybrid of the spectral-element time-domain method (SETD) and the finite-element time-domain (FETD) method. An hp-refinement technique is applied to decrease the Degrees-of-Freedom (DoFs) and computational requirements. The collocated E-J scheme facilitates solving the auxiliary equations by converting the inversions of matrices to simpler vector manipulations. A new hybrid time stepping approach, which couples the Runge-Kutta and Newmark methods, is proposed to solve the temporal auxiliary differential equations (ADEs) with a high degree of efficiency. The advantages of this new approach, in terms of computational resource overhead and accuracy, are validated through comparison with well-known commercial software for three diverse cases, which cover both near-field and far-field properties with plane wave and lumped port sources. The presented work provides the missing link between DCP dispersive models and FETD and/or SETD based algorithms. It is a competitive candidate for numerically studying the wideband plasmonic properties of DCP media.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1988-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to react chemically and reach states in thermal nonequilibrium. In this paper, a new procedure based on Gauss-Seidel line relaxation is shown to solve the equations of hypersonic flow fields containing finite reaction rate chemistry and thermal nonequilibrium. The method requires a few hundred time steps and small computer times for axisymmetric flows about simple body shapes. The extension to more complex two-dimensional body geometries appears straightforward.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1988-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to react chemically and reach states in thermal nonequilibrium. In this paper, a new procedure based on Gauss-Seidel line relaxation is shown to solve the equations of hypersonic flow fields containing finite reaction rate chemistry and thermal nonequilibrium. The method requires a few hundred time steps and small computer times for axisymmetric flows about simple body shapes. The extension to more complex two-dimensional body geometries appears straightforward.
Numerical methods for hypersonic boundary layer stability
NASA Technical Reports Server (NTRS)
Malik, M. R.
1990-01-01
Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.
Numerical analysis of core catcher efficiency for VVER-1200
Zvonarev, Yu. A.; Tsurikov, D. F.; Kobzar, V. L.; Volchek, A. M.; Kiselev, N. P.; Strizhov, V. F.; Filippov, A. S.; Moiseenko, E. V.
2011-12-15
A brief description of the HEFEST-ULR code and numerical results for corium behavior in a core catcher for the VVER-1200 (NPP-2006 project) are presented. Physical, chemical, and thermal processes during corium pool formation and cooling in the core catcher are examined for the case of severe accidents in NPP-2006 with the VVER-1200. Basic corium parameters, including its composition, structure, temperature evolution, density, and aggregative state, are determined. The minimum margin for critical heat flux at the external surface of the core catcher is estimated.
Efficient and robust implementation of the TLISMNI method
NASA Astrophysics Data System (ADS)
Aboubakr, Ahmed K.; Shabana, Ahmed A.
2015-09-01
The dynamics of large scale and complex multibody systems (MBS) that include flexible bodies and contact/impact pairs is governed by stiff equations. Because explicit integration methods can be inefficient and often fail in the case of stiff problems, the use of implicit numerical integration methods is recommended in this case. This paper presents a new and efficient implementation of the two-loop implicit sparse matrix numerical integration (TLISMNI) method proposed for the solution of constrained rigid and flexible MBS differential and algebraic equations. The TLISMNI method has desirable features that include avoiding numerical differentiation of the forces, allowing for an efficient sparse matrix implementation, and ensuring that the kinematic constraint equations are satisfied at the position, velocity and acceleration levels. In this method, a sparse Lagrangian augmented form of the equations of motion that ensures that the constraints are satisfied at the acceleration level is used to solve for all the accelerations and Lagrange multipliers. The generalized coordinate partitioning or recursive methods can be used to satisfy the constraint equations at the position and velocity levels. In order to improve the efficiency and robustness of the TLISMNI method, the simple iteration and the Jacobian-Free Newton-Krylov approaches are used in this investigation. The new implementation is tested using several low order formulas that include Hilber-Hughes-Taylor (HHT), L-stable Park, A-stable Trapezoidal, and A-stable BDF methods. The HHT method allows for including numerical damping. Discussion on which method is more appropriate to use for a certain application is provided. The paper also discusses TLISMNI implementation issues including the step size selection, the convergence criteria, the error control, and the effect of the numerical damping. The use of the computer algorithm described in this paper is demonstrated by solving complex rigid and flexible tracked
Efficiency of Runge-Kutta methods in solving Kepler problem
NASA Astrophysics Data System (ADS)
Gorgey, Annie; Muhammad, Hafizul
2017-05-01
The aim of this research is to study the efficiency of symplectic and non-symplectic Runge-Kutta methods in solving Kepler problem. The numerical behavior of the Runge-Kutta (RK) methods that are symmetric such as the implicit midpoint rule (IMR), implicit trapezoidal rule (ITR), 2-stage and 2-stage Gauss (G2) method are compared with the non-symmetric Runge-Kutta methods such as the explicit and implicit Euler (EE and IE), explicit midpoint rule (EIMR), explicit trapezoidal rules (EITR), explicit 4-stage Runge-Kutta (RK4) method and 2-stage Radau IIA method (R2A). Kepler problem is one type of nonlinear Hamiltonian problem that describes the motion in a plane of a material point that is attracted towards the origin with a force inversely proportional to the distance squared. The exact solutions phase diagram produces a unit circle. The non-symplectic methods only reproduce a unit circle at certain time intervals while the symplectic methods do produce a unit circle at any time intervals. Some phase diagram show spiral in or spiral out patterns which means the solutions are running away from the unit circle. This also means that the absolute error will be increasing in long time integration. The numerical experiments for the Kepler problem are given for many time intervals and the results show that the most efficient method is G2 of order-4 and surprisingly RK4 seems to be efficient too although it is not a symplectic nor a symmetric method. The numerical results on Kepler problem concluded that, the higher the order of the method, the most efficient the method can be in solving Kepler problem despite whether they are explicit or implicit or symmetric and symplectic.
Efficient calculation of degenerate atomic rates by numerical quadrature on GPUs
NASA Astrophysics Data System (ADS)
Aslanyan, V.; Aslanyan, A. G.; Tallents, G. J.
2017-10-01
The rates of atomic processes in cold, dense plasma are governed strongly by effects of quantum degeneracy. The electrons follow Fermi-Dirac statistics and their high density limits the number of quantum states available for occupation after a collision. These factors preclude a direct solution to the usual rate coefficient integrals. We summarize the formulation of this problem and present a simple, but efficient method of evaluating collisional rate coefficients via direct numerical integration. Numerical quadrature has an intrinsically high level of parallelism, ideally suited for graphics processor units. GPUs are particularly suited to this problem because of the large number of integrals which must be carried out simultaneously for a given atomic model. A CUDA code to calculate the rates of significant atomic processes as part of a collisional-radiative model is presented and discussed. This approach may be readily extended to other applications where rapid and repeated evaluation of many integrals is required.
NASA Astrophysics Data System (ADS)
Cheng, Qing; Yang, Xiaofeng; Shen, Jie
2017-07-01
In this paper, we consider numerical approximations of a hydro-dynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching schemes for this system using the ;Invariant Energy Quadratization; approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable. Various numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.
Numerical methods for analyzing electromagnetic scattering
NASA Technical Reports Server (NTRS)
Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.
1985-01-01
Attenuation properties of the normal modes in an overmoded waveguide coated with a lossy material were analyzed. It is found that the low-order modes, can be significantly attenuated even with a thin layer of coating if the coating material is not too lossy. A thinner layer of coating is required for large attenuation of the low-order modes if the coating material is magnetic rather than dielectric. The Radar Cross Section (RCS) from an uncoated circular guide terminated by a perfect electric conductor was calculated and compared with available experimental data. It is confirmed that the interior irradiation contributes to the RCS. The equivalent-current method based on the geometrical theory of diffraction (GTD) was chosen for the calculation of the contribution from the rim diffraction. The RCS reduction from a coated circular guide terminated by a PEC are planned schemes for the experiments are included. The waveguide coated with a lossy magnetic material is suggested as a substitute for the corrugated waveguide.
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver.
Comparisons of numerical methods with respect to convectively dominated problems
NASA Astrophysics Data System (ADS)
Wang, Yongqi; Hutter, Kolumban
2001-11-01
A series of numerical schemes: first-order upstream, Lax-Friedrichs; second-order upstream, central difference, Lax-Wendroff, Beam-Warming, Fromm; third-order QUICK, QUICKEST and high resolution flux-corrected transport and total variation diminishing (TVD) methods are compared for one-dimensional convection-diffusion problems. Numerical results show that the modified TVD Lax-Friedrichs method is the most competent method for convectively dominated problems with a steep spatial gradient of the variables. Copyright
Numerical Analysis of Microdischarge Oxygen Plasma and Prediction of Ozone Production Efficiency
NASA Astrophysics Data System (ADS)
Kawano, Satoyuki; Misaka, Takashi
In this research, numerical simulation of oxygen plasma produced by dielectric barrier discharge (DBD) is made as a basic research for the application of bioprocesses such as sterilization. Numerical simulation is based on an appropriate modeling of microdischarges including 9 kinds of species and 54 chemical reactions. Behavior of the oxygen plasma is analyzed by finite difference method in two-dimensional computational region. The detailed characteristics of filamentous discharge formed between parallel dielectric surfaces which cover the electrodes are investigated. The qualitative tendency of the discharge formation process agrees with the previous experimental observation. Ozone production efficiency (OPE) is obtained and compared with experimental results. Dependency of reduced electric field E/n on OPE is investigated by comparing the numerical results with previous experimental results by other researcher, where E/n is the ratio of electric field EE to number density n of neutral molecule in the gas. It is confirmed that the present numerical simulation has practically enough accuracy for the evaluation of the OPE to optimize the oxygen plasma sterilization devices.
A numerical method for vortex sheet roll-up
NASA Technical Reports Server (NTRS)
Krasny, R.
1986-01-01
The problem of computing vortex sheet roll-up from periodic analytic initial data is studied. Previous theoretical and numerical work is reviewed. Computational difficulties arising from ill posedness and singularity formation are discussed. A desingularization method is proposed to diminish these difficulties. Computations indicate that this approach converges past the time at which previous numerical investigations have failed to converge.
Numerical Analysis on the Vortex Pattern and Flux Particle Dispersion in KR Method Using MPS Method
NASA Astrophysics Data System (ADS)
Hirata, N.; Xu, Y.; Anzai, K.
2015-06-01
The mechanically-stirring vessel is widely used in many fields, such as chemical reactor, bioreactor, and metallurgy, etc. The type of vortex mode that formed during impeller stirring has great effect on stirring efficiency, chemical reacting rate and air entrapment. Many efforts have been made to numerically simulate the fluid flow in the stirring vessel with classical Eulerian method. However, it is difficult to directly investigate the vortex mode and flux particle dispersion. Therefore, moving particle semi-implicit (MPS) method, which is based on Lagrangian method, is applied to simulate the fluid flow in a KR method in this practice. Top height and bottom heights of vortex surface in a steady state under several rotation speed was taken as key parameters to compare the results of numerical and published results. Flux particle dispersion behaviour under a rotation speed range from 80 to 480 rpm was also compared with the past study. The result shows that the numerical calculation has high consistency with experimental results. It is confirmed that the calculation using MPS method well reflected the vortex mode and flux particle dispersion in a mechanically-stirring vessel.
Photometry of dark atmosphereless planetary bodies: an efficient numerical model
NASA Astrophysics Data System (ADS)
Wilkman, Olli; Muinonen, Karri; Peltoniemi, Jouni
2015-12-01
We present a scattering model for regolith-covered Solar System bodies. It can be used to compute the intensity of light scattered by a surface consisting of packed, mutually shadowing particles. Our intention is to provide a model in which other researchers can apply in studies of Solar System photometry. Our model is a Lommel-Seeliger type model, representing a medium composed of individual scatterers with small single-scattering albedo. This means that it is suitable for dark regolith surfaces such as the Moon and many classes of asteroids. Our model adds an additional term which takes into account the mutual shadowing between the scatterers. The scatterers can have an arbitrary phase function. We use a numerical ray-tracing simulation to compute the shadowing contribution. We present the model in a form which makes implementing it in existing software straightforward and fast. The model in practice is implemented as files containing pre-computed values of the surface reflection coefficient, which can be loaded into a user's program and used to compute the scattering in the desired viewing geometries. As the usage requires only a little simple arithmetic and a table look-up, it is as fast to use as common analytical models.
2012-01-01
Background Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations. This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. Results Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. Conclusions In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the
Methods for studying close-track efficiency
Mac Mestayer; Konstantin Mikhaylov; Aleksey Stavinskiy; Alexander Vlassov
2004-05-01
Wire chambers used for particle tracking suffer a loss of efficiency when the trajectories of two particles from the same event are very close together in space. We describe two new methods for the study of this close-track efficiency. One is based on the study of a correlation function for particles with different masses as a function of their relative momenta in the laboratory reference system. The other method is based on the analysis of artificial events, constructed by merging raw data from separate events. Both methods and the standard Monte Carlo method were applied to data from the CLAS detector at Jefferson Laboratory. All three methods provide the same result for close-track efficiency with an accuracy sufficient for practical application.
An efficient method for the analysis of the space-charge region of diffused junctions
NASA Astrophysics Data System (ADS)
Eltoukhy, A. A.; Roulston, D. J.
1982-08-01
An efficient numerical method is presented which gives the solution for electrostatic potential, carrier density and space charge density distribution of an asymetrical junction. This method is based on the numerical solution of Poisson's equation assuming a zero-current approximation. A comparison between the present method and two different methods is made.
A numerical solution method for acoustic radiation from axisymmetric bodies
NASA Technical Reports Server (NTRS)
Caruthers, John E.; Raviprakash, G. K.
1995-01-01
A new and very efficient numerical method for solving equations of the Helmholtz type is specialized for problems having axisymmetric geometry. It is then demonstrated by application to the classical problem of acoustic radiation from a vibrating piston set in a stationary infinite plane. The method utilizes 'Green's Function Discretization', to obtain an accurate resolution of the waves using only 2-3 points per wave. Locally valid free space Green's functions, used in the discretization step, are obtained by quadrature. Results are computed for a range of grid spacing/piston radius ratios at a frequency parameter, omega R/c(sub 0), of 2 pi. In this case, the minimum required grid resolution appears to be fixed by the need to resolve a step boundary condition at the piston edge rather than by the length scale imposed by the wave length of the acoustic radiation. It is also demonstrated that a local near-field radiation boundary procedure allows the domain to be truncated very near the radiating source with little effect on the solution.
Efficient numerical solution of excitation number conserving quantum systems
NASA Astrophysics Data System (ADS)
Zhang, Zheyong; Ding, Jianping; Wang, Hui-Tian
2017-08-01
A system composed of a harmonic oscillator coupled to a two-level atom is one of the quantum systems, which can be completely solved. Although this system is simple, it is never a easy work for the quantum calculations, especially when the system consists of many such simple constituent parts. In this paper, we present a programming method, by which the calculation tasks for the matrix representation of the Hamiltonian of system can be automatically fulfilled. Coupled-cavity array systems are used to demonstrate our programming method. Some quantum properties of these systems are also discussed.
Efficient elastoplastic analysis with the boundary element method
NASA Astrophysics Data System (ADS)
Ribeiro, T. S. A.; Beer, G.; Duenser, C.
2008-02-01
Conventional numerical implementation of the boundary element method (BEM) for elasto-plastic analysis requires a domain discretization into cells. This requires more effort for the discretization of the problem and additional computational effort. A new technique is proposed here for the analysis of 2D and 3D elasto-plastic problems with the boundary element method. In this approach the domain does not need to be discretised into cells prior to the analysis. Plasticity is assumed to start from the boundary and the cells are generated from the boundary data automatically during the analysis. Using the cell generation process, elasto-plastic analysis with the BEM becomes much more user friendly and efficient than the standard approach with a pre-definition of cells. The accuracy and efficiency of the solution obtained by the new approach is verified by several numerical examples.
Some Comments on Numerical Methods for Chaos Problems
NASA Astrophysics Data System (ADS)
Miller, R. H.
1996-03-01
Hamiltonian systems with chaotic regions are particularly slippery to treat numerically. Numerical treatments can introduce nonphysical features. Simple examples illustrate some of the pitfalls. Integer, or discrete, arithmetic is a favorite “workaround.” While it does not cure chaos, it clarifies the interaction of computational methods with the underlying mathematical structure. Be forewarned: I won't give any prescription that is guaranteed to give a good and reliable method to handle chaotic problems numerically. Instead, I'll stress a few of the concerns and describe one or two pitfalls.
Efficient planning and numerical analysis of industrial hemming processes
NASA Astrophysics Data System (ADS)
Burchitz, Igor; Fritsche, David; Grundmann, Göran; Hillmann, Matthias
2011-08-01
Hemming is a forming operation used in the automotive industry to join inner and outer components during the assembly of closures. These are typically opening parts of the body-in-white with additional requirements to their visual appearance. A suitable production concept of hemming operation which satisfies quality, capacity and cost requirements is determined during hemming planning activities. A digital tool to facilitate these activities and minimize the amount of trial and error iterations in try-out phase is presented in this paper. This tool can be used to define process plan, active tool surfaces and suitable process parameters for both die hemming and roll hemming operations. In case of early feasibility studies, when the die layout of the drawing operation is still not available, 3D part geometry is used directly to develop the concept of hemming process. Advanced validation studies, aimed at process optimization and controlling defects associated with hemming, can be based on complete simulation of all forming operations. Validation and analysis of developed concepts of hemming operation is done using the standard AutoForm-Incremental solver. Submesh strategy and special algorithm for contact description between inner and outer parts were implemented to ensure that accurate simulation results can be obtained within reasonable calculation time. Performance of the new software tool for hemming planning and accuracy of simulation results are demonstrated using several simple benchmarks and a real industrial part. It is shown that the new software tool can help to secure the efficient production launch by providing adequate support in try-out phase.
Efficient Methods for Multi-Label Classification
2015-05-22
annotation and retrieval of music and sound effects . IEEE Transactions on Audio, Speech and Language Processing 16(2), 467–476 (2008) 19. Vens, C., Struyf...advertising [2] and music categorization [18]. In these applications there are usually tens or hundreds of thousands of labels, while the number is...Efficient Methods for Multi-label Classiffication 165 and testing efficiency, memory usage is also a bottleneck as the number of labels becoming larger
Application of higher-order numerical methods to the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1978-01-01
A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
Critical study of higher order numerical methods for solving the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1978-01-01
A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.
Effective numerical method of spectral analysis of quantum graphs
NASA Astrophysics Data System (ADS)
Barrera-Figueroa, Víctor; Rabinovich, Vladimir S.
2017-05-01
We present in the paper an effective numerical method for the determination of the spectra of periodic metric graphs equipped by Schrödinger operators with real-valued periodic electric potentials as Hamiltonians and with Kirchhoff and Neumann conditions at the vertices. Our method is based on the spectral parameter power series method, which leads to a series representation of the dispersion equation, which is suitable for both analytical and numerical calculations. Several important examples demonstrate the effectiveness of our method for some periodic graphs of interest that possess potentials usually found in quantum mechanics.
Asymptotic-induced numerical methods for conservation laws
NASA Technical Reports Server (NTRS)
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
A Numerical Method for Simulation of Three Dimensional Ice Accretion on Aircrafts
NASA Astrophysics Data System (ADS)
Yi, X.; Wang, K. C.; Zhu, G. L.; Gui, Y. W.
2011-09-01
A numerical method for simulation of three dimensional ice accretion on aircraft is proposed in this paper. An Eulerian method for computation of collection efficiency on icing surface is presented at first. The external flow field of gas phase is calculated with computational fluid dynamics (CFD) method, based on which the governing equations of water phase are solved, and the corresponding collection efficiency is obtained. A three-dimensional model, considering effects of runback water, is then presented, and an iterative arithmetic for solving the model is developed. The impingement characteristics of a three elements wing are computed to evaluate the numerical method for collection efficiency calculation. Ice accretion on a MS-317 swept wing is calculated, and the consequent ice shape is compared with that of an experiment and Lewice3D. All the computational results are in good agreement with data of the experiment and reference, which indicates that the proposed method is feasible.
Numerical methods for solving ODEs on the infinity computer
NASA Astrophysics Data System (ADS)
Mazzia, F.; Sergeyev, Ya. D.; Iavernaro, F.; Amodio, P.; Mukhametzhanov, M. S.
2016-10-01
New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial conditions are proposed. They are designed for working on a new kind of a supercomputer - the Infinity Computer - that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods are able to work with the exact values of the derivatives, instead of their approximations. Within this context, variants of one-step multi-point methods closely related to the classical Taylor formulae and to the Obrechkoff methods are considered. To get numerical evidence of the theoretical results, test problems are solved by means of the new methods and the results compared with the performance of classical methods.
Reduced-complexity numerical method for optimal gate synthesis
NASA Astrophysics Data System (ADS)
Sridharan, Srinivas; Gu, Mile; James, Matthew R.; McEneaney, William M.
2010-10-01
Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate-design problem is equivalent to the solution of an associated optimal-control problem; the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality-free techniques) that determine the optimal control, thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control-set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, which is used in previous research. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on SU(4)—a problem that is computationally intractable by grid-based approaches.
A critical study of higher-order numerical methods for solving the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1977-01-01
A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
NASA Technical Reports Server (NTRS)
Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.
1992-01-01
The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.
Application of Efficient Methods for Inspection Sensitivity
2009-04-01
reliability of structural components. NDE inspecitons are simulated using a Probability-of-Detection curve ( POD ) that is obtained experimentally. In this...parameters of the POD via Monte Carlo Sampling. The methodology scales to any number of inspections and can be integrated with existing Monte Carlo...sampling methods. Sensitivities of the probability-of-failure with respect to the parameters of a POD curve were calculated for several numerical examples
EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY
FRANCOIS, MARIANNE M.; DENDY, EDWARD D.; LOWRIE, ROBERT B.; LIVESCU, DANIEL; STEINKAMP, MICHAEL J.
2007-01-11
The authors compare the effects of different numerical schemes for the advection and material interface treatments on the single-mode Rayleigh-Taylor instability, using the RAGE hydro-code. The interface growth and its surface density (interfacial area) versus time are investigated. The surface density metric shows to be better suited to characterize the difference in the flow, than the conventional interface growth metric. They have found that Van Leer's limiter combined to no interface treatment leads to the largest surface area. Finally, to quantify the difference between the numerical methods they have estimated the numerical viscosity in the linear-regime at different scales.
Numeric Modified Adomian Decomposition Method for Power System Simulations
Dimitrovski, Aleksandar D; Simunovic, Srdjan; Pannala, Sreekanth
2016-01-01
This paper investigates the applicability of numeric Wazwaz El Sayed modified Adomian Decomposition Method (WES-ADM) for time domain simulation of power systems. WESADM is a numerical method based on a modified Adomian decomposition (ADM) technique. WES-ADM is a numerical approximation method for the solution of nonlinear ordinary differential equations. The non-linear terms in the differential equations are approximated using Adomian polynomials. In this paper WES-ADM is applied to time domain simulations of multimachine power systems. WECC 3-generator, 9-bus system and IEEE 10-generator, 39-bus system have been used to test the applicability of the approach. Several fault scenarios have been tested. It has been found that the proposed approach is faster than the trapezoidal method with comparable accuracy.
Algorithms for the Fractional Calculus: A Selection of Numerical Methods
NASA Technical Reports Server (NTRS)
Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.
2003-01-01
Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.
Investigating Convergence Patterns for Numerical Methods Using Data Analysis
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2013-01-01
The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…
Investigating Convergence Patterns for Numerical Methods Using Data Analysis
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2013-01-01
The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…
A numerical method for solving singular De`s
Mahaver, W.T.
1996-12-31
A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.
Efficient Methods to Compute Genomic Predictions
USDA-ARS?s Scientific Manuscript database
Efficient methods for processing genomic data were developed to increase reliability of estimated breeding values and simultaneously estimate thousands of marker effects. Algorithms were derived and computer programs tested on simulated data for 50,000 markers and 2,967 bulls. Accurate estimates of ...
Toward cost-efficient sampling methods
NASA Astrophysics Data System (ADS)
Luo, Peng; Li, Yongli; Wu, Chong; Zhang, Guijie
2015-09-01
The sampling method has been paid much attention in the field of complex network in general and statistical physics in particular. This paper proposes two new sampling methods based on the idea that a small part of vertices with high node degree could possess the most structure information of a complex network. The two proposed sampling methods are efficient in sampling high degree nodes so that they would be useful even if the sampling rate is low, which means cost-efficient. The first new sampling method is developed on the basis of the widely used stratified random sampling (SRS) method and the second one improves the famous snowball sampling (SBS) method. In order to demonstrate the validity and accuracy of two new sampling methods, we compare them with the existing sampling methods in three commonly used simulation networks that are scale-free network, random network, small-world network, and also in two real networks. The experimental results illustrate that the two proposed sampling methods perform much better than the existing sampling methods in terms of achieving the true network structure characteristics reflected by clustering coefficient, Bonacich centrality and average path length, especially when the sampling rate is low.
Defining Efficient Stress Transfer in Binary Particle Systems Using Numerical Simulation
2016-11-01
model simulates the 3-D movement of spherical particles as they interact with one another and rigid solid objects defined by finite elements . The...numerical testing methods were employed including consolidated- undrained triaxial testing and numerical modeling using the discrete element method (DEM...9 3 Discrete Element Method
Efficient stochastic Galerkin methods for random diffusion equations
Xiu Dongbin Shen Jie
2009-02-01
We discuss in this paper efficient solvers for stochastic diffusion equations in random media. We employ generalized polynomial chaos (gPC) expansion to express the solution in a convergent series and obtain a set of deterministic equations for the expansion coefficients by Galerkin projection. Although the resulting system of diffusion equations are coupled, we show that one can construct fast numerical methods to solve them in a decoupled fashion. The methods are based on separation of the diagonal terms and off-diagonal terms in the matrix of the Galerkin system. We examine properties of this matrix and show that the proposed method is unconditionally stable for unsteady problems and convergent for steady problems with a convergent rate independent of discretization parameters. Numerical examples are provided, for both steady and unsteady random diffusions, to support the analysis.
An efficient broadband coupled-mode model using the Hamiltonian method for modal solutions
NASA Astrophysics Data System (ADS)
Yang, XueFeng; Luo, WenYu; Wang, HaoZhong; Hu, ChangQing
2017-09-01
A numerically efficient broadband, range-dependent propagation model is proposed, which incorporates the Hamiltonian method into the coupled-mode model DGMCM. The Hamiltonian method is highly efficient for finding broadband eigenvalues, and DGMCM is an accurate model for range-dependent propagation in the frequency domain. Consequently, the proposed broadband model combining the Hamiltonian method and DGMCM has significant virtue in terms of both efficiency and accuracy. Numerical simulations are also provided. The numerical results indicate that the proposed model has a better performance over the broadband model using the Fourier synthesis and COUPLE, while retaining the same level of accuracy.
25 Years of Self-organized Criticality: Numerical Detection Methods
NASA Astrophysics Data System (ADS)
McAteer, R. T. James; Aschwanden, Markus J.; Dimitropoulou, Michaila; Georgoulis, Manolis K.; Pruessner, Gunnar; Morales, Laura; Ireland, Jack; Abramenko, Valentyna
2016-01-01
The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.
Numerical investigation of the thrust efficiency of a laser propelled vehicle
mulroy jr
1990-08-01
The flow situation for a thruster propelled by ablated gas which is energized by a laser pulse is numerically simulated. The flow is axisymmetric and nonsteady, and is assumed to be inviscid due to its high Reynolds number. The high pressure expansion of the laser heated gas generates thrust as it pushes against the vehicle. Gas expansion lateral to the thrust vector causes performance to decrease. The vehicle geometry and the laser pulse characteristics determine the degree to which the flow is one dimensional. As the thruster's parameters are varied, its impulse is calculated and compared to the limiting impulse of a one-dimensional system, and thus the thrust efficiency is computed. Lateral expansion losses computed by simulating the flow of the expanding gas time-accurately on a computer are far less than losses predicted using the method of characteristics, which is the best alternate means of computation. Flows which exhibit a substantial amount of lateral expansion can still yield an expansion efficiency which exceeds 70%. This finding has significant implications on the eventual design of flight hardware. Steger and Warming's flux split numerics for the Euler equations are modified for blast simulations into near vacuum ambient conditions. At the interface between the near vacuum ambient and the wave front, the solution is first order accurate but sufficiently robust to handle pressure ratios exceeding one million and density ratios exceeding 10,000 between the thrust gas and the ambient gas. Elsewhere the solution is second order accurate. The majority of the calculations performed assume an ideal gas equation of state with {gamma} = 1.2. The propellant Lithium Hydride has shown excellent promise in the laboratory, yielding I{sub sp} = 800-1000 sec. Equilibrium and kinetic modeling of LiH is undertaken, with a variable {gamma} of from 1.25 to 1.66 resulting from the kinetic assumptions of ionization equilibrium and frozen chemistry. These additional
Applying multi-resolution numerical methods to geodynamics
NASA Astrophysics Data System (ADS)
Davies, David Rhodri
Computational models yield inaccurate results if the underlying numerical grid fails to provide the necessary resolution to capture a simulation's important features. For the large-scale problems regularly encountered in geodynamics, inadequate grid resolution is a major concern. The majority of models involve multi-scale dynamics, being characterized by fine-scale upwelling and downwelling activity in a more passive, large-scale background flow. Such configurations, when coupled to the complex geometries involved, present a serious challenge for computational methods. Current techniques are unable to resolve localized features and, hence, such models cannot be solved efficiently. This thesis demonstrates, through a series of papers and closely-coupled appendices, how multi-resolution finite-element methods from the forefront of computational engineering can provide a means to address these issues. The problems examined achieve multi-resolution through one of two methods. In two-dimensions (2-D), automatic, unstructured mesh refinement procedures are utilized. Such methods improve the solution quality of convection dominated problems by adapting the grid automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. Thermal and thermo-chemical validation tests illustrate that the technique is robust and highly successful, improving solution accuracy whilst increasing computational efficiency. These points are reinforced when the technique is applied to geophysical simulations of mid-ocean ridge and subduction zone magmatism. To date, successful goal-orientated/error-guided grid adaptation techniques have not been utilized within the field of geodynamics. The work included herein is therefore the first geodynamical application of such methods. In view of the existing three-dimensional (3-D) spherical mantle dynamics codes, which are built upon a quasi-uniform discretization of the sphere and closely coupled
Efficient revised simplex method for SVM training.
Sentelle, Christopher; Anagnostopoulos, Georgios C; Georgiopoulos, Michael
2011-10-01
Existing active set methods reported in the literature for support vector machine (SVM) training must contend with singularities when solving for the search direction. When a singularity is encountered, an infinite descent direction can be carefully chosen that avoids cycling and allows the algorithm to converge. However, the algorithm implementation is likely to be more complex and less computationally efficient than would otherwise be required for an algorithm that does not have to contend with the singularities. We show that the revised simplex method introduced by Rusin provides a guarantee of nonsingularity when solving for the search direction. This method provides for a simpler and more computationally efficient implementation, as it avoids the need to test for rank degeneracies and also the need to modify factorizations or solution methods based upon those rank degeneracies. In our approach, we take advantage of the guarantee of nonsingularity by implementing an efficient method for solving the search direction and show that our algorithm is competitive with SVM-QP and also that it is a particularly effective when the fraction of nonbound support vectors is large. In addition, we show competitive performance of the proposed algorithm against two popular SVM training algorithms, SVMLight and LIBSVM. © 2011 IEEE
The numerical mirage method for photothermal characterization of materials.
Demko, Michael T; Hostler, Stephen R; Abramson, Alexis R
2008-04-01
Noncontact thermal measurement techniques offer rapid thermal characterization without modification or destruction of the sample being studied. A simple and versatile method has been developed, termed the "numerical mirage method," that utilizes the transient photothermal deflection of a laser beam traversing a modulated temperature gradient. This method expands the range and simplifies the experimental procedure of traditional mirage methods. A numerical solver is used to create accurate deflection profile models and a linear curve fitting routine is developed, from which the thermal diffusivity of a material may be determined. This method allows for rapid modification of sample and heating configurations. Verification of the method is performed on bismuth and fused quartz reference samples, and good agreement with literature is obtained.
Havu, V. Blum, V.; Havu, P.; Scheffler, M.
2009-12-01
We consider the problem of developing O(N) scaling grid-based operations needed in many central operations when performing electronic structure calculations with numeric atom-centered orbitals as basis functions. We outline the overall formulation of localized algorithms, and specifically the creation of localized grid batches. The choice of the grid partitioning scheme plays an important role in the performance and memory consumption of the grid-based operations. Three different top-down partitioning methods are investigated, and compared with formally more rigorous yet much more expensive bottom-up algorithms. We show that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as the more rigorous bottom-up approaches.
Numerical results for extended field method applications. [thin plates
NASA Technical Reports Server (NTRS)
Donaldson, B. K.; Chander, S.
1973-01-01
This paper presents the numerical results obtained when a new method of analysis, called the extended field method, was applied to several thin plate problems including one with non-rectangular geometry, and one problem involving both beams and a plate. The numerical results show that the quality of the single plate solutions was satisfactory for all cases except those involving a freely deflecting plate corner. The results for the beam and plate structure were satisfactory even though the structure had a freely deflecting corner.
Nonlinear vibrations of buckled plates by an asymptotic numerical method
NASA Astrophysics Data System (ADS)
Benchouaf, Lahcen; Boutyour, El Hassan
2016-03-01
This work deals with nonlinear vibrations of a buckled von Karman plate by an asymptotic numerical method and harmonic balance approach. The coupled nonlinear static and dynamic problems are transformed into a sequence of linear ones solved by a finite-element method. The static behavior of the plate is first computed. The fundamental frequency of nonlinear vibrations of the plate, about any equilibrium state, is obtained. To improve the validity range of the power series, Padé approximants are incorporated. A continuation technique is used to get the whole solution. To show the effectiveness of the proposed methodology, numerical tests are presented.
A numerical method for acoustic oscillations in tubes
NASA Technical Reports Server (NTRS)
Gary, John M.
1988-01-01
A numerical method to obtain the neutral curve for the onset of acoustic oscillations in a helium-filled tube is described. Such oscillations can cause a serious heat loss in the plumbing associated with liquid helium dewars. The problem is modelled by a second-order, ordinary differential eigenvalue problem for the pressure perturbation. The numerical method to find the eigenvalues and track the resulting points along the neutral curve is tailored to this problem. The results show that a tube with a uniform temperature gradient along it is much more stable than one where the temperature suddenly jumps from the cold to the hot value in the middle of the tube.
NASA Technical Reports Server (NTRS)
Williams, S. D.; Curry, D. M.
1974-01-01
Three minimizing techniques are evaluated to determine the most efficient method for minimizing the weight of a thermal protection system and for reducing computer usage time. The methods used (numerical optimization and nonlinear least squares) for solving the minimum-weight problem involving more than one material and more than one constraint are discussed. In addition, the one material and one constraint problem is discussed.
Assessment of Efficiency and Performance in Tsunami Numerical Modeling with GPU
NASA Astrophysics Data System (ADS)
Yalciner, Bora; Zaytsev, Andrey
2017-04-01
Non-linear shallow water equations (NSWE) are used to solve the propagation and coastal amplification of long waves and tsunamis. Leap Frog scheme of finite difference technique is one of the satisfactory numerical methods which is widely used in these problems. Tsunami numerical models are necessary for not only academic but also operational purposes which need faster and accurate solutions. Recent developments in information technology provide considerably faster numerical solutions in this respect and are becoming one of the crucial requirements. Tsunami numerical code NAMI DANCE uses finite difference numerical method to solve linear and non-linear forms of shallow water equations for long wave problems, specifically for tsunamis. In this study, the new code is structured for Graphical Processing Unit (GPU) using CUDA API. The new code is applied to different (analytical, experimental and field) benchmark problems of tsunamis for tests. One of those applications is 2011 Great East Japan tsunami which was instrumentally recorded on various types of gauges including tide and wave gauges and offshore GPS buoys cabled Ocean Bottom Pressure (OBP) gauges and DART buoys. The accuracy of the results are compared with the measurements and fairly well agreements are obtained. The efficiency and performance of the code is also compared with the version using multi-core Central Processing Unit (CPU). Dependence of simulation speed with GPU on linear or non-linear solutions is also investigated. One of the results is that the simulation speed is increased up to 75 times comparing to the process time in the computer using single 4/8 thread multi-core CPU. The results are presented with comparisons and discussions. Furthermore how multi-dimensional finite difference problems fits towards GPU architecture is also discussed. The research leading to this study has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement No
An Improved Method for Determining Barometric Efficiency
NASA Astrophysics Data System (ADS)
Rahi, K. A.; Halihan, T.
2008-12-01
The barometric efficiency (BE) is the ratio of water-level changes in a well to the changes in barometric pressure that produces them. An estimate of barometric efficiency is needed to remove the atmospheric pressure effects on groundwater fluctuation to be able to analyze the influence of other stresses such as earth tides or groundwater pumping tests. The BE is currently determined by the Clark method. This research examines the Clark method as applied to water level fluctuations of several wells in the Arbuckle- Simpson aquifer located in south-central Oklahoma. The study was consistent with previous researchers findings in that the Clark method is inconsistent in the values that it produces and may overestimate the BE . In at least two instances, the Clark method produced physically unrealistic BE values greater than 100 percent. An improved method to determine the BE is presented which overcomes the deficiencies in the Clark method. The new model is tested using water level fluctuation data in two wells collected over a one year period to evaluate the consistency of the new method in a single well. Additional data was evaluated from three other wells to evaluate consistency across the aquifer. The new model demonstrates a consistent, realistic set of values that did not produce BE values exceeding 100 percent.
Numerical methods for solving terminal optimal control problems
NASA Astrophysics Data System (ADS)
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
An Efficient Synchronization Method for Wireless Networks
2013-06-01
group-wise synchronization which is more e cient than rsync, is possible. This paper describes Dandelion , an algorithm that builds on the ideas of the...which is more efficient than rsync, is possible. This paper describes Dandelion , an algorithm that builds on the ideas of the rsync algorithm to...methods analyzed in this paper are compared using this metric. To meet this goal, this paper defines an epidemic-like algorithm called Dandelion that is
Numerical methods and calculations for droplet flow, heating and ignition
NASA Technical Reports Server (NTRS)
Dwyer, H. A.; Sanders, B. R.; Dandy, D.
1982-01-01
A numerical method was devised and employed to solve a variety of problems related to liquid droplet combustion. The basic transport equations of mass, momentum and energy were formulated in terms of generalized nonorthogonal coordinates, which allows for adaptive griding and arbitrary particle shape. Example problems are solved for internal droplet heating, droplet ignition and high Reynolds number flow over a droplet.
A numerical method for unsteady aerodynamics via acoustics
NASA Technical Reports Server (NTRS)
Hodge, Steve
1991-01-01
Formal solutions to the wave equation may be conveniently described within the framework of generalized function theory. A generalized function theory is used to yield a formulation and formal solution of a wave equation describing oscillation of a flat plate from which a numerical method may be derived.
Runkel, Robert L.; Chapra, Steven C.
1993-01-01
Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g., pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50% reduction in simulation run time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run time is of concern.
COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE
Kritsuk, Alexei G.; Collins, David; Norman, Michael L.; Xu Hao E-mail: dccollins@lanl.gov
2011-08-10
Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the
Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence
NASA Astrophysics Data System (ADS)
Kritsuk, Alexei G.; Nordlund, Åke; Collins, David; Padoan, Paolo; Norman, Michael L.; Abel, Tom; Banerjee, Robi; Federrath, Christoph; Flock, Mario; Lee, Dongwook; Li, Pak Shing; Müller, Wolf-Christian; Teyssier, Romain; Ustyugov, Sergey D.; Vogel, Christian; Xu, Hao
2011-08-01
Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvénic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the
Efficient variational Bayesian approximation method based on subspace optimization.
Zheng, Yuling; Fraysse, Aurélia; Rodet, Thomas
2015-02-01
Variational Bayesian approximations have been widely used in fully Bayesian inference for approximating an intractable posterior distribution by a separable one. Nevertheless, the classical variational Bayesian approximation (VBA) method suffers from slow convergence to the approximate solution when tackling large dimensional problems. To address this problem, we propose in this paper a more efficient VBA method. Actually, variational Bayesian issue can be seen as a functional optimization problem. The proposed method is based on the adaptation of subspace optimization methods in Hilbert spaces to the involved function space, in order to solve this optimization problem in an iterative way. The aim is to determine an optimal direction at each iteration in order to get a more efficient method. We highlight the efficiency of our new VBA method and demonstrate its application to image processing by considering an ill-posed linear inverse problem using a total variation prior. Comparisons with state of the art variational Bayesian methods through a numerical example show a notable improvement in computation time.
Numerical methods for aerothermodynamic design of hypersonic space transport vehicles
NASA Astrophysics Data System (ADS)
Wanie, K. M.; Brenneis, A.; Eberle, A.; Heiss, S.
1993-04-01
The requirement of the design process of hypersonic vehicles to predict flow past entire configurations with wings, fins, flaps, and propulsion system represents one of the major challenges for aerothermodynamics. In this context computational fluid dynamics has come up as a powerful tool to support the experimental work. A couple of numerical methods developed at MBB designed to fulfill the needs of the design process are described. The governing equations and fundamental details of the solution methods are shortly reviewed. Results are given for both geometrically simple test cases and realistic hypersonic configurations. Since there is still a considerable lack of experience for hypersonic flow calculations an extensive testing and verification is essential. This verification is done by comparison of results with experimental data and other numerical methods. The results presented prove that the methods used are robust, flexible, and accurate enough to fulfill the strong needs of the design process.
Advanced numerical methods for three dimensional two-phase flow calculations
Toumi, I.; Caruge, D.
1997-07-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.
Numerical aperture of multimode fibers by several methods - Resolving differences
NASA Astrophysics Data System (ADS)
Franzen, Douglas L.; Young, Matt; Cherin, Allen H.; Head, E. D.; Hackert, Michael J.
1989-06-01
An industry-wide study among members of the Electronic Industries Association was conducted to document differences among three numerical aperture measurement methods. Results on 12 multimode graded-index fibers indicate systematic differences exist among commonly used far-field and index-profile techniques. Differences can be explained by a wavelength-dependent factor and choice of definitions. Conversion factors can be used to relate the various methods.
Numerical methods and computers used in elastohydrodynamic lubrication
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Tripp, J. H.
1982-01-01
Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.
Anastassi, Z. A.; Simos, T. E.
2010-09-30
We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.
NASA Technical Reports Server (NTRS)
Chen, Y. S.
1986-01-01
In the present paper, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BEC) systems has been developed and evaluated. 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 and a central differencing plus artificial dissipation scheme are used to approximate the convection terms in the governing equations. Effects of these two schemes on the accuracy of numerical predictions are studied. 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 numerical method.
Singularity Preserving Numerical Methods for Boundary Integral Equations
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki (Principal Investigator)
1996-01-01
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
Path Integrals and Exotic Options:. Methods and Numerical Results
NASA Astrophysics Data System (ADS)
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
On Efficient Large Margin Semisupervised Learning: Method and Theory.
Wang, Junhui; Shen, Xiaotong; Pan, Wei
2009-03-01
In classification, semisupervised learning usually involves a large amount of unlabeled data with only a small number of labeled data. This imposes a great challenge in that it is difficult to achieve good classification performance through labeled data alone. To leverage unlabeled data for enhancing classification, this article introduces a large margin semisupervised learning method within the framework of regularization, based on an efficient margin loss for unlabeled data, which seeks efficient extraction of the information from unlabeled data for estimating the Bayes decision boundary for classification. For implementation, an iterative scheme is derived through conditional expectations. Finally, theoretical and numerical analyses are conducted, in addition to an application to gene function prediction. They suggest that the proposed method enables to recover the performance of its supervised counterpart based on complete data in rates of convergence, when possible.
On Efficient Large Margin Semisupervised Learning: Method and Theory
Wang, Junhui; Shen, Xiaotong; Pan, Wei
2012-01-01
In classification, semisupervised learning usually involves a large amount of unlabeled data with only a small number of labeled data. This imposes a great challenge in that it is difficult to achieve good classification performance through labeled data alone. To leverage unlabeled data for enhancing classification, this article introduces a large margin semisupervised learning method within the framework of regularization, based on an efficient margin loss for unlabeled data, which seeks efficient extraction of the information from unlabeled data for estimating the Bayes decision boundary for classification. For implementation, an iterative scheme is derived through conditional expectations. Finally, theoretical and numerical analyses are conducted, in addition to an application to gene function prediction. They suggest that the proposed method enables to recover the performance of its supervised counterpart based on complete data in rates of convergence, when possible. PMID:24678270
A numerical method for interface problems in elastodynamics
NASA Technical Reports Server (NTRS)
Mcghee, D. S.
1984-01-01
The numerical implementation of a formulation for a class of interface problems in elastodynamics is discussed. This formulation combines the use of the finite element and boundary integral methods to represent the interior and the exteriro regions, respectively. In particular, the response of a semicylindrical alluvial valley in a homogeneous halfspace to incident antiplane SH waves is considered to determine the accuracy and convergence of the numerical procedure. Numerical results are obtained from several combinations of the incidence angle, frequency of excitation, and relative stiffness between the inclusion and the surrounding halfspace. The results tend to confirm the theoretical estimates that the convergence is of the order H(2) for the piecewise linear elements used. It was also observed that the accuracy descreases as the frequency of excitation increases or as the relative stiffness of the inclusion decreases.
An iterative analytic—numerical method for scattering from a target buried beneath a rough surface
NASA Astrophysics Data System (ADS)
Xu, Run-Wen; Guo, Li-Xin; Wang, Rui
2014-11-01
An efficiently iterative analytical—numerical method is proposed for two-dimensional (2D) electromagnetic scattering from a perfectly electric conducting (PEC) target buried under a dielectric rough surface. The basic idea is to employ the Kirchhoff approximation (KA) to accelerate the boundary integral method (BIM). Below the rough surface, an iterative system is designed between the rough surface and the target. The KA is used to simulate the initial field on the rough surface based on the Fresnel theory, while the target is analyzed by the boundary integral method to obtain a precise result. The fields between the rough surface and the target can be linked by the boundary integral equations below the rough surface. The technique presented here is highly efficient in terms of computational memory, time, and versatility. Numerical simulations of two typical models are carried out to validate the method.
Numerical methods for solving the Boltzmann equation (a review)
NASA Technical Reports Server (NTRS)
Limar, Y. F.; Shakhov, Y. M.; Shidlovskiy, V. P.
1972-01-01
The methods are reviewed which are utilized in principal attempts to obtain the numerical solution or modeling of the Boltzmann equation over a broad range of Knudsen numbers. The primary methods considered are the Monte Carlo and the discrete velocities methods. The conculsions drawn from the analysis include the following: (1) The Monte Carlo methods are not well suited in the area of small Knudsen numbers. (2) Among the Monte Carlo methods, the Bird method appears to be the most attractive, since it is more directly related to the Boltzmann equation. (3) The deterministic methods, which include the discrete ordinate technique, offer great possibilities but require exceedingly large computer times. (4) The use of approximating equations in combination with the discrete velocities method will possibly improve computation time and reduce the required memory volume.
An efficient method for inverse problems
NASA Technical Reports Server (NTRS)
Daripa, Prabir
1987-01-01
A new inverse method for aerodynamic design of subcritical airfoils is presented. The pressure distribution in this method can be prescribed in a natural way, i.e. as a function of arclength of the as yet unknown body. This inverse problem is shown to be mathematically equivalent to solving a single nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the free stream Mach number M(sub x) and the upstream flow direction theta(sub x). The existence of a solution for any given pressure distribution is discussed. The method is easy to implement and extremely efficient. We present a series of results for which comparisons are made with the known airfoils.
Neonatal thyroid screening: methods-efficiency-failures.
Yordam, N; Ozon, A
2003-12-01
Newborn screening for congenital hypothyroidism (CH) is one of the major achievements of preventive medicine, as the condition occurs frequently (1/4000 newborns) and results in brain damage if not detected and treated in the first few days of life. Measurement of T4 and/or TSH in dried blood spots collected on the second through fifth days of life are the most widely used methods in screening programs for CH currently. Some children with the disease may be missd in any screening program, however, owing to factors related to the disease itself and the methods employed in its detection, as well as factors ascribed to the element of human error, ie screening errors. The methods employed in newborn screening programs for CH, their efficiency in disease detecetion, and biological factors as well as screening errors leading to missed cases are discussed.
Feng, S; Ng, C W W; Leung, A K; Liu, H W
2017-10-01
Microbial aerobic methane oxidation in unsaturated landfill cover involves coupled water, gas and heat reactive transfer. The coupled process is complex and its influence on methane oxidation efficiency is not clear, especially in steep covers where spatial variations of water, gas and heat are significant. In this study, two-dimensional finite element numerical simulations were carried out to evaluate the performance of unsaturated sloping cover. The numerical model was calibrated using a set of flume model test data, and was then subsequently used for parametric study. A new method that considers transient changes of methane concentration during the estimation of the methane oxidation efficiency was proposed and compared against existing methods. It was found that a steeper cover had a lower oxidation efficiency due to enhanced downslope water flow, during which desaturation of soil promoted gas transport and hence landfill gas emission. This effect was magnified as the cover angle and landfill gas generation rate at the bottom of the cover increased. Assuming the steady-state methane concentration in a cover would result in a non-conservative overestimation of oxidation efficiency, especially when a steep cover was subjected to rainfall infiltration. By considering the transient methane concentration, the newly-modified method can give a more accurate oxidation efficiency. Copyright © 2017. Published by Elsevier Ltd.
Numerical Polynomial Homotopy Continuation Method and String Vacua
Mehta, Dhagash
2011-01-01
Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less
A Numerical Method for Incompressible Flow with Heat Transfer
NASA Technical Reports Server (NTRS)
Sa, Jong-Youb; Kwak, Dochan
1997-01-01
A numerical method for the convective heat transfer problem is developed for low speed flow at mild temperatures. A simplified energy equation is added to the incompressible Navier-Stokes formulation by using Boussinesq approximation to account for the buoyancy force. A pseudocompressibility method is used to solve the resulting set of equations for steady-state solutions in conjunction with an approximate factorization scheme. A Neumann-type pressure boundary condition is devised to account for the interaction between pressure and temperature terms, especially near a heated or cooled solid boundary. It is shown that the present method is capable of predicting the temperature field in an incompressible flow.
Numerical Method and Analysis of Consistency for Electrodiffusion Problem
NASA Astrophysics Data System (ADS)
Filipek, R.; Szyszkiewicz, K.; Danielewski, M.; Lewenstam, A.
2007-12-01
Numerical procedure based on method of lines for time-dependent electrodiffusion transport is developed. Finite difference space discretization with suitably selected weights based on a non-uniform grid is applied. Consistency of this method and the method put forward by Brumleve and Buck are analyzed and compared. The resulting stiff system of ODEs is effectively solved using the Radau IIa integrator. The applications to selected electrochemical systems: liquid junction, bi-ionic case and fused salts have been tested. Results for ion-selective electrodes are demonstrated.
Projected discrete ordinates methods for numerical transport problems
Larsen, E.W.
1985-01-01
A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.
Vectorization on the star computer of several numerical methods for a fluid flow problem
NASA Technical Reports Server (NTRS)
Lambiotte, J. J., Jr.; Howser, L. M.
1974-01-01
A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.
Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly
2016-01-01
This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.
Efficient Numerical Methods for Evolution Partial Differential Equations
1989-09-30
public lease; distribution mlim ed.-.... 13. ABSTRACT (Maxmum 200 woard Generalized Korteweg - de Vries equation (GKdV). This equation is written as...McKinney. On Optimal high-order in time approxiniations.for the Korteweg -de Vries equation ..To appear in Math. Comp.. 3. J.L. Bona, V.A. Dougalis...O.Karakashian and W. Mckinney, Conservative high-order schemes for the Generalized Korteweg -de Vries equation . In preparation. 4. G. D. Akrivis, V.A
Fast and stable numerical method for neuronal modelling
NASA Astrophysics Data System (ADS)
Hashemi, Soheil; Abdolali, Ali
2016-11-01
Excitable cell modelling is of a prime interest in predicting and targeting neural activity. Two main limits in solving related equations are speed and stability of numerical method. Since there is a tradeoff between accuracy and speed, most previously presented methods for solving partial differential equations (PDE) are focused on one side. More speed means more accurate simulations and therefore better device designing. By considering the variables in finite differenced equation in proper time and calculating the unknowns in the specific sequence, a fast, stable and accurate method is introduced in this paper for solving neural partial differential equations. Propagation of action potential in giant axon is studied by proposed method and traditional methods. Speed, consistency and stability of the methods are compared and discussed. The proposed method is as fast as forward methods and as stable as backward methods. Forward methods are known as fastest methods and backward methods are stable in any circumstances. Complex structures can be simulated by proposed method due to speed and stability of the method.
NASA Astrophysics Data System (ADS)
Lathuilière, Cyril; Baraille, Rémy; Le Boyer, Arnaud
2015-04-01
The French navy hydrographic service uses a modified version of the Hybrid coordinate ocean model (HYCOM) for operational oceanographic applications. In the framework of the COMODO project, a series of test cases has been carried out to measure the numerical efficiency of the model. It addresses a wide panel of oceanic processes (baroclinic eddy, baroclinic jet, coastal upwelling, internal tides) and is useful to examine most of numerical schemes (advection schemes, time stepping, pressure gradient, …). The objectives of this study are first to assess the numerical performance of the present model to guide the modelers to make the suitable choices, and second to examine how the performances may be improved in the next years. We examine the sensitivity of the main choices for Hycom (2th or 4th order advection schemes, and viscosity values) in baroclinic eddy and baroclinic jet test cases. Both test cases are run using increasing resolution. The highest resolution provides a reference for studying the coarser resolutions. In the baroclinic vortex test case, the second order vector form scheme is well performing whereas the 4th order scheme appears to be more accurate in the baroclinic jet test case. This is probably due to the lack of fine scale energy in the baroclinic vortex test case allowing simulations with very tiny dissipation rates. We focus then on the sensitivity of the performance to vertical coordinate choices. The ability of Hycom to switch between isopycnal coordinate and quasi geopotential coordinate provides useful insights for example on the sensitivity of numerical diapycnal mixing to remapping scheme. This is particularly visible on the internal tide test case. The type of vertical coordinate is also important for potential vorticity structures. The shape of the baroclinic vortex is found to be different in geopotential and isopycnal coordinates. At coarse resolution, the potential vorticity structures seem to be better resolved in isopycnal
Automatic numerical integration methods for Feynman integrals through 3-loop
NASA Astrophysics Data System (ADS)
de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.
2015-05-01
We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.
NASA Technical Reports Server (NTRS)
Zeng, S.; Wesseling, P.
1993-01-01
The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.
Numerical methods for control optimization in linear systems
NASA Astrophysics Data System (ADS)
Tyatyushkin, A. I.
2015-05-01
Numerical methods are considered for solving optimal control problems in linear systems, namely, terminal control problems with control and phase constraints and time-optimal control problems. Several algorithms with various computer storage requirements are proposed for solving these problems. The algorithms are intended for finding an optimal control in linear systems having certain features, for example, when the reachable set of a system has flat faces.
Fast Numerical Methods for Stochastic Partial Differential Equations
2016-04-15
AFRL-AFOSR-VA-TR-2016-0156 Fast Numerical Methods for Stochastic Partial Differential Equations Hongmei Chi Florida Agricultural and Mechanical...University Tallahassee Final Report 04/15/2016 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research (AFOSR)/ RTA2...Arlington, Virginia 22203 Air Force Research Laboratory Air Force Materiel Command REPORT DOCUMENTATION PAGE Form ApprovedOMB No. 0704-0188 1. REPORT
NASA Astrophysics Data System (ADS)
Chen, Changxin; Zhang, Wei; Zhao, Bo; Zhang, Yafei
2009-12-01
An efficient semi-classical numerical modeling approach has been developed to simulate the coaxial Schottky-barrier carbon nanotube field-effect transistor (SB-CNTFET). In the modeling, the electrostatic potential of the CNT is obtained by self-consistently solving the analytic expression of CNT carrier distribution and the cylindrical Poisson equation, which significantly enhances the computational efficiency and simultaneously present a result in good agreement to that obtained from the non-equilibrium Green's function (NEGF) formalism based on the first principle. With this method, the effects of the CNT diameter, power supply voltage, thickness and dielectric constant of gate insulator on the device performance are investigated.
A high-efficiency aerothermoelastic analysis method
NASA Astrophysics Data System (ADS)
Wan, ZhiQiang; Wang, YaoKun; Liu, YunZhen; Yang, Chao
2014-06-01
In this paper, a high-efficiency aerothermoelastic analysis method based on unified hypersonic lifting surface theory is established. The method adopts a two-way coupling form that couples the structure, aerodynamic force, and aerodynamic thermo and heat conduction. The aerodynamic force is first calculated based on unified hypersonic lifting surface theory, and then the Eckert reference temperature method is used to solve the temperature field, where the transient heat conduction is solved using Fourier's law, and the modal method is used for the aeroelastic correction. Finally, flutter is analyzed based on the p-k method. The aerothermoelastic behavior of a typical hypersonic low-aspect ratio wing is then analyzed, and the results indicate the following: (1) the combined effects of the aerodynamic load and thermal load both deform the wing, which would increase if the flexibility, size, and flight time of the hypersonic aircraft increase; (2) the effect of heat accumulation should be noted, and therefore, the trajectory parameters should be considered in the design of hypersonic flight vehicles to avoid hazardous conditions, such as flutter.
Modeling collisional processes in plasmas using discontinuous numerical methods
NASA Astrophysics Data System (ADS)
Miller, Sean
Fluid-based plasma models are typically applied to parameter regimes where a local thermal equilibrium is assumed. The applicability of this regime is valid for many plasmas, however, it is limited to plasma dynamics dominated by collisional effects. This study attempts to extend the validity of the collisional fluid regime using an anisotropic 13-moment fluid model derived from the Pearson type-IV probability distribution. The model explicitly evolves the heat flux hyperbolically alongside the density, momentum, and energy in order to capture dynamics usually restricted to costly kinetic models. Each particle species is modeled individually and collectively coupled through electromagnetic and collision operators. To remove electromagnetic divergence errors inherent to numerical representations of Maxwell's equations, both hyperbolic and parabolic cleaning methods are presented. The plasma models are implemented using high-order finite volume and discontinuous Galerkin numerical methods designed for unstructured meshes. The unstructured code framework, numerical methods, and plasma models were developed in the University of Washington's WARPXM code for use on heterogeneous accelerated clusters.
Numerical methods in vehicle system dynamics: state of the art and current developments
NASA Astrophysics Data System (ADS)
Arnold, M.; Burgermeister, B.; Führer, C.; Hippmann, G.; Rill, G.
2011-07-01
Robust and efficient numerical methods are an essential prerequisite for the computer-based dynamical analysis of engineering systems. In vehicle system dynamics, the methods and software tools from multibody system dynamics provide the integration platform for the analysis, simulation and optimisation of the complex dynamical behaviour of vehicles and vehicle components and their interaction with hydraulic components, electronical devices and control structures. Based on the principles of classical mechanics, the modelling of vehicles and their components results in nonlinear systems of ordinary differential equations (ODEs) or differential-algebraic equations (DAEs) of moderate dimension that describe the dynamical behaviour in the frequency range required and with a level of detail being characteristic of vehicle system dynamics. Most practical problems in this field may be transformed to generic problems of numerical mathematics like systems of nonlinear equations in the (quasi-)static analysis and explicit ODEs or DAEs with a typical semi-explicit structure in the dynamical analysis. This transformation to mathematical standard problems allows to use sophisticated, freely available numerical software that is based on well approved numerical methods like the Newton-Raphson iteration for nonlinear equations or Runge-Kutta and linear multistep methods for ODE/DAE time integration. Substantial speed-ups of these numerical standard methods may be achieved exploiting some specific structure of the mathematical models in vehicle system dynamics. In the present paper, we follow this framework and start with some modelling aspects being relevant from the numerical viewpoint. The focus of the paper is on numerical methods for static and dynamic problems, including software issues and a discussion which method fits best for which class of problems. Adaptive components in state-of-the-art numerical software like stepsize and order control in time integration are
Efficient and robust methods for quantum tomography
NASA Astrophysics Data System (ADS)
Baldwin, Charles Heber
The development of large-scale platforms that implement quantum information processing protocols requires new methods for verification and validation of quantum behavior. Quantum tomography (QT) is the standard tool for diagnosing quantum states, process, and readout devices by providing complete information about each. However, QT is limited since it is expensive to not only implement experimentally, but also requires heavy classical post-processing of experimental data. In this dissertation, we introduce new methods for QT that are more efficient to implement and robust to noise and errors, thereby making QT a more widely practical tool for current quantum information experiments. The crucial detail that makes these new, efficient, and robust methods possible is prior information about the quantum system. This prior information is prompted by the goals of most experiments in quantum information. Most quantum information processing protocols require pure states, unitary processes, and rank-1 POVM operators. Therefore, most experiments are designed to operate near this ideal regime, and have been tested by other methods to verify this objective. We show that when this is the case, QT can be accomplished with significantly fewer resources, and produce a robust estimate of the state, process, or readout device in the presence of noise and errors. Moreover, the estimate is robust even if the state is not exactly pure, the process is not exactly unitary, or the POVM is not exactly rank-1. Such compelling methods are only made possible by the positivity constraint on quantum states, processes, and POVMs. This requirement is an inherent feature of quantum mechanics, but has powerful consequences to QT. Since QT is necessarily an experimental tool for diagnosing quantum systems, we discuss a test of these new methods in an experimental setting. The physical system is an ensemble of laser-cooled cesium atoms in the laboratory of Prof. Poul Jessen. The atoms are prepared in
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
NASA Astrophysics Data System (ADS)
Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.
2015-05-01
We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.
NASA Astrophysics Data System (ADS)
Vaughan, P. J.
2001-12-01
Multicomponent solute transport models require efficient computation of chemical speciation. Transport in soils should also consider cation exchange and dissolution/precipitation reactions. Several numerical techniques were programmed to provide simultaneous solution of a set of mole balance equations in order to compare efficiencies when solving the same problem. A non-simultaneous solution was also programmed using Picard iteration. This was the fastest method but true convergence was not obtained except when cation exchange was not included. Two simplex methods and a tensor (quadratic) method converged to the correct result. The tensor method was faster by a factor of 10 to 100 compared to either simplex method. These results suggest that, among these methods, the tensor method would be most appropriate for transport calculations.
An explicit mixed numerical method for mesoscale model
NASA Technical Reports Server (NTRS)
Hsu, H.-M.
1981-01-01
A mixed numerical method has been developed for mesoscale models. The technique consists of a forward difference scheme for time tendency terms, an upstream scheme for advective terms, and a central scheme for the other terms in a physical system. It is shown that the mixed method is conditionally stable and highly accurate for approximating the system of either shallow-water equations in one dimension or primitive equations in three dimensions. Since the technique is explicit and two time level, it conserves computer and programming resources.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
Lucas, D.S.
2004-10-03
This paper covers the basics of the implementation of the control volume method in the context of the Homogeneous Equilibrium Model (HEM)(T/H) code using the conservation equations of mass, momentum, and energy. This primer uses the advection equation as a template. The discussion will cover the basic equations of the control volume portion of the course in the primer, which includes the advection equation, numerical methods, along with the implementation of the various equations via FORTRAN into computer programs and the final result for a three equation HEM code and its validation.
New numerical method to study phase transitions and its applications
Lee, Jooyoung; Kosterlitz, J.M.
1991-11-01
We present a powerful method of identifying the nature of transitions by numerical simulation of finite systems. By studying the finite size scaling properties of free energy barrier between competing states, we can identify unambiguously a weak first order transition even when accessible system sizes are L/{xi} < 0.05 as in the five state Potts model in two dimensions. When studying a continuous phase transition we obtain quite accurate estimates of critical exponents by treating it as a field driven first order transition. The method has been successfully applied to various systems.
Integrated numerical methods for hypersonic aircraft cooling systems analysis
NASA Technical Reports Server (NTRS)
Petley, Dennis H.; Jones, Stuart C.; Dziedzic, William M.
1992-01-01
Numerical methods have been developed for the analysis of hypersonic aircraft cooling systems. A general purpose finite difference thermal analysis code is used to determine areas which must be cooled. Complex cooling networks of series and parallel flow can be analyzed using a finite difference computer program. Both internal fluid flow and heat transfer are analyzed, because increased heat flow causes a decrease in the flow of the coolant. The steady state solution is a successive point iterative method. The transient analysis uses implicit forward-backward differencing. Several examples of the use of the program in studies of hypersonic aircraft and rockets are provided.
Flexible, reconfigurable, power efficient transmitter and method
NASA Technical Reports Server (NTRS)
Bishop, James W. (Inventor); Zaki, Nazrul H. Mohd (Inventor); Newman, David Childress (Inventor); Bundick, Steven N. (Inventor)
2011-01-01
A flexible, reconfigurable, power efficient transmitter device and method is provided. In one embodiment, the method includes receiving outbound data and determining a mode of operation. When operating in a first mode the method may include modulation mapping the outbound data according a modulation scheme to provide first modulation mapped digital data, converting the first modulation mapped digital data to an analog signal that comprises an intermediate frequency (IF) analog signal, upconverting the IF analog signal to produce a first modulated radio frequency (RF) signal based on a local oscillator signal, amplifying the first RF modulated signal to produce a first RF output signal, and outputting the first RF output signal via an isolator. In a second mode of operation method may include modulation mapping the outbound data according a modulation scheme to provide second modulation mapped digital data, converting the second modulation mapped digital data to a first digital baseband signal, conditioning the first digital baseband signal to provide a first analog baseband signal, modulating one or more carriers with the first analog baseband signal to produce a second modulated RF signal based on a local oscillator signal, amplifying the second RF modulated signal to produce a second RF output signal, and outputting the second RF output signal via the isolator. The digital baseband signal may comprise an in-phase (I) digital baseband signal and a quadrature (Q) baseband signal.
NASA Astrophysics Data System (ADS)
Min, Xiaoyi
This thesis first presents the study of the interaction of electromagnetic waves with three-dimensional heterogeneous, dielectric, magnetic, and lossy bodies by surface integral equation modeling. Based on the equivalence principle, a set of coupled surface integral equations is formulated and then solved numerically by the method of moments. Triangular elements are used to model the interfaces of the heterogeneous body, and vector basis functions are defined to expand the unknown current in the formulation. The validity of this formulation is verified by applying it to concentric spheres for which an exact solution exists. The potential applications of this formulation to a partially coated sphere and a homogeneous human body are discussed. Next, this thesis also introduces an efficient new set of integral equations for treating the scattering problem of a perfectly conducting body coated with a thin magnetically lossy layer. These electric field integral equations and magnetic field integral equations are numerically solved by the method of moments (MoM). To validate the derived integral equations, an alternative method to solve the scattering problem of an infinite circular cylinder coated with a thin magnetic lossy layer has also been developed, based on the eigenmode expansion. Results for the radar cross section and current densities via the MoM and the eigenmode expansion method are compared. The agreement is excellent. The finite difference time domain method is subsequently implemented to solve a metallic object coated with a magnetic thin layer and numerical results are compared with that by the MoM. Finally, this thesis presents an application of the finite-difference time-domain approach to the problem of electromagnetic receiving and scattering by a cavity -backed antenna situated on an infinite conducting plane. This application involves modifications of Yee's model, which applies the difference approximations of field derivatives to differential
NASA Astrophysics Data System (ADS)
Simmel, Martin; Trautmann, Thomas; Tetzlaff, Gerd
The Linear Discrete Method is used to solve the Stochastic Collection Equation (SCE) numerically. Comparisons are made with the Method of Moments, the Berry-Reinhardt model and the Linear Flux Method. Simulations for all numerical methods are shown for the kernel after Golovin [Bull. Acad. Sci. USSR, Geophys. Ser. 5 (1963) 783] and are compared with the analytical solution for two different initial distributions. BRM seems to give the best results and LDM gives good results, too. LFM overestimates the drop growth for the right tail of the distribution and MOM does the same but over the entire drop spectrum. For the hydrodynamic kernel after Long [J. Atmos. Sci. 31 (1974) 1040], simulations are presented using the four numerical methods (LDM, MOM, BRM, LFM). Especially for high resolutions, the solutions of LDM and LFM approach each other very closely. In addition, LDM simulations using the hydrodynamic kernel after Böhm [Atmos. Res. 52 (1999) 167] are presented, which show good correspondence between low- and high-resolution results. Computation efficiency is especially important when numerical schemes are to be included in larger models. Therefore, the computation times of the four methods were compared for the cases with the Golovin kernel. The result is that LDM is the fastest method by far, needing less time than other methods by a factor of 2-7, depending on the case and the bin resolution. For high resolutions, MOM is the slowest. For the lowest resolution, this holds for LFM.
A Numerical Method for Synthesizing Atmospheric Temperature and Humidity Profiles.
NASA Astrophysics Data System (ADS)
Tatarskaia, Maia S.; Lataitis, Richard J.; Boba Stankov, B.; Tatarskii, Viatcheslav V.
1998-07-01
A numerical technique is described for synthesizing realistic atmospheric temperature and humidity profiles. The method uses an ensemble of radiosonde measurements collected at a site of interest. Erroneous profiles are removed by comparing their likelihood with prevailing meteorological conditions. The remaining profiles are decomposed using the method of empirical orthogonal functions. The corresponding eigenprofiles and the statistics of the expansion coefficients are used to numerically generate synthetic profiles that obey the same statistics (i.e., have the same mean, variability, and vertical correlation) as the initial dataset. The technique was applied to a set of approximately 1000 temperature and humidity soundings made in Denver, Colorado, during the winter months of 1991-95. This dataset was divided into four cloud classification categories and daytime and nighttime launches to better characterize typical profiles for the eight cases considered. It was found that 97% of the variance in the soundings could be accounted for by using only five eigenprofiles in the reconstructions. Ensembles of numerically generated profiles can be used to test the accuracy of various retrieval algorithms under controlled conditions not usually available in practice.
A three-scale offline-online numerical method for fluid flow in porous media
NASA Astrophysics Data System (ADS)
Abdulle, Assyr; Budáč, Ondrej; Imboden, Antoine
2017-05-01
A new multiscale method combined with model order reduction is proposed for flow problems in a three-scale porous material. We derive an effective three-scale model that couples a macroscopic Darcy equation, a mesoscopic Stokes-Brinkman equation, and a microscopic Stokes equation. A corresponding three-scale numerical method is then derived using the finite element discretization with numerical quadrature, where the macroscopic and mesoscopic permeability is upscaled at quadrature points from mesoscopic and microscopic problems, respectively. The computational cost of solving numerous mesoscopic and microscopic flow problems is further reduced by applying a Petrov-Galerkin reduced basis method at the mesoscopic and microscopic scales. As there is no natural way to obtain an affine decomposition of the mesoscopic problems, which is instrumental for the efficiency of the model order reduction, we derive a mesoscopic solver that makes use of empirical interpolation techniques. A priori and a posteriori error estimates are derived for the new method that is also tested numerically to corroborate the theoretical convergence rates and illustrate its efficiency.
Ryabinkin, Ilya G; Nagesh, Jayashree; Izmaylov, Artur F
2015-11-05
We have developed a numerical differentiation scheme that eliminates evaluation of overlap determinants in calculating the time-derivative nonadiabatic couplings (TDNACs). Evaluation of these determinants was the bottleneck in previous implementations of mixed quantum-classical methods using numerical differentiation of electronic wave functions in the Slater determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals and then to apply a finite-difference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive several-order-of-magnitude speedups of the TDNAC calculation step for midsize molecules.
Numerical integration of population models satisfying conservation laws: NSFD methods.
Mickens, Ronald E
2007-10-01
Population models arising in ecology, epidemiology and mathematical biology may involve a conservation law, i.e. the total population is constant. In addition to these cases, other situations may occur for which the total population, asymptotically in time, approach a constant value. Since it is rarely the situation that the equations of motion can be analytically solved to obtain exact solutions, it follows that numerical techniques are needed to provide solutions. However, numerical procedures are only valid if they can reproduce fundamental properties of the differential equations modeling the phenomena of interest. We show that for population models, involving a dynamical conservation law the use of nonstandard finite difference (NSFD) methods allows the construction of discretization schemes such that they are dynamically consistent (DC) with the original differential equations. The paper will briefly discuss the NSFD methodology, the concept of DC, and illustrate their application to specific problems for population models.
Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems
Hykes, J. M.; Ferrer, R. M.
2013-07-01
The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is {sup 98}Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)
Numerical renormalization group method for quantum impurity systems
NASA Astrophysics Data System (ADS)
Bulla, Ralf; Costi, Theo A.; Pruschke, Thomas
2008-04-01
In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.
[An efficient mutational method for photosynthetic bacteria].
Lin, J Q; Xiao, M; Long, M T; Han, B; Quian, W; Du, J
2006-01-01
The pigment and auxotrophic mutants of Rhodobacter sphaeroides Y6 were obtained by treatment with ethyl methanesulfonate (EMS) followed by lithium chloride (LiCI). Treatment with 0.081 M EPS and subsequent treatment with 0.071 M LiCI resulted in 12% higher frequency of pigment mutations than application of 0.081 M EMS alone; the frequency of auxotrophic mutations increased 2.5-fold when treatment with lithium chloride was applied. A blue shift 10 nm was recorded in the absorption spectrum of carotenoids form YM5-3 green mutant; considerable accumulation of neurosporine was revealed by HPLC and mass spectrometry. The method is efficient for isolating mutants of photosynthetic bacteria.
An Efficient Method for Computing All Reducts
NASA Astrophysics Data System (ADS)
Bao, Yongguang; Du, Xiaoyong; Deng, Mingrong; Ishii, Naohiro
In the process of data mining of decision table using Rough Sets methodology, the main computational effort is associated with the determination of the reducts. Computing all reducts is a combinatorial NP-hard computational problem. Therefore the only way to achieve its faster execution is by providing an algorithm, with a better constant factor, which may solve this problem in reasonable time for real-life data sets. The purpose of this presentation is to propose two new efficient algorithms to compute reducts in information systems. The proposed algorithms are based on the proposition of reduct and the relation between the reduct and discernibility matrix. Experiments have been conducted on some real world domains in execution time. The results show it improves the execution time when compared with the other methods. In real application, we can combine the two proposed algorithms.
NASA Astrophysics Data System (ADS)
Tang, Xiaojun
2016-04-01
The main purpose of this work is to provide multiple-interval integral Gegenbauer pseudospectral methods for solving optimal control problems. The latest developed single-interval integral Gauss/(flipped Radau) pseudospectral methods can be viewed as special cases of the proposed methods. We present an exact and efficient approach to compute the mesh pseudospectral integration matrices for the Gegenbauer-Gauss and flipped Gegenbauer-Gauss-Radau points. Numerical results on benchmark optimal control problems confirm the ability of the proposed methods to obtain highly accurate solutions.
A numerical study of 2D detonation waves with adaptive finite volume methods on unstructured grids
NASA Astrophysics Data System (ADS)
Hu, Guanghui
2017-02-01
In this paper, a framework of adaptive finite volume solutions for the reactive Euler equations on unstructured grids is proposed. The main ingredients of the algorithm include a second order total variation diminishing Runge-Kutta method for temporal discretization, and the finite volume method with piecewise linear solution reconstruction of the conservative variables for the spatial discretization in which the least square method is employed for the reconstruction, and weighted essentially nonoscillatory strategy is used to restrain the potential numerical oscillation. To resolve the high demanding on the computational resources due to the stiffness of the system caused by the reaction term and the shock structure in the solutions, the h-adaptive method is introduced. OpenMP parallelization of the algorithm is also adopted to further improve the efficiency of the implementation. Several one and two dimensional benchmark tests on the ZND model are studied in detail, and numerical results successfully show the effectiveness of the proposed method.
Novel Parallel Numerical Methods for Radiation& Neutron Transport
Brown, P N
2001-03-06
In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both.
Numerical methods and measurement systems for nonlinear magnetic circuits (abstract)
NASA Astrophysics Data System (ADS)
Heitbrink, Axel; Dieter Storzer, Hans; Beyer, Adalbert
1994-05-01
In the past years an increasing interest in calculation methods of circuits containing magnetic nonlinearities could be observed. For this reason a new method was developed which makes it possible to calculate the steady state solution of such circuits by the help of an interactive cad program. The modular concept of the software allows to separate the circuit into nonlinear and linear subnetworks. When regarding nonlinear magnetic elements one can choose between several numerical models for the description of the hysteresis loops or an inbuilt realtime measurement system can be activated to get the dynamic hysteresis loops. The measurement system is also helpful for the parameter extraction for the numerical hysteresis models. A modified harmonic-balance algorithm and a set of iteration schemes is used for solving the network function. The combination of the realtime measurement system and modern numerical methods brings up a productive total concept for the exact calculation of nonlinear magnetic circuits. A special application class will be discussed which is given by earth-leakage circuit breakers. These networks contain a toroidal high permeable NiFe alloy and a relay as nonlinear elements (cells) and some resistors, inductors, and capacitors as linear elements. As input dc signals at the primary winding of the core any curveform must be regarded, especially 135° phasecutted pulses. These signals with extreme higher frequency components make it impossible to use numerical models for the description of the nonlinear behavior of the core and the relays. So for both elements the realtime measurement system must be used during the iteration process. During each iteration step the actual magnetization current is sent to the measurement system, which measures the dynamic hysteresis loop at the probe. These values flow back into the iteration process. A graphic subsystem allows a look at the waveforms of all voltages and current when the iterations take place. One
Efficient sensitivity analysis method for chaotic dynamical systems
Liao, Haitao
2016-05-15
The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results in an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.
Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems
2014-10-13
Triangle Park, NC 27709-2211 Transport, Electromagnetic Phenomena, nano-electronics, ion channels , layered media REPORT DOCUMENTATION PAGE 11. SPONSOR...DFT for quantum systems. (3) numerical methods for computation of electrostatics in ion- channel transport, (4) a new parallel solver for elliptic...10.00 Received Paper 9.00 Huimin Lin, Huazhong Tang, Wei Cai. Accuracy and efficiency in computing electrostatic potentialfor an ion channel model in
NASA Astrophysics Data System (ADS)
Dadashzadeh, N.; Duzgun, H. S. B.; Yesiloglu-Gultekin, N.
2017-08-01
While advanced numerical techniques in slope stability analysis are successfully used in deterministic studies, they have so far found limited use in probabilistic analyses due to their high computation cost. The first-order reliability method (FORM) is one of the most efficient probabilistic techniques to perform probabilistic stability analysis by considering the associated uncertainties in the analysis parameters. However, it is not possible to directly use FORM in numerical slope stability evaluations as it requires definition of a limit state performance function. In this study, an integrated methodology for probabilistic numerical modeling of rock slope stability is proposed. The methodology is based on response surface method, where FORM is used to develop an explicit performance function from the results of numerical simulations. The implementation of the proposed methodology is performed by considering a large potential rock wedge in Sumela Monastery, Turkey. The accuracy of the developed performance function to truly represent the limit state surface is evaluated by monitoring the slope behavior. The calculated probability of failure is compared with Monte Carlo simulation (MCS) method. The proposed methodology is found to be 72% more efficient than MCS, while the accuracy is decreased with an error of 24%.
Efficient Fully Implicit Time Integration Methods for Modeling Cardiac Dynamics
Rose, Donald J.; Henriquez, Craig S.
2013-01-01
Implicit methods are well known to have greater stability than explicit methods for stiff systems, but they often are not used in practice due to perceived computational complexity. This paper applies the Backward Euler method and a second-order one-step two-stage composite backward differentiation formula (C-BDF2) for the monodomain equations arising from mathematically modeling the electrical activity of the heart. The C-BDF2 scheme is an L-stable implicit time integration method and easily implementable. It uses the simplest Forward Euler and Backward Euler methods as fundamental building blocks. The nonlinear system resulting from application of the Backward Euler method for the monodomain equations is solved for the first time by a nonlinear elimination method, which eliminates local and non-symmetric components by using a Jacobian-free Newton solver, called Newton-Krylov solver. Unlike other fully implicit methods proposed for the monodomain equations in the literature, the Jacobian of the global system after the nonlinear elimination has much smaller size, is symmetric and possibly positive definite, which can be solved efficiently by standard optimal solvers. Numerical results are presented demonstrating that the C-BDF2 scheme can yield accurate results with less CPU times than explicit methods for both a single patch and spatially extended domains. PMID:19126449
Comparison of four stable numerical methods for Abel's integral equation
NASA Technical Reports Server (NTRS)
Murio, Diego A.; Mejia, Carlos E.
1991-01-01
The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.
Numerical Analysis of a Finite Element/Volume Penalty Method
NASA Astrophysics Data System (ADS)
Maury, Bertrand
The penalty method makes it possible to incorporate a large class of constraints in general purpose Finite Element solvers like freeFEM++. We present here some contributions to the numerical analysis of this method. We propose an abstract framework for this approach, together with some general error estimates based on the discretization parameter ɛ and the space discretization parameter h. As this work is motivated by the possibility to handle constraints like rigid motion for fluid-particle flows, we shall pay a special attention to a model problem of this kind, where the constraint is prescribed over a subdomain. We show how the abstract estimate can be applied to this situation, in the case where a non-body-fitted mesh is used. In addition, we describe how this method provides an approximation of the Lagrange multiplier associated to the constraint.
Efficient Method for Optimizing Placement of Sensors
NASA Technical Reports Server (NTRS)
Fijany, Amir; Vatan, Farrokh
2009-01-01
A computationally efficient method has been developed to enable optimization of the placement of sensors for the purpose of diagnosis of a complex engineering system (e.g., an aircraft or spacecraft). The method can be used both in (1) designing a sensor system in which the number and positions of sensors are initially not known and must be determined and (2) adding sensors to a pre-existing system to increase the diagnostic capability. The optimal-sensor-placement problem can be summarized as involving the following concepts, issues, and subproblems: a) Degree of Diagnosability - This is a concept for characterizing the set of faults that can be discriminated by use of a given set of sensors. b) Minimal Sensor Set - The idea is one of finding a minimal set of sensors that guarantees a specific degree of diagnosability. c) Minimal-Cost Sensors - In a case in which different sensors are assigned with different costs, it is desired to choose the least costly set of sensors that affords a specific degree of diagnosability.
Numerical methods for high-dimensional probability density function equations
Cho, H.; Venturi, D.; Karniadakis, G.E.
2016-01-15
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Numerical methods for high-dimensional probability density function equations
NASA Astrophysics Data System (ADS)
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016-01-01
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Calculation of free-fall trajectories using numerical optimization methods.
NASA Technical Reports Server (NTRS)
Hull, D. G.; Fowler, W. T.; Gottlieb, R. G.
1972-01-01
An important problem in space flight is the calculation of trajectories for nonthrusting vehicles between fixed points in a given time. A new procedure based on Hamilton's principle for solving such two-point boundary-value problems is presented. It employs numerical optimization methods to perform the extremization required by Hamilton's principle. This procedure is applied to the calculation of an Earth-Moon trajectory. The results show that the initial guesses required to obtain an iteration procedure which converges are not critical and that convergence can be obtained to any predetermined degree of accuracy.
Numerical Methods for Computing Turbulence-Induced Noise
2005-12-16
consider the finite dimensional subspace Vhl C Vh . Let vhi -= phlu be the optimal representation of u in Vhl and phi : V+_+ Vhl be the appropriate...mapping. We consider the following numerical method which is obtained by replacing h with hi in (2.4). Find uhl E Vhi , such that B(whi, uhl) + M(whUhl, f...the same functional form of the model that leads to the optimal solution on Vh, also leads to the optimal solution on Vhi . Thus, requiring uhl = vh
Simple numerical method for predicting steady compressible flows
NASA Technical Reports Server (NTRS)
Von Lavante, E.; Melson, N. Duane
1987-01-01
The present numerical method for the solution of the isenthalpic form of the governing equations for compressible viscous and inviscid flows has its basis in the concept of flux vector splitting in its implicit form, and has been tested in the cases of several difficult viscous and inviscid configurations. An acceleration of time-marching to steady state is accomplished by implementing a multigrid procedure which effectively increases the convergence rate. The steady state results obtained are largely of good quality, and required only short computational times.
Calculation of free-fall trajectories using numerical optimization methods.
NASA Technical Reports Server (NTRS)
Hull, D. G.; Fowler, W. T.; Gottlieb, R. G.
1972-01-01
An important problem in space flight is the calculation of trajectories for nonthrusting vehicles between fixed points in a given time. A new procedure based on Hamilton's principle for solving such two-point boundary-value problems is presented. It employs numerical optimization methods to perform the extremization required by Hamilton's principle. This procedure is applied to the calculation of an Earth-Moon trajectory. The results show that the initial guesses required to obtain an iteration procedure which converges are not critical and that convergence can be obtained to any predetermined degree of accuracy.
Numerical prediction of interfacial instabilities: Sharp interface method (SIM)
NASA Astrophysics Data System (ADS)
Nourgaliev, R. R.; Liou, M.-S.; Theofanous, T. G.
2008-04-01
We introduce a sharp interface method (SIM) for the direct numerical simulation of unstable fluid-fluid interfaces. The method is based on the level set approach and the structured adaptive mesh refinement technology, endowed with a corridor of irregular, cut-cell grids that resolve the interfacial region to third-order spatial accuracy. Key in that regard are avoidance of numerical mixing, and a least-squares interpolation method that is supported by irregular datasets distinctly on each side of the interface. Results on test problems show our method to be free of the spurious current problem of the continuous surface force method and to converge, on grid refinement, at near-theoretical rates. Simulations of unstable Rayleigh-Taylor and viscous Kelvin-Helmholtz flows are found to converge at near-theoretical rates to the exact results over a wide range of conditions. Further, we show predictions of neutral-stability maps of the viscous Kelvin-Helmholtz flows (Yih instability), as well as self-selection of the most unstable wave-number in multimode simulations of Rayleigh-Taylor instability. All these results were obtained with a simple seeding of random infinitesimal disturbances of interface-shape, as opposed to seeding by a complete eigenmode. For other than elementary flows the latter would normally not be available, and extremely difficult to obtain if at all. Sample comparisons with our code adapted to mimic typical diffuse interface treatments were not satisfactory for shear-dominated flows. On the other hand the sharp dynamics of our method would appear to be compatible and possibly advantageous to any interfacial flow algorithm in which the interface is represented as a discrete Heaviside function.
NASA Astrophysics Data System (ADS)
Mehrling, T. J.; Robson, R. E.; Erbe, J.-H.; Osterhoff, J.
2016-09-01
This paper introduces a semi-analytic numerical approach (SANA) for the rapid computation of the transverse emittance of beams with finite energy spread in plasma wakefield accelerators in the blowout regime. The SANA method is used to model the beam emittance evolution when injected into and extracted from realistic plasma profiles. Results are compared to particle-in-cell simulations, establishing the accuracy and efficiency of the procedure. In addition, it is demonstrated that the tapering of vacuum-to-plasma and plasma-to-vacuum transitions is a viable method for the mitigation of emittance growth of beams during their injection and extraction from and into plasma cells.
Liu, Li; Lai, Choi-Hong; Zhou, Shao-Dan; Xie, Fen; Rui, Lu
2011-04-01
In order to predict variations of drug concentration during a given period of time, numerical solutions of pharmacokinetic models need to be obtained efficiently. Analytical solutions of linear pharmacokinetic models are usually obtained using the Laplace transform and inverse Laplace tables. The derivations of solutions to complex nonlinear models are tedious, and such solution process may be difficult to implement as a robust software code. For nonlinear models, the fourth-order Runge-Kutta (RK4) is the most classical numerical method in obtaining approximate numerical solutions, which is impossible to be implemented in distributed computing environments without much modification. The reason is that numerical solutions obtained by using RK4 can only be computed in sequential time steps. In this paper, time-domain decomposition methods are adapted for nonlinear pharmacokinetic models. The numerical Inverse Laplace method for PharmacoKinetic models (ILPK) is implemented to solve pharmacokinetic models with iterative inverse Laplace transform in each time interval. The distributed ILPK algorithm, which is based on a two-level time-domain decomposition concept, is proposed to improve its efficiency. Solutions on the coarser temporal mesh at the top level are obtained one by one, and then those on the finer temporal mesh at the bottom level are calculated concurrently by using those initial solutions that have been obtained at the top level decomposition. Accuracy and efficiency of the proposed algorithm and its distributed equivalent are investigated by using several test models. Results indicate that the ILPK algorithm and its distributed equivalent are good candidates for both linear and nonlinear pharmacokinetic models.
Efficient algorithm for level set method preserving distance function.
Estellers, Virginia; Zosso, Dominique; Lai, Rongjie; Osher, Stanley; Thiran, Jean-Philippe; Bresson, Xavier
2012-12-01
The level set method is a popular technique for tracking moving interfaces in several disciplines, including computer vision and fluid dynamics. However, despite its high flexibility, the original level set method is limited by two important numerical issues. First, the level set method does not implicitly preserve the level set function as a distance function, which is necessary to estimate accurately geometric features, s.a. the curvature or the contour normal. Second, the level set algorithm is slow because the time step is limited by the standard Courant-Friedrichs-Lewy (CFL) condition, which is also essential to the numerical stability of the iterative scheme. Recent advances with graph cut methods and continuous convex relaxation methods provide powerful alternatives to the level set method for image processing problems because they are fast, accurate, and guaranteed to find the global minimizer independently to the initialization. These recent techniques use binary functions to represent the contour rather than distance functions, which are usually considered for the level set method. However, the binary function cannot provide the distance information, which can be essential for some applications, s.a. the surface reconstruction problem from scattered points and the cortex segmentation problem in medical imaging. In this paper, we propose a fast algorithm to preserve distance functions in level set methods. Our algorithm is inspired by recent efficient l(1) optimization techniques, which will provide an efficient and easy to implement algorithm. It is interesting to note that our algorithm is not limited by the CFL condition and it naturally preserves the level set function as a distance function during the evolution, which avoids the classical re-distancing problem in level set methods. We apply the proposed algorithm to carry out image segmentation, where our methods prove to be 5-6 times faster than standard distance preserving level set techniques. We
Willis, Catherine; Rubin, Jacob
1987-01-01
In this paper we consider examples of chemistry-affected transport processes in porous media. A moving boundary problem which arises during transport with precipitation-dissolution reactions is solved by three different numerical methods. Two of these methods (one explicit and one implicit) are based on an integral formulation of mass balance and lead to an approximation of a weak solution. These methods are compared to a front-tracking scheme. Although the two approaches are conceptually different, the numerical solutions showed good agreement. As the ratio of dispersion to convection decreases, the methods based on the integral formulation become computationally more efficient. Specific reactions were modeled to examine the dependence of the system on the physical and chemical parameters.
Efficient parallel implicit methods for rotary-wing aerodynamics calculations
NASA Astrophysics Data System (ADS)
Wissink, Andrew M.
Euler/Navier-Stokes Computational Fluid Dynamics (CFD) methods are commonly used for prediction of the aerodynamics and aeroacoustics of modern rotary-wing aircraft. However, their widespread application to large complex problems is limited lack of adequate computing power. Parallel processing offers the potential for dramatic increases in computing power, but most conventional implicit solution methods are inefficient in parallel and new techniques must be adopted to realize its potential. This work proposes alternative implicit schemes for Euler/Navier-Stokes rotary-wing calculations which are robust and efficient in parallel. The first part of this work proposes an efficient parallelizable modification of the Lower Upper-Symmetric Gauss Seidel (LU-SGS) implicit operator used in the well-known Transonic Unsteady Rotor Navier Stokes (TURNS) code. The new hybrid LU-SGS scheme couples a point-relaxation approach of the Data Parallel-Lower Upper Relaxation (DP-LUR) algorithm for inter-processor communication with the Symmetric Gauss Seidel algorithm of LU-SGS for on-processor computations. With the modified operator, TURNS is implemented in parallel using Message Passing Interface (MPI) for communication. Numerical performance and parallel efficiency are evaluated on the IBM SP2 and Thinking Machines CM-5 multi-processors for a variety of steady-state and unsteady test cases. The hybrid LU-SGS scheme maintains the numerical performance of the original LU-SGS algorithm in all cases and shows a good degree of parallel efficiency. It experiences a higher degree of robustness than DP-LUR for third-order upwind solutions. The second part of this work examines use of Krylov subspace iterative solvers for the nonlinear CFD solutions. The hybrid LU-SGS scheme is used as a parallelizable preconditioner. Two iterative methods are tested, Generalized Minimum Residual (GMRES) and Orthogonal s-Step Generalized Conjugate Residual (OSGCR). The Newton method demonstrates good
A numerical method for the solution of the bidomain equations in cardiac tissue.
Keener, J. P.; Bogar, K.
1998-03-01
A numerical scheme for efficient integration of the bidomain model of action potential propagation in cardiac tissue is presented. The scheme is a mixed implicit-explicit scheme with no stability time step restrictions and requires that only linear systems of equations be solved at each time step. The method is faster than a fully explicit scheme and there is no increase in algorithmic complexity to use this method instead of a fully explicit method. The speedup factor depends on the timestep size, which can be set solely on the basis of the demands for accuracy. (c) 1998 American Institute of Physics.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
D. S. Lucas
2004-10-01
A graduate level course for Thermal Hydraulics (T/H) was taught through Idaho State University in the spring of 2004. A numerical approach was taken for the content of this course since the students were employed at the Idaho National Laboratory and had been users of T/H codes. The majority of the students had expressed an interest in learning about the Courant Limit, mass error, semi-implicit and implicit numerical integration schemes in the context of a computer code. Since no introductory text was found the author developed notes taught from his own research and courses taught for Westinghouse on the subject. The course started with a primer on control volume methods and the construction of a Homogeneous Equilibrium Model (HEM) (T/H) code. The primer was valuable for giving the students the basics behind such codes and their evolution to more complex codes for Thermal Hydraulics and Computational Fluid Dynamics (CFD). The course covered additional material including the Finite Element Method and non-equilibrium (T/H). The control volume primer and the construction of a three-equation (mass, momentum and energy) HEM code are the subject of this paper . The Fortran version of the code covered in this paper is elementary compared to its descendants. The steam tables used are less accurate than the available commercial version written in C Coupled to a Graphical User Interface (GUI). The Fortran version and input files can be downloaded at www.microfusionlab.com.
Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
NASA Astrophysics Data System (ADS)
Wu, Lei; White, Craig; Scanlon, Thomas J.; Reese, Jason M.; Zhang, Yonghao
2013-10-01
The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method [36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard-Jones, and rigid attracting potentials. The accuracy of the fast spectral method is checked by comparing our numerical solutions of the space-homogeneous Boltzmann equation with the exact Bobylev-Krook-Wu solutions for a gas of Maxwell molecules. It is found that the accuracy is improved by replacing the trapezoidal rule with Gauss-Legendre quadrature in the calculation of the kernel mode, and the conservation of momentum and energy are ensured by the Lagrangian multiplier method without loss of spectral accuracy. The relax-to-equilibrium processes of different collision kernels with the same value of shear viscosity are then compared; the numerical results indicate that different forms of the collision kernels can be used as long as the shear viscosity (not only the value, but also its temperature dependence) is recovered. An iteration scheme is employed to obtain stationary solutions of the space-inhomogeneous Boltzmann equation, where the numerical errors decay exponentially. Four classical benchmarking problems are investigated: the normal shock wave, and the planar Fourier/Couette/force-driven Poiseuille flows. For normal shock waves, our numerical results are compared with a finite difference solution of the Boltzmann equation for hard sphere molecules, experimental data, and molecular dynamics simulation of argon using the realistic Lennard-Jones potential. For planar Fourier/Couette/force-driven Poiseuille flows, our results are compared with the direct simulation Monte Carlo method. Excellent agreements are observed in all test cases
NASA Astrophysics Data System (ADS)
Muthuvalu, Mohana Sundaram; Aruchunan, Elayaraja; Akhir, Mohd Kamalrulzaman Md; Sulaiman, Jumat; Karim, Samsul Ariffin Abdul
2014-10-01
In this paper, application of the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is extended by solving second order composite closed Newton-Cotes quadrature (2-CCNC) system. The performance of HSSOR method in solving 2-CCNC system is comparatively studied by their application on linear Fredholm integral equations of the second kind. The derivation and implementation of the method are discussed. In addition, numerical results by solving two test problems are included and compared with the standard Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) methods. Numerical results demonstrate that HSSOR method is an efficient method among the tested methods.
Numerical modeling of spray combustion with an advanced VOF method
NASA Technical Reports Server (NTRS)
Chen, Yen-Sen; Shang, Huan-Min; Shih, Ming-Hsin; Liaw, Paul
1995-01-01
This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.
NASA Astrophysics Data System (ADS)
Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.
2010-10-01
Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.
Liu, Haofei; Sun, Wei
2016-01-01
In this study, we evaluated computational efficiency of finite element (FE) simulations when a numerical approximation method was used to obtain the tangent moduli. A fiber-reinforced hyperelastic material model for nearly incompressible soft tissues was implemented for 3D solid elements using both the approximation method and the closed-form analytical method, and validated by comparing the components of the tangent modulus tensor (also referred to as the material Jacobian) between the two methods. The computational efficiency of the approximation method was evaluated with different perturbation parameters and approximation schemes, and quantified by the number of iteration steps and CPU time required to complete these simulations. From the simulation results, it can be seen that the overall accuracy of the approximation method is improved by adopting the central difference approximation scheme compared to the forward Euler approximation scheme. For small-scale simulations with about 10,000 DOFs, the approximation schemes could reduce the CPU time substantially compared to the closed-form solution, due to the fact that fewer calculation steps are needed at each integration point. However, for a large-scale simulation with about 300,000 DOFs, the advantages of the approximation schemes diminish because the factorization of the stiffness matrix will dominate the solution time. Overall, as it is material model independent, the approximation method simplifies the FE implementation of a complex constitutive model with comparable accuracy and computational efficiency to the closed-form solution, which makes it attractive in FE simulations with complex material models.
Numerical Methods and Simulations of Complex Multiphase Flows
NASA Astrophysics Data System (ADS)
Brady, Peter
Multiphase flows are an important part of many natural and technological phenomena such as ocean-air coupling (which is important for climate modeling) and the atomization of liquid fuel jets in combustion engines. The unique challenges of multiphase flow often make analytical solutions to the governing equations impossible and experimental investigations very difficult. Thus, high-fidelity numerical simulations can play a pivotal role in understanding these systems. This dissertation describes numerical methods developed for complex multiphase flows and the simulations performed using these methods. First, the issue of multiphase code verification is addressed. Code verification answers the question "Is this code solving the equations correctly?" The method of manufactured solutions (MMS) is a procedure for generating exact benchmark solutions which can test the most general capabilities of a code. The chief obstacle to applying MMS to multiphase flow lies in the discontinuous nature of the material properties at the interface. An extension of the MMS procedure to multiphase flow is presented, using an adaptive marching tetrahedron style algorithm to compute the source terms near the interface. Guidelines for the use of the MMS to help locate coding mistakes are also detailed. Three multiphase systems are then investigated: (1) the thermocapillary motion of three-dimensional and axisymmetric drops in a confined apparatus, (2) the flow of two immiscible fluids completely filling an enclosed cylinder and driven by the rotation of the bottom endwall, and (3) the atomization of a single drop subjected to a high shear turbulent flow. The systems are simulated numerically by solving the full multiphase Navier-Stokes equations coupled to the various equations of state and a level set interface tracking scheme based on the refined level set grid method. The codes have been parallelized using MPI in order to take advantage of today's very large parallel computational
Efficient Numerical Modeling of Slow-Slip and Quasi-Dynamic Earthquake Ruptures
NASA Astrophysics Data System (ADS)
Bradley, A. M.; Segall, P.
2010-12-01
the nonlinear equations. For efficiency, we group fault cells by physical properties, perform only one sparse LU factorization per group, and efficiently update the LU factorization at each solve, yielding a method that is linear in the number of diffusion profile nodes. We parallelize the nonlinear solves to work on a shared-memory system using OpenMP. We approximate the elasticity matrix relating slip and stress by a hierarchical low-rank representation to speed up matrix-vector products. This presentation will describe our software and numerical methods, and simulation results that highlight our software's capabilities.
A computationally efficient spectral method for modeling core dynamics
NASA Astrophysics Data System (ADS)
Marti, P.; Calkins, M. A.; Julien, K.
2016-08-01
An efficient, spectral numerical method is presented for solving problems in a spherical shell geometry that employs spherical harmonics in the angular dimensions and Chebyshev polynomials in the radial direction. We exploit the three-term recurrence relation for Chebyshev polynomials that renders all matrices sparse in spectral space. This approach is significantly more efficient than the collocation approach and is generalizable to both the Galerkin and tau methodologies for enforcing boundary conditions. The sparsity of the matrices reduces the computational complexity of the linear solution of implicit-explicit time stepping schemes to O(N) operations, compared to O>(N2>) operations for a collocation method. The method is illustrated by considering several example problems of important dynamical processes in the Earth's liquid outer core. Results are presented from both fully nonlinear, time-dependent numerical simulations and eigenvalue problems arising from the investigation of the onset of convection and the inertial wave spectrum. We compare the explicit and implicit temporal discretization of the Coriolis force; the latter becomes computationally feasible given the sparsity of the differential operators. We find that implicit treatment of the Coriolis force allows for significantly larger time step sizes compared to explicit algorithms; for hydrodynamic and dynamo problems at an Ekman number of E=10-5, time step sizes can be increased by a factor of 3 to 16 times that of the explicit algorithm, depending on the order of the time stepping scheme. The implementation with explicit Coriolis force scales well to at least 2048 cores, while the implicit implementation scales to 512 cores.
An unconditionally stable method for numerically solving solar sail spacecraft equations of motion
NASA Astrophysics Data System (ADS)
Karwas, Alex
Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach
Numerical methods for assessment of the ship's pollutant emissions
NASA Astrophysics Data System (ADS)
Jenaru, A.; Acomi, N.
2016-08-01
The maritime transportation sector constitutes a source of atmospheric pollution. To avoid or minimize ships pollutant emissions the first step is to assess them. Two methods of estimation of the ships’ emissions are proposed in this paper. These methods prove their utility for shipboard and shore based management personnel from the practical perspective. The methods were demonstrated for a product tanker vessel where a permanent monitoring system for the pollutant emissions has previously been fitted. The values of the polluting agents from the exhaust gas were determined for the ship from the shipyard delivery and were used as starting point. Based on these values, the paper aimed at numerical assessing of ship's emissions in order to determine the ways for avoiding environmental pollution: the analytical method of determining the concentrations of the exhaust gas components, by using computation program MathCAD, and the graphical method of determining the concentrations of the exhaust gas components, using variation diagrams of the parameters, where the results of the on board measurements were introduced, following the application of pertinent correction factors. The results should be regarded as a supporting tool during the decision making process linked to the reduction of ship's pollutant emissions.
Assessment of inlet efficiency through a 3D simulation: numerical and experimental comparison.
Gómez, Manuel; Recasens, Joan; Russo, Beniamino; Martínez-Gomariz, Eduardo
2016-10-01
Inlet efficiency is a requirement for characterizing the flow transfers between surface and sewer flow during rain events. The dual drainage approach is based on the joint analysis of both upper and lower drainage levels, and the flow transfer is one of the relevant elements to define properly this joint behaviour. This paper presents the results of an experimental and numerical investigation about the inlet efficiency definition. A full scale (1:1) test platform located in the Technical University of Catalonia (UPC) reproduces both the runoff process in streets and the water entering the inlet. Data from tests performed on this platform allow the inlet efficiency to be estimated as a function of significant hydraulic and geometrical parameters. A reproduction of these tests through a numerical three-dimensional code (Flow-3D) has been carried out simulating this type of flow by solving the RANS equations. The aim of the work was to reproduce the hydraulic performance of a previously tested grated inlet under several flow and geometric conditions using Flow-3D as a virtual laboratory. This will allow inlet efficiencies to be obtained without previous experimental tests. Moreover, the 3D model allows a better understanding of the hydraulics of the flow interception and the flow patterns approaching the inlet.
Numerical solution of the Rosenau-KdV-RLW equation by using RBFs collocation method
NASA Astrophysics Data System (ADS)
Korkmaz, Bahar; Dereli, Yilmaz
2016-04-01
In this study, a meshfree method based on the collocation with radial basis functions (RBFs) is proposed to solve numerically an initial-boundary value problem of Rosenau-KdV-regularized long-wave (RLW) equation. Numerical values of invariants of the motion are computed to examine the fundamental conservative properties of the equation. Computational experiments for the simulation of solitary waves examine the accuracy of the scheme in terms of error norms L2 and L∞. Linear stability analysis is investigated to determine whether the present method is stable or unstable. The scheme gives unconditionally stable, and second-order convergent. The obtained results are compared with analytical solution and some other earlier works in the literature. The presented results indicate the accuracy and efficiency of the method.
Estimation of region of attraction for polynomial nonlinear systems: a numerical method.
Khodadadi, Larissa; Samadi, Behzad; Khaloozadeh, Hamid
2014-01-01
This paper introduces a numerical method to estimate the region of attraction for polynomial nonlinear systems using sum of squares programming. This method computes a local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. The invariant set is an estimation of the region of attraction for the equilibrium point. In order to enlarge the estimation, a subset of the invariant set defined by a shape factor is enlarged by solving a sum of squares optimization problem. In this paper, a new algorithm is proposed to select the shape factor based on the linearized dynamic model of the system. The shape factor is updated in each iteration using the computed local Lyapunov function from the previous iteration. The efficiency of the proposed method is shown by a few numerical examples.
A method for improving time-stepping numerics
NASA Astrophysics Data System (ADS)
Williams, P. D.
2012-04-01
In contemporary numerical simulations of the atmosphere, evidence suggests that time-stepping errors may be a significant component of total model error, on both weather and climate time-scales. This presentation will review the available evidence, and will then suggest a simple but effective method for substantially improving the time-stepping numerics at no extra computational expense. The most common time-stepping method is the leapfrog scheme combined with the Robert-Asselin (RA) filter. This method is used in the following atmospheric models (and many more): ECHAM, MAECHAM, MM5, CAM, MESO-NH, HIRLAM, KMCM, LIMA, SPEEDY, IGCM, PUMA, COSMO, FSU-GSM, FSU-NRSM, NCEP-GFS, NCEP-RSM, NSEAM, NOGAPS, RAMS, and CCSR/NIES-AGCM. Although the RA filter controls the time-splitting instability in these models, it also introduces non-physical damping and reduces the accuracy. This presentation proposes a simple modification to the RA filter. The modification has become known as the RAW filter (Williams 2011). When used in conjunction with the leapfrog scheme, the RAW filter eliminates the non-physical damping and increases the amplitude accuracy by two orders, yielding third-order accuracy. (The phase accuracy remains second-order.) The RAW filter can easily be incorporated into existing models, typically via the insertion of just a single line of code. Better simulations are obtained at no extra computational expense. Results will be shown from recent implementations of the RAW filter in various atmospheric models, including SPEEDY and COSMO. For example, in SPEEDY, the skill of weather forecasts is found to be significantly improved. In particular, in tropical surface pressure predictions, five-day forecasts made using the RAW filter have approximately the same skill as four-day forecasts made using the RA filter (Amezcua, Kalnay & Williams 2011). These improvements are encouraging for the use of the RAW filter in other models.
Numerical flow simulation and efficiency prediction for axial turbines by advanced turbulence models
NASA Astrophysics Data System (ADS)
Jošt, D.; Škerlavaj, A.; Lipej, A.
2012-11-01
Numerical prediction of an efficiency of a 6-blade Kaplan turbine is presented. At first, the results of steady state analysis performed by different turbulence models for different operating regimes are compared to the measurements. For small and optimal angles of runner blades the efficiency was quite accurately predicted, but for maximal blade angle the discrepancy between calculated and measured values was quite large. By transient analysis, especially when the Scale Adaptive Simulation Shear Stress Transport (SAS SST) model with zonal Large Eddy Simulation (ZLES) in the draft tube was used, the efficiency was significantly improved. The improvement was at all operating points, but it was the largest for maximal discharge. The reason was better flow simulation in the draft tube. Details about turbulent structure in the draft tube obtained by SST, SAS SST and SAS SST with ZLES are illustrated in order to explain the reasons for differences in flow energy losses obtained by different turbulence models.
Numerical Simulation of the Thermal Efficiency During Laser Deep Penetration Welding
NASA Astrophysics Data System (ADS)
Ganser, A.; Pieper, J.; Liebl, S.; Zaeh, M. F.
The advantages of laser beam welding, such as its high flexibility, its high local energy input, and its fast processing speed, led to a substantial increase of industrial applications of the technology. High losses can be observed during laser welding of materials with a high thermal conductivity, such as aluminum or copper. This is caused by the heat conduction losses in the surrounding area of the process zone and due to reflections. These energy losses lead to a reduced efficiency of the laser welding process. A numerical model based on a CFD simulation is presented, which enables to calculate the molten pool isotherms. The thermal efficiency is determined for different keyhole geometries and welding velocities. This efficiency is defined as the ratio between the energy which is required to melt the volume of metal in the fusion zone and the absorbed laser beam power.
Application of a numerical simulation to improve the separation efficiency of a sperm sorter.
Hyakutake, Toru; Hashimoto, Yuki; Yanase, Shinichiro; Matsuura, Koji; Naruse, Keiji
2009-02-01
This paper describes a study in which numerical simulations were applied to improve the separation efficiency of a microfluidic-based sperm sorter. Initially, the motion of 31 sperm were modeled as a sinusoidal wave. The modeled sperm were expected to move while vibrating in the fluid within the microchannel. In this analysis, the number of sperm extracted at the outlet channel and the rate of movement of the highly motile sperm were obtained for a wide range of flow velocities within the microchannel. By varying the channel height, and the width and the position of the sperm-inlet channel, we confirmed that the separation efficiency was highly dependent on the fluid velocity within the channel. These results will be valuable for improving the device configuration, and might help to realize further improvements in efficiency in the future.
Numerical method for the stochastic projected Gross-Pitaevskii equation
NASA Astrophysics Data System (ADS)
Rooney, S. J.; Blakie, P. B.; Bradley, A. S.
2014-01-01
We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional weakly interacting Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes in the low-energy classical region of the system, and evaluating terms from the number-conserving scattering reservoir process. We give an accurate and efficient procedure for evaluating the scattering terms using a Hermite-polynomial based spectral-Galerkin representation, which allows us to precisely implement the low-energy mode restriction. Stochastic integration is performed using the weak semi-implicit Euler method. We extensively characterize the accuracy of our method, finding a faster-than-expected rate of stochastic convergence. Physical consistency of the algorithm is demonstrated by considering thermalization of initially random states.
Numerical method for the stochastic projected Gross-Pitaevskii equation.
Rooney, S J; Blakie, P B; Bradley, A S
2014-01-01
We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional weakly interacting Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes in the low-energy classical region of the system, and evaluating terms from the number-conserving scattering reservoir process. We give an accurate and efficient procedure for evaluating the scattering terms using a Hermite-polynomial based spectral-Galerkin representation, which allows us to precisely implement the low-energy mode restriction. Stochastic integration is performed using the weak semi-implicit Euler method. We extensively characterize the accuracy of our method, finding a faster-than-expected rate of stochastic convergence. Physical consistency of the algorithm is demonstrated by considering thermalization of initially random states.
A semi-analytical method for simulating matrix diffusion in numerical transport models
NASA Astrophysics Data System (ADS)
Falta, Ronald W.; Wang, Wenwen
2017-02-01
A semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates.
A semi-analytical method for simulating matrix diffusion in numerical transport models.
Falta, Ronald W; Wang, Wenwen
2017-02-01
A semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates. Copyright © 2017 Elsevier B.V. All rights reserved.
Methods for increased computational efficiency of multibody simulations
NASA Astrophysics Data System (ADS)
Epple, Alexander
This thesis is concerned with the efficient numerical simulation of finite element based flexible multibody systems. Scaling operations are systematically applied to the governing index-3 differential algebraic equations in order to solve the problem of ill conditioning for small time step sizes. The importance of augmented Lagrangian terms is demonstrated. The use of fast sparse solvers is justified for the solution of the linearized equations of motion resulting in significant savings of computational costs. Three time stepping schemes for the integration of the governing equations of flexible multibody systems are discussed in detail. These schemes are the two-stage Radau IIA scheme, the energy decaying scheme, and the generalized-a method. Their formulations are adapted to the specific structure of the governing equations of flexible multibody systems. The efficiency of the time integration schemes is comprehensively evaluated on a series of test problems. Formulations for structural and constraint elements are reviewed and the problem of interpolation of finite rotations in geometrically exact structural elements is revisited. This results in the development of a new improved interpolation algorithm, which preserves the objectivity of the strain field and guarantees stable simulations in the presence of arbitrarily large rotations. Finally, strategies for the spatial discretization of beams in the presence of steep variations in cross-sectional properties are developed. These strategies reduce the number of degrees of freedom needed to accurately analyze beams with discontinuous properties, resulting in improved computational efficiency.
NASA Astrophysics Data System (ADS)
Menshov, I. S.; Pavlukhin, P. V.
2016-09-01
For problems with complex geometry, a numerical method is proposed for solving the three-dimensional nonstationary Euler equations on Cartesian grids with the use of hybrid computing systems. The baseline numerical scheme, a method for implementing internal boundary conditions on body-unfitted grids, and an iterative matrix-free LU-SGS method for solving the discretized equations are described. An efficient software implementation of the numerical algorithm on a multiprocessor hybrid CPU/GPU computing system is considered. Results of test computations are presented.
A numerical simulation method for aircraft infrared imaging
NASA Astrophysics Data System (ADS)
Zhou, Yue; Wang, Qiang; Li, Ting; Hu, Haiyang
2017-06-01
Numerical simulation of infrared (IR) emission from aircraft is of great significance for military and civilian applications. In this paper, the narrow band k-distribution (NBK) model is used to calculate radiative properties of non-gray gases in the hot exhaust plume. With model parameters derived from the high resolution spectral database HITEMP 2010, the NBK model is validated by comparisons with exact line by line (LBL) results and experimental data. Based on the NBK model, a new finite volume and back ray tracing (FVBRT) method is proposed to solve the radiative transfer equations and produce IR imaging. Calculated results by the FVBRT method are compared with experimental data and available results in open references, which shows the FVBRT method can maintain good accuracy while producing IR images with better rendering effects. Finally, the NBK model and FVBRT method are integrated to calculate IR signature of an aircraft. The IR images and spatial distributions of radiative intensity are compared and analyzed in both 3 - 5 μm band and 8 - 12 μm band to provide references for engineering applications.
Space-time adaptive numerical methods for geophysical applications.
Castro, C E; Käser, M; Toro, E F
2009-11-28
In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space-time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost.
A Hybrid Numerical Analysis Method for Structural Health Monitoring
NASA Technical Reports Server (NTRS)
Forth, Scott C.; Staroselsky, Alexander
2001-01-01
A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.
Lim, Fong Yin; Bao, Weizhu
2008-12-01
We propose efficient and accurate numerical methods for computing the ground-state solution of spin-1 Bose-Einstein condensates subjected to a uniform magnetic field. The key idea in designing the numerical method is based on the normalized gradient flow with the introduction of a third normalization condition, together with two physical constraints on the conservation of total mass and conservation of total magnetization. Different treatments of the Zeeman energy terms are found to yield different numerical accuracies and stabilities. Numerical comparison between different numerical schemes is made, and the best scheme is identified. The numerical scheme is then applied to compute the condensate ground state in a harmonic plus optical lattice potential, and the effect of the periodic potential, in particular to the relative population of each hyperfine component, is investigated through comparison to the condensate ground state in a pure harmonic trap.
Method for computationally efficient design of dielectric laser accelerator structures.
Hughes, Tyler; Veronis, Georgios; Wootton, Kent P; Joel England, R; Fan, Shanhui
2017-06-26
Dielectric microstructures have generated much interest in recent years as a means of accelerating charged particles when powered by solid state lasers. The acceleration gradient (or particle energy gain per unit length) is an important figure of merit. To design structures with high acceleration gradients, we explore the adjoint variable method, a highly efficient technique used to compute the sensitivity of an objective with respect to a large number of parameters. With this formalism, the sensitivity of the acceleration gradient of a dielectric structure with respect to its entire spatial permittivity distribution is calculated by the use of only two full-field electromagnetic simulations, the original and 'adjoint'. The adjoint simulation corresponds physically to the reciprocal situation of a point charge moving through the accelerator gap and radiating. Using this formalism, we perform numerical optimizations aimed at maximizing acceleration gradients, which generate fabricable structures of greatly improved performance in comparison to previously examined geometries.
An efficient method for solving the steady Euler equations
NASA Technical Reports Server (NTRS)
Liou, M.-S.
1986-01-01
An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.
Numerical method for evolving the projected Gross-Pitaevskii equation.
Blakie, P Blair
2008-08-01
In this paper we describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator potential. The central difficulty in solving this equation is the requirement that the classical field is restricted to a small set of prescribed modes that constitute the low energy classical region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the PGPE. We show equilibrium and nonequilibrium results from the application of the PGPE to an anisotropic trapped three-dimensional Bose gas.
Numerical optimization method for packing regular convex polygons
NASA Astrophysics Data System (ADS)
Galiev, Sh. I.; Lisafina, M. S.
2016-08-01
An algorithm is presented for the approximate solution of the problem of packing regular convex polygons in a given closed bounded domain G so as to maximize the total area of the packed figures. On G a grid is constructed whose nodes generate a finite set W on G, and the centers of the figures to be packed can be placed only at some points of W. The problem of packing these figures with centers in W is reduced to a 0-1 linear programming problem. A two-stage algorithm for solving the resulting problems is proposed. The algorithm finds packings of the indicated figures in an arbitrary closed bounded domain on the plane. Numerical results are presented that demonstrate the effectiveness of the method.
A mathematical model and numerical method for thermoelectric DNA sequencing
NASA Astrophysics Data System (ADS)
Shi, Liwei; Guilbeau, Eric J.; Nestorova, Gergana; Dai, Weizhong
2014-05-01
Single nucleotide polymorphisms (SNPs) are single base pair variations within the genome that are important indicators of genetic predisposition towards specific diseases. This study explores the feasibility of SNP detection using a thermoelectric sequencing method that measures the heat released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a DNA strand. We propose a three-dimensional mathematical model that governs the DNA sequencing device with a reaction zone that contains DNA template/primer complex immobilized to the surface of the lower channel wall. The model is then solved numerically. Concentrations of reactants and the temperature distribution are obtained. Results indicate that when the nucleoside is complementary to the next base in the DNA template, polymerization occurs lengthening the complementary polymer and releasing thermal energy with a measurable temperature change, implying that the thermoelectric conceptual device for sequencing DNA may be feasible for identifying specific genes in individuals.
Performance of Several High Order Numerical Methods for Supersonic Combustion
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.; Don, Wai Sun; Mansour, Nagi N. (Technical Monitor)
2001-01-01
The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.
Numerical simulation on snow melting phenomena by CIP method
NASA Astrophysics Data System (ADS)
Mizoe, H.; Yoon, Seong Y.; Josho, M.; Yabe, T.
2001-04-01
A numerical scheme based on the C-CUP method to simulate melting phenomena in snow is proposed. To calculate these complex phenomena we introduce the phase change, elastic-plastic model, porous model, and verify each model by using some simple examples. This scheme is applied to a practical model, such as the snow piled on the insulator of electrical transmission line, in which snow is modeled as a compound material composed of air, water, and ice, and is calculated by elastic-plastic model. The electric field between two electrodes is solved by the Poisson equation giving the Joule heating in the energy conservation that eventually leads to snow melting. Comparison is made by changing the fraction of water in the snow to see its effect on melting process for the cases of applied voltage of 50 and 500 kV on the two electrodes.
Performance of Several High Order Numerical Methods for Supersonic Combustion
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.; Don, Wai Sun; Mansour, Nagi N. (Technical Monitor)
2001-01-01
The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.
Travel Efficiency Assessment Method: Three Case Studies
This slide presentation summarizes three case studies EPA conducted in partnership with Boston, Kansas City, and Tucson, to assess the potential benefits of employing travel efficiency strategies in these areas.
Fictitious boundary and moving mesh methods for the numerical simulation of rigid particulate flows
NASA Astrophysics Data System (ADS)
Wan, Decheng; Turek, Stefan
2007-03-01
In this paper, we investigate the numerical simulation of particulate flows using a new moving mesh method combined with the multigrid fictitious boundary method (FBM) [S. Turek, D.C. Wan, L.S. Rivkind, The fictitious boundary method for the implicit treatment of Dirichlet boundary conditions with applications to incompressible flow simulations. Challenges in Scientific Computing, Lecture Notes in Computational Science and Engineering, vol. 35, Springer, Berlin, 2003, pp. 37-68; D.C. Wan, S. Turek, L.S. Rivkind, An efficient multigrid FEM solution technique for incompressible flow with moving rigid bodies. Numerical Mathematics and Advanced Applications, ENUMATH 2003, Springer, Berlin, 2004, pp. 844-853; D.C. Wan, S. Turek, Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method, Int. J. Numer. Method Fluids 51 (2006) 531-566]. With this approach, the mesh is dynamically relocated through a (linear) partial differential equation to capture the surface of the moving particles with a relatively small number of grid points. The complete system is realized by solving the mesh movement and the partial differential equations of the flow problem alternately via an operator-splitting approach. The flow is computed by a special ALE formulation with a multigrid finite element solver, and the solid particles are allowed to move freely through the computational mesh which is adaptively aligned by the moving mesh method in every time step. One important aspect is that the data structure of the undeformed initial mesh, in many cases a tensor-product mesh or a semi-structured grid consisting of many tensor-product meshes, is preserved, while only the spacing between the grid points is adapted in each time step so that the high efficiency of structured meshes can be exploited. Numerical results demonstrate that the interaction between the fluid and the particles can be accurately and efficiently handled by the presented
A numerically efficient damping model for acoustic resonances in microfluidic cavities
Hahn, P. Dual, J.
2015-06-15
Bulk acoustic wave devices are typically operated in a resonant state to achieve enhanced acoustic amplitudes and high acoustofluidic forces for the manipulation of microparticles. Among other loss mechanisms related to the structural parts of acoustofluidic devices, damping in the fluidic cavity is a crucial factor that limits the attainable acoustic amplitudes. In the analytical part of this study, we quantify all relevant loss mechanisms related to the fluid inside acoustofluidic micro-devices. Subsequently, a numerical analysis of the time-harmonic visco-acoustic and thermo-visco-acoustic equations is carried out to verify the analytical results for 2D and 3D examples. The damping results are fitted into the framework of classical linear acoustics to set up a numerically efficient device model. For this purpose, all damping effects are combined into an acoustofluidic loss factor. Since some components of the acoustofluidic loss factor depend on the acoustic mode shape in the fluid cavity, we propose a two-step simulation procedure. In the first step, the loss factors are deduced from the simulated mode shape. Subsequently, a second simulation is invoked, taking all losses into account. Owing to its computational efficiency, the presented numerical device model is of great relevance for the simulation of acoustofluidic particle manipulation by means of acoustic radiation forces or acoustic streaming. For the first time, accurate 3D simulations of realistic micro-devices for the quantitative prediction of pressure amplitudes and the related acoustofluidic forces become feasible.
Simultaneous source-mask optimization: a numerical combining method
NASA Astrophysics Data System (ADS)
Mülders, Thomas; Domnenko, Vitaliy; Küchler, Bernd; Klimpel, Thomas; Stock, Hans-Jürgen; Poonawala, Amyn A.; Taravade, Kunal N.; Stanton, William A.
2010-09-01
A new method for simultaneous Source-Mask Optimization (SMO) is presented. In order to produce optimum imaging fidelity with respect to exposure lattitude, depth of focus (DoF) and mask error enhancement factor (MEEF) the presented method aims to leverage both, the available degrees of freedom of a pixelated source and those available for the mask layout. The approach described in this paper is designed as to work with dissected mask polygons. The dissection of the mask patterns is to be performed in advance (before SMO) with the Synopsys Proteus OPC engine, providing the available degrees of freedom for mask pattern optimization. This is similar to mask optimization done for optical proximity correction (OPC). Additionally, however, the illumination source will be simultaneously optimized. The SMO approach borrows many of the performance enhancement methods of OPC software for mask correction, but is especially designed as to simultaneously optimize a pixelated source shape as nowadays available in production environments. Designed as a numerical optimization approach the method is able to assess in acceptable times several hundreds of thousands source-mask combinations for small, critical layout snippets. This allows a global optimization scheme to be applied to the SMO problem which is expected to better explore the optimization space and thus to yield an improved solution quality compared to local optimizations methods. The method is applied to an example system for investigating the impact of source constraints on the SMO results. Also, it is investigated how well possibly conflicting goals of low MEEF and large DoF can be balanced.
NASA Technical Reports Server (NTRS)
Golik, W. L.
1996-01-01
A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with finite differences, and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and efficiency. Different smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.
A method for data handling numerical results in parallel OpenFOAM simulations
Anton, Alin; Muntean, Sebastian
2015-12-31
Parallel computational fluid dynamics simulations produce vast amount of numerical result data. This paper introduces a method for reducing the size of the data by replaying the interprocessor traffic. The results are recovered only in certain regions of interest configured by the user. A known test case is used for several mesh partitioning scenarios using the OpenFOAM toolkit{sup ®}[1]. The space savings obtained with classic algorithms remain constant for more than 60 Gb of floating point data. Our method is most efficient on large simulation meshes and is much better suited for compressing large scale simulation results than the regular algorithms.
AN ACCURATE AND EFFICIENT ALGORITHM FOR NUMERICAL SIMULATION OF CONDUCTION-TYPE PROBLEMS. (R824801)
A modification of the finite analytic numerical method for conduction-type (diffusion) problems is presented. The finite analytic discretization scheme is derived by means of the Fourier series expansion for the most general case of nonuniform grid and variabl...
AN ACCURATE AND EFFICIENT ALGORITHM FOR NUMERICAL SIMULATION OF CONDUCTION-TYPE PROBLEMS. (R824801)
A modification of the finite analytic numerical method for conduction-type (diffusion) problems is presented. The finite analytic discretization scheme is derived by means of the Fourier series expansion for the most general case of nonuniform grid and variabl...
Advanced numerical methods and software approaches for semiconductor device simulation
CAREY,GRAHAM F.; PARDHANANI,A.L.; BOVA,STEVEN W.
2000-03-23
In this article the authors concisely present several modern strategies that are applicable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of upwind and artificial dissipation schemes, generalization of the traditional Scharfetter-Gummel approach, Petrov-Galerkin and streamline-upwind Petrov Galerkin (SUPG), entropy variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. They have included numerical examples from the recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and they emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, they briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.
Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation
Carey, Graham F.; Pardhanani, A. L.; Bova, S. W.
2000-01-01
In this article we concisely present several modern strategies that are applicable to driftdominated carrier transport in higher-order deterministic models such as the driftdiffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of “upwind” and artificial dissipation schemes, generalization of the traditional Scharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind Petrov Galerkin (SUPG), “entropy” variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of themore » methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.« less
Introduction to finite-difference methods for numerical fluid dynamics
Scannapieco, E.; Harlow, F.H.
1995-09-01
This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.
NASA Technical Reports Server (NTRS)
Hu, Fang Q.
1994-01-01
It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.
Milani, Massimo; Montorsi, Luca; Stefani, Matteo; Saponelli, Roberto; Lizzano, Maurizio
2017-04-05
The paper focuses on the analysis of an industrial ceramic kiln in order to improve the energy efficiency and thus the fuel consumption and the corresponding carbon dioxide emissions. A lumped and distributed parameter model of the entire system is constructed to simulate the performance of the kiln under actual operating conditions. The model is able to predict accurately the temperature distribution along the different modules of the kiln and the operation of the many natural gas burners employed to provide the required thermal power. Furthermore, the temperature of the tiles is also simulated so that the quality of the final product can be addressed by the modelling. Numerical results are validated against experimental measurements carried out on a real ceramic kiln during regular production operations. The developed numerical model demonstrates to be an efficient tool for the investigation of different design solutions for the kiln's components. In addition, a number of control strategies for the system working conditions can be simulated and compared in order to define the best trade off in terms of fuel consumption and product quality. In particular, the paper analyzes the effect of a new burner type characterized by internal heat recovery capability aimed at improving the energy efficiency of the ceramic kiln. The fuel saving and the relating reduction of carbon dioxide emissions resulted in the order of 10% when compared to the standard burner. Copyright © 2017 Elsevier Ltd. All rights reserved.
Efficient Training Methods for Conditional Random Fields
2008-02-01
Proceedings of the 42nd Annual Meeting of the Association for Computational Linguistics, 2004. [15] Richard H. Byrd, Jorge Nocedal, and Robert B...entropy parameter estimation. In Dan Roth and Antal van den Bosch , editors, Conference on Natural Language Learning (CoNLL), pages 49–55, 2002. [66...Processing Systems 14, pages 841–848, Cambridge, MA, 2002. MIT Press. [89] Jorge Nocedal and Stephen J. Wright. Numerical Optimization. Springer
Efficient resampling methods for nonsmooth estimating functions
ZENG, DONGLIN
2009-01-01
Summary We propose a simple and general resampling strategy to estimate variances for parameter estimators derived from nonsmooth estimating functions. This approach applies to a wide variety of semiparametric and nonparametric problems in biostatistics. It does not require solving estimating equations and is thus much faster than the existing resampling procedures. Its usefulness is illustrated with heteroscedastic quantile regression and censored data rank regression. Numerical results based on simulated and real data are provided. PMID:17925303
Numerical Comparison of Periodic MoM (Method of Moments) and BMIA (Banded Matrix Iteration Method)
NASA Technical Reports Server (NTRS)
Kim, Y.; Rodriguez, E.; Michel, T.
1995-01-01
The most popular numerical technique in rough surface scattering is the Method of Moments (MoM). Since the scattering patch size is finite, the edge current must be suppressed to obtain accurate scattering cross sections. Two standard ways to minimize the edge current are periodic boundary conditions and incident wave tapering. We compare the accuracy & computational requirements of these methods.
Numerical Comparison of Periodic MoM (Method of Moments) and BMIA (Banded Matrix Iteration Method)
NASA Technical Reports Server (NTRS)
Kim, Y.; Rodriguez, E.; Michel, T.
1995-01-01
The most popular numerical technique in rough surface scattering is the Method of Moments (MoM). Since the scattering patch size is finite, the edge current must be suppressed to obtain accurate scattering cross sections. Two standard ways to minimize the edge current are periodic boundary conditions and incident wave tapering. We compare the accuracy & computational requirements of these methods.
Borazjani, Iman; Westerdale, John; McMahon, Eileen M; Rajaraman, Prathish K; Heys, Jeffrey J; Belohlavek, Marek
2013-01-01
The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation. The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics. Improved understanding of LV hemodynamics is expected to provide important clinical diagnostic and prognostic information. We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV), due to its potential for broad and practical utility. Future research directions to advance patient-specific LV simulations include development of methods capable of resolving heart valves, higher temporal resolution, automated generation of three-dimensional (3D) geometry, and incorporating actual flow measurements into the numerical solution of the 3D cardiovascular fluid dynamics.
Chevaugeon, Nicolas . E-mail: chevaugeon@gce.ucl.ac.be; Hillewaert, Koen; Gallez, Xavier; Ploumhans, Paul; Remacle, Jean-Francois . E-mail: remacle@gce.ucl.ac.be
2007-04-10
This paper deals with the high-order discontinuous Galerkin (DG) method for solving wave propagation problems. First, we develop a one-dimensional DG scheme and numerically compute dissipation and dispersion errors for various polynomial orders. An optimal combination of time stepping scheme together with the high-order DG spatial scheme is presented. It is shown that using a time stepping scheme with the same formal accuracy as the DG scheme is too expensive for the range of wave numbers that is relevant for practical applications. An efficient implementation of a high-order DG method in three dimensions is presented. Using 1D convergence results, we further show how to adequately choose elementary polynomial orders in order to equi-distribute a priori the discretization error. We also show a straightforward manner to allow variable polynomial orders in a DG scheme. We finally propose some numerical examples in the field of aero-acoustics.
Borazjani, Iman; Westerdale, John; McMahon, Eileen M.; Rajaraman, Prathish K.; Heys, Jeffrey J.
2013-01-01
The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation. The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics. Improved understanding of LV hemodynamics is expected to provide important clinical diagnostic and prognostic information. We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV), due to its potential for broad and practical utility. Future research directions to advance patient-specific LV simulations include development of methods capable of resolving heart valves, higher temporal resolution, automated generation of three-dimensional (3D) geometry, and incorporating actual flow measurements into the numerical solution of the 3D cardiovascular fluid dynamics. PMID:23690874
A Newton/upwind method and numerical study of shock wave/boundary layer interactions
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1989-01-01
The objective of the paper is two-fold. First, an upwind/central differencing method for solving the steady Navier-Stokes equations is described. The symmetric line relation method is used to solve the resulting algebraic system to achieve high computational efficiency. The grid spacings used in the calculations are determined from the triple-deck theory, in terms of Mach and Reynolds numbers and other flow parameters. Thus the accuracy of the numerical solutions is improved by comparing them with experimental, analytical, and other computational results. Secondly, the shock wave/boundary layer interactions are studied numerically, with special attention given to the flow separation. The concept of free interaction is confirmed. Although the separated region varies with Mach and Reynolds numbers, it is found that the transverse velocity component behind the incident shock, which has not been identified heretofore, is also an important parameter. A small change of this quantity is sufficient to eliminate the flow separation entirely.
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Reynolds, Daniel R. . E-mail: drreynolds@ucsd.edu; Samtaney, Ravi . E-mail: samtaney@pppl.gov; Woodward, Carol S. . E-mail: cswoodward@llnl.gov
2006-11-20
We present a nonlinearly implicit, conservative numerical method for integration of the single-fluid resistive MHD equations. The method uses a high-order spatial discretization that preserves the solenoidal property of the magnetic field. The fully coupled PDE system is solved implicitly in time, providing for increased interaction between physical processes as well as additional stability over explicit-time methods. A high-order adaptive time integration is employed, which in many cases enables time steps ranging from one to two orders of magnitude larger than those constrained by the explicit CFL condition. We apply the solution method to illustrative examples relevant to stiff magnetic fusion processes which challenge the efficiency of explicit methods. We provide computational evidence showing that for such problems the method is comparably accurate with explicit-time simulations, while providing a significant runtime improvement due to its increased temporal stability.
A new numerical method for calculating extrema of received power for polarimetric SAR
Zhang, Y.; Zhang, Jiahua; Lu, Zhiming; Gong, W.
2009-01-01
A numerical method called cross-step iteration is proposed to calculate the maximal/minimal received power for polarized imagery based on a target's Kennaugh matrix. This method is much more efficient than the systematic method, which searches for the extrema of received power by varying the polarization ellipse angles of receiving and transmitting polarizations. It is also more advantageous than the Schuler method, which has been adopted by the PolSARPro package, because the cross-step iteration method requires less computation time and can derive both the maximal and minimal received powers, whereas the Schuler method is designed to work out only the maximal received power. The analytical model of received-power optimization indicates that the first eigenvalue of the Kennaugh matrix is the supremum of the maximal received power. The difference between these two parameters reflects the depolarization effect of the target's backscattering, which might be useful for target discrimination. ?? 2009 IEEE.
NASA Astrophysics Data System (ADS)
Lambert, J.; Josselin, E.; Ryde, N.; Faure, A.
2015-08-01
Context. The solution of the nonlocal thermodynamical equilibrium (non-LTE) radiative transfer equation usually relies on stationary iterative methods, which may falsely converge in some cases. Furthermore, these methods are often unable to handle large-scale systems, such as molecular spectra emerging from, for example, cool stellar atmospheres. Aims: Our objective is to develop a new method, which aims to circumvent these problems, using nonstationary numerical techniques and taking advantage of parallel computers. Methods: The technique we develop may be seen as a generalization of the coupled escape probability method. It solves the statistical equilibrium equations in all layers of a discretized model simultaneously. The numerical scheme adopted is based on the generalized minimum residual method. Results: The code has already been applied to the special case of the water spectrum in a red supergiant stellar atmosphere. This demonstrates the fast convergence of this method, and opens the way to a wide variety of astrophysical problems.
Efficient randomized methods for stability analysis of fluids systems
NASA Astrophysics Data System (ADS)
Dawson, Scott; Rowley, Clarence
2016-11-01
We show that probabilistic algorithms that have recently been developed for the approximation of large matrices can be utilized to numerically evaluate the properties of linear operators in fluids systems. In particular, we present an algorithm that is well suited for optimal transient growth (i.e., nonmodal stability) analysis. For non-normal systems, such analysis can be important for analyzing local regions of convective instability, and in identifying high-amplitude transients that can trigger nonlinear instabilities. Our proposed algorithms are easy to wrap around pre-existing timesteppers for linearized forward and adjoint equations, are highly parallelizable, and come with known error bounds. Furthermore, they allow for efficient computation of optimal growth modes for numerous time horizons simultaneously. We compare the proposed algorithm to both direct matrix-forming and Krylov subspace approaches on a number of test problems. We will additionally discuss the potential for randomized methods to assist more broadly in the speed-up of algorithms for analyzing both fluids data and operators. Supported by AFOSR Grant FA9550-14-1-0289.
On the efficient and reliable numerical solution of rate-and-state friction problems
NASA Astrophysics Data System (ADS)
Pipping, Elias; Kornhuber, Ralf; Rosenau, Matthias; Oncken, Onno
2016-03-01
We present a mathematically consistent numerical algorithm for the simulation of earthquake rupture with rate-and-state friction. Its main features are adaptive time stepping, a novel algebraic solution algorithm involving nonlinear multigrid and a fixed point iteration for the rate-and-state decoupling. The algorithm is applied to a laboratory scale subduction zone which allows us to compare our simulations with experimental results. Using physical parameters from the experiment, we find a good fit of recurrence time of slip events as well as their rupture width and peak slip. Computations in 3-D confirm efficiency and robustness of our algorithm.
Numerical methods for determining interstitial oxygen in silicon
Stevenson, J.O.; Medernach, J.W.
1995-01-01
The interstitial oxygen (O{sub i}) concentration in Czochralski silicon and the subsequent SiO{sub x} precipitation are important parameters for integrated circuit fabrication. Uncontrolled SiO{sub x} precipitation during processing can create detrimental mechanical and electrical effects that contribute to poor performance. An inability to consistently and accurately measure the initial O{sub i} concentration in heavily doped silicon has led to contradictory results regarding the effects of dopant type and concentration on SiO{sub x} precipitation. The authors have developed a software package for reliably determining and comparing O{sub i} in heavily doped silicon. The SiFTIR{copyright} code implements three independent oxygen analysis methods in a single integrated package. Routine oxygen measurements are desirable over a wide range of silicon resistivities, but there has been confusion concerning which of the three numerical methods is most suitable for the low resistivity portion of the continuum. A major strength of the software is an ability to rapidly produce results for all three methods using only a single Fourier Transform Infrared Spectroscopy (FTIR) spectrum as input. This ability to perform three analyses on a single data set allows a detailed comparison of the three methods across the entire range of resistivities in question. Integrated circuit manufacturers could use the enabling technology provided by SiFTIR{copyright} to monitor O{sub i} content. Early detection of O{sub i} using this diagnostic could be beneficial in controlling SiO{sub x} precipitation during integrated circuit processing.
Numerical Methods for Forward and Inverse Problems in Discontinuous Media
Chartier, Timothy P.
2011-03-08
The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.
Exact and quasi exact numerical methods for giant magnetic molecules
NASA Astrophysics Data System (ADS)
Schnack, Jürgen
2012-02-01
The determination of the energy spectra of large magnetic molecules is a demanding numerical problem. In this contribution we demonstrate that theory has advanced very much in recent years. We first show that it is possible to diagonalize the Heisenberg Hamiltonian by employing the spin-rotational symmetry SU(2) in combination with arbitrary point-group symmetries [1]. This goes far beyond earlier approaches and enables us to evaluate thermodynamic observables such as the magnetization and spectroscopic data for molecules as large as the famous ferric wheel Fe10 with a Hilbert space dimension of more than 60 Millions. Then we explain how the finite-temperature Lanczos method can be applied to magnetic molecules in order to determine thermodynamic functions for Hilbert spaces as large as up to 1 Billion [2]. The new method enables us to discuss the magnetic properties of the highly frustrated Keplerate molecule W72V30 which behaves like a finite size Kagome lattice antiferromagnet. [4pt] [1] R. Schnalle and J. Schnack, Int. Rev. Phys. Chem. 29 (2010) 403; R. Schnalle, J. Schnack, Phys. Rev. B 79 (2009) 104419. [0pt] [2] J. Schnack, O. Wendland, Eur. Phys. J. B 78 (2010) 535-541.
Numerical modelling methods for predicting antenna performance on aircraft
NASA Astrophysics Data System (ADS)
Kubina, S. J.
1983-09-01
Typical case studies that involve the application of Moment Methods to the prediction of the radiation characteristics of antennas in the HF frequency band are examined. The examples consist of the analysis of a shorted transmission line HF antenna on a CHSS-2/Sea King helicopter, wire antennas on the CP-140/Aurora patrol aircraft and a long dipole antenna on the Space Shuttle Orbiter spacecraft. In each of these cases the guidelines for antenna modeling by the use of the program called the Numerical Electromagnetic Code are progressively applied and results are compared to measurements made by the use of scale-model techniques. In complex examples of this type comparisons based on individual radiation patterns are insufficient for the validation of computer models. A volumetric method of radiation pattern comparison is used based on criteria that result from pattern integration and that are related to communication system performance. This is supplemented by hidden-surface displays of an entire set of conical radiation patterns resulting from measurements and computations. Antenna coupling considerations are discussed for the case of the dual HF installation on the CP-140/Aurora aircraft.
An efficient catalytic method for fulvene synthesis
Coşkun, Necdet; Erden, Ihsan
2011-01-01
The effects of the nature and amount of base, substrate structure, amount of added water and solvent on the condensation of carbonyl compounds with cyclopentadiene in the presence of secondary amines were investigated. Based on these studies, a new efficient and green synthesis of fulvenes was developed. PMID:22021940
Handwritten numeral verification method using distribution maps of structural features
NASA Astrophysics Data System (ADS)
Itoh, Nobuyasu; Takahashi, Hiroyasu
1990-08-01
Character recognition methods can be categorized into two major approaches. One is pattern matching, which is little affected by topological changes such as breaks in strokes. The other is structural analysis, which tolerates distorted characters only if the topological features of their undistorted versions are kept. We developed a new recognition method for hand-written numerals by combining the merits of the two approaches. The recognition process consists of three steps: (1) an input character is recognized by a patternmatching method, which reduces the number of possible categories to 1.5 on the average, (2) the character is yenfled to be true, false, or uncertain by a structural analysis method that we have newly developed, and (3) special heuristic verification logics are applied to uncertain characters. In the second step, the new structural analysis method uses the positions and directions of terminal points extracted from thinned character images as a main feature. The extracted terminal points are labeled according to a structural-feature distribution map prepared for each category. The generated labels are matched with template label sets constructed by statistical analysis. The characteristics of the method are as follows: (1) it copes with distortion of hand-written characters by using distribution maps for the positions and directions of feature points, and (2) distribution maps can be automatically generated from statistical data in learning samples and easily tuned interactively. The merits of combining the two methods are as follows: (1) the advantages of both pattern matching and structural analysis are obtained, (2) the probabilities of steps 2 and 3 needing to be executed are 22% and 9% respectively, which hardly affect the total processing time, and (3) as a result of steps 1 and 2, only a small number of special logics are required. In a test using unconstrained hand-written characters of low quality, the recognition rate and substitution
Conway, A; Wang, T; Deo, N; Cheung, C; Nikolic, R
2008-06-24
This work reports numerical simulations of a novel three-dimensionally integrated, {sup 10}boron ({sup 10}B) and silicon p+, intrinsic, n+ (PIN) diode micropillar array for thermal neutron detection. The inter-digitated device structure has a high probability of interaction between the Si PIN pillars and the charged particles (alpha and {sup 7}Li) created from the neutron - {sup 10}B reaction. In this work, the effect of both the 3-D geometry (including pillar diameter, separation and height) and energy loss mechanisms are investigated via simulations to predict the neutron detection efficiency and gamma discrimination of this structure. The simulation results are demonstrated to compare well with the measurement results. This indicates that upon scaling the pillar height, a high efficiency thermal neutron detector is possible.
Numerical study of a highly efficient solar cell with graded band gap design
NASA Astrophysics Data System (ADS)
Tan, Ming-Hsuan; Tseng, Hung-Ruei; Kuo, Chien-Ting; Hsu, Shun-Chieh; Lo, Yen-Hua; Tsai, Che-Pin; Cheng, Yuh-Jen; Lin, Chien-Chung
2015-05-01
A linearly graded band gap design in the intrinsic layer of a p-i-n solar cell is studied numerically. An ideal model using Matlab® is built and the device performance is calculated using continuity equations and an effective band gap model under various band gap combinations. The power conversion efficiency (PCE) can be as high as 30.21%, while the abrupt junction reference device only exhibits 29.25% under the same parameters. This design is also evaluated using the commercial TCAD software APSYS®, and the calculations show optimal efficiency enhancements of about 1.14-fold that of the abrupt junction device in an AlAs/GaAs system and 2.05-fold that in an InGaN/GaN system.
Simplified method for numerical modeling of fiber lasers.
Shtyrina, O V; Yarutkina, I A; Fedoruk, M P
2014-12-29
A simplified numerical approach to modeling of dissipative dispersion-managed fiber lasers is examined. We present a new numerical iteration algorithm for finding the periodic solutions of the system of nonlinear ordinary differential equations describing the intra-cavity dynamics of the dissipative soliton characteristics in dispersion-managed fiber lasers. We demonstrate that results obtained using simplified model are in good agreement with full numerical modeling based on the corresponding partial differential equations.
NASA Astrophysics Data System (ADS)
Katsaounis, T. D.
2005-02-01
equations in Diffpack can be used to derive fully implicit solvers for systems. The proposed techniques are illustrated in terms of two applications, namely a system of PDEs modelling pipeflow and a two-phase porous media flow. Stochastic PDEs is the topic of chapter 7. The first part of the chapter is a simple introduction to stochastic PDEs; basic analytical properties are presented for simple models like transport phenomena and viscous drag forces. The second part considers the numerical solution of stochastic PDEs. Two basic techniques are presented, namely Monte Carlo and perturbation methods. The last part explains how to implement and incorporate these solvers into Diffpack. Chapter 8 describes how to operate Diffpack from Python scripts. The main goal here is to provide all the programming and technical details in order to glue the programming environment of Diffpack with visualization packages through Python and in general take advantage of the Python interfaces. Chapter 9 attempts to show how to use numerical experiments to measure the performance of various PDE solvers. The authors gathered a rather impressive list, a total of 14 PDE solvers. Solvers for problems like Poisson, Navier--Stokes, elasticity, two-phase flows and methods such as finite difference, finite element, multigrid, and gradient type methods are presented. The authors provide a series of numerical results combining various solvers with various methods in order to gain insight into their computational performance and efficiency. In Chapter 10 the authors consider a computationally challenging problem, namely the computation of the electrical activity of the human heart. After a brief introduction on the biology of the problem the authors present the mathematical models involved and a numerical method for solving them within the framework of Diffpack. Chapter 11 and 12 are closely related; actually they could have been combined in a single chapter. Chapter 11 introduces several mathematical
Numerical Weather Predictions Evaluation Using Spatial Verification Methods
NASA Astrophysics Data System (ADS)
Tegoulias, I.; Pytharoulis, I.; Kotsopoulos, S.; Kartsios, S.; Bampzelis, D.; Karacostas, T.
2014-12-01
During the last years high-resolution numerical weather prediction simulations have been used to examine meteorological events with increased convective activity. Traditional verification methods do not provide the desired level of information to evaluate those high-resolution simulations. To assess those limitations new spatial verification methods have been proposed. In the present study an attempt is made to estimate the ability of the WRF model (WRF -ARW ver3.5.1) to reproduce selected days with high convective activity during the year 2010 using those feature-based verification methods. Three model domains, covering Europe, the Mediterranean Sea and northern Africa (d01), the wider area of Greece (d02) and central Greece - Thessaly region (d03) are used at horizontal grid-spacings of 15km, 5km and 1km respectively. By alternating microphysics (Ferrier, WSM6, Goddard), boundary layer (YSU, MYJ) and cumulus convection (Kain--Fritsch, BMJ) schemes, a set of twelve model setups is obtained. The results of those simulations are evaluated against data obtained using a C-Band (5cm) radar located at the centre of the innermost domain. Spatial characteristics are well captured but with a variable time lag between simulation results and radar data. Acknowledgements: This research is cofinanced by the European Union (European Regional Development Fund) and Greek national funds, through the action "COOPERATION 2011: Partnerships of Production and Research Institutions in Focused Research and Technology Sectors" (contract number 11SYN_8_1088 - DAPHNE) in the framework of the operational programme "Competitiveness and Entrepreneurship" and Regions in Transition (OPC II, NSRF 2007--2013).
a Numerical Method for Scattering from Acoustically Soft and Hard Thin Bodies in Two Dimensions
NASA Astrophysics Data System (ADS)
YANG, S. A.
2002-03-01
This paper presents a numerical method for predicting the acoustic scattering from two-dimensional (2-D) thin bodies. Both the Dirichlet and Neumann problems are considered. Applying the thin-body formulation leads to the boundary integral equations involving weakly singular and hypersingular kernels. Completely regularizing these kinds of singular kernels is thus the main concern of this paper. The basic subtraction-addition technique is adopted. The purpose of incorporating a parametric representation of the boundary surface with the integral equations is two-fold. The first is to facilitate the numerical implementation for arbitrarily shaped bodies. The second one is to facilitate the expansion of the unknown function into a series of Chebyshev polynomials. Some of the resultant integrals are evaluated by using the Gauss-Chebyshev integration rules after moving the series coefficients to the outside of the integral sign; others are evaluated exactly, including the modified hypersingular integral. The numerical implementation basically includes only two parts, one for evaluating the ordinary integrals and the other for solving a system of algebraic equations. Thus, the current method is highly efficient and accurate because these two solution procedures are easy and straightforward. Numerical calculations consist of the acoustic scattering by flat and curved plates. Comparisons with analytical solutions for flat plates are made.
Transforming Mean and Osculating Elements Using Numerical Methods
NASA Technical Reports Server (NTRS)
Ely, Todd A.
2010-01-01
Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order
Power Measurement Methods for Energy Efficient Applications
Calandrini, Guilherme; Gardel, Alfredo; Bravo, Ignacio; Revenga, Pedro; Lázaro, José L.; Toledo-Moreo, F. Javier
2013-01-01
Energy consumption constraints on computing systems are more important than ever. Maintenance costs for high performance systems are limiting the applicability of processing devices with large dissipation power. New solutions are needed to increase both the computation capability and the power efficiency. Moreover, energy efficient applications should balance performance vs. consumption. Therefore power data of components are important. This work presents the most remarkable alternatives to measure the power consumption of different types of computing systems, describing the advantages and limitations of available power measurement systems. Finally, a methodology is proposed to select the right power consumption measurement system taking into account precision of the measure, scalability and controllability of the acquisition system. PMID:23778191
NASA Astrophysics Data System (ADS)
Liu, Xiao-Di; Xu, Lu; Liang, Xiao-Yan
2017-01-01
We theoretically analyzed output beam quality of broad bandwidth non-collinear optical parametric chirped pulse amplification (NOPCPA) in LiB3O5 (LBO) centered at 800 nm. With a three-dimensional numerical model, the influence of the pump intensity, pump and signal spatial modulations, and the walk-off effect on the OPCPA output beam quality are presented, together with conversion efficiency and the gain spectrum. The pump modulation is a dominant factor that affects the output beam quality. Comparatively, the influence of signal modulation is insignificant. For a low-energy system with small beam sizes, walk-off effect has to be considered. Pump modulation and walk-off effect lead to asymmetric output beam profile with increased modulation. A special pump modulation type is found to optimize output beam quality and efficiency. For a high-energy system with large beam sizes, the walk-off effect can be neglected, certain back conversion is beneficial to reduce the output modulation. A trade-off must be made between the output beam quality and the conversion efficiency, especially when the pump modulation is large since. A relatively high conversion efficiency and a low output modulation are both achievable by controlling the pump modulation and intensity.
NASA Astrophysics Data System (ADS)
Tian, Liang; Yang, Zhibing; Fagerlund, Fritjof; Niemi, Auli
2015-04-01
We study effect of geological heterogeneity on the injection of supercritical CO2 into a deep saline aquifer at the scale of a pilot test site, based on numerical modeling. The effect of heterogeneity on storage capacity is investigated by assessing the effect on sweep efficiency and on injectivity. Log-normally distributed random permeability fields characterized by their standard deviation (σ) and correlation length (λ) are generated and injection simulations conducted for each realization of the permeability fields with TOUGH2/ECO2N code. A range of injection pressures is tested as well. The results indicate that injectivity increases with the increased horizontal correlation length given that the vertical correlation length is fixed and significant inter-realization variation is seen when changing the standard deviation. Sweep efficiency is favored by smaller horizontal correlation length. For cases with increased standard deviation, the sweep efficiency shows significant inter-realization variability. Finally, it can be shown that both sweep efficiency and injectivity can be expressed as simple functions of medium heterogeneity characteristics, standard deviation (σ) and correlation length (λ).
Numerical Research of Steam and Gas Plant Efficiency of Triple Cycle for Extreme North Regions
NASA Astrophysics Data System (ADS)
Galashov, Nikolay; Tsibulskii, Svjatoslav; Matveev, Aleksandr; Masjuk, Vladimir
2016-02-01
The present work shows that temperature decrease of heat rejection in a cycle is necessary for energy efficiency of steam turbine plants. Minimum temperature of heat rejection at steam turbine plant work on water steam is 15°C. Steam turbine plant of triple cycle where lower cycle of steam turbine plant is organic Rankine cycle on low-boiling substance with heat rejection in air condenser, which safely allows rejecting heat at condensation temperatures below 0°C, has been offered. Mathematical model of steam and gas plant of triple cycle, which allows conducting complex researches with change of working body appearance and parameters defining thermodynamic efficiency of cycles, has been developed. On the basis of the model a program of parameters and index cycles design of steam and gas plants has been developed in a package of electron tables Excel. Numerical studies of models showed that energy efficiency of steam turbine plants of triple cycle strongly depend on low-boiling substance type in a lower cycle. Energy efficiency of steam and gas plants net 60% higher can be received for steam and gas plants on the basis of gas turbine plant NK-36ST on pentane and its condensation temperature below 0°C. It was stated that energy efficiency of steam and gas plants net linearly depends on condensation temperature of low-boiling substance type and temperature of gases leaving reco very boiler. Energy efficiency increases by 1% at 10% decrease of condensation temperature of pentane, and it increases by 0.88% at 15°C temperature decrease of gases leaving recovery boiler.
Numerical study of MPS method with large eddy simulation for fluid solid coupling problem
NASA Astrophysics Data System (ADS)
YANG, Chao; ZHANG, Huaixin; YAO, Huilan
2017-02-01
The Moving-Particle Semi-implicit method (MPS) is a kind of meshless Lagrangian calculation method. This method uses particles instead of mesh. In the pretreatment it works simply and conveniently and has high computational efficiency. In practical engineering, many of fluid problems are turbulent flows. Large eddy simulation is a major means of studying turbulence. Fluid-structure coupling is an independent branch of mechanics combined with fluid dynamics and solid mechanics, which is the hot and difficult area of research in many fields at present. In this paper, for the numerical simulation of turbulent flow with interaction of fluid-structure, the modified MPS-LES method is applied in two dimensional dam-break problem. It proves that MPS-LES method can be extended on solving the fluid-solid coupled problem.
An efficient method for solving the steady Euler equations
NASA Technical Reports Server (NTRS)
Liou, M. S.
1986-01-01
An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.
Cilfone, Nicholas A.; Kirschner, Denise E.; Linderman, Jennifer J.
2015-01-01
Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level. PMID:26366228
Numerical methods for incompressible viscous flows with engineering applications
NASA Technical Reports Server (NTRS)
Rose, M. E.; Ash, R. L.
1988-01-01
A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.
Numerical methods for problems involving the Drazin inverse
NASA Technical Reports Server (NTRS)
Meyer, C. D., Jr.
1979-01-01
The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.
Energy efficiency assessment methods and tools evaluation
McMordie, K.L.; Richman, E.E.; Keller, J.M.; Dixon, D.R.
1994-08-01
Many different methods of assessing the energy savings potential at federal installations, and identifying attractive projects for capital investment have been used by the different federal agencies. These methods range from high-level estimating tools to detailed design tools, both manual and software assisted. These methods have different purposes and provide results that are used for different parts of the project identification, and implementation process. Seven different assessment methods are evaluated in this study. These methods were selected by the program managers at the DoD Energy Policy Office, and DOE Federal Energy Management Program (FEMP). Each of the methods was applied to similar buildings at Bolling Air Force Base (AFB), unless it was inappropriate or the method was designed to make an installation-wide analysis, rather than focusing on particular buildings. Staff at Bolling AFB controlled the collection of data.
Riser Feeding Evaluation Method for Metal Castings Using Numerical Analysis
NASA Astrophysics Data System (ADS)
Ahmad, Nadiah
One of the design aspects that continues to create a challenge for casting designers is the optimum design of casting feeders (risers). As liquid metal solidifies, the metal shrinks and forms cavities inside the casting. In order to avoid shrinkage cavities, risers are added to the casting shape to supply additional molten metal when shrinkage occurs during solidification. The shrinkage cavities in the casting are compensated by controlling the cooling rate to promote directional solidification. This control can be achieved by designing the casting such that the cooling begins at the sections that are farthest away from the risers and ends at the risers. Therefore, the risers will solidify last and feed the casting with the molten metal. As a result, the shrinkage cavities formed during solidification are in the risers which are later removed from the casting. Since casting designers have to usually go through iterative processes of validating the casting designs which are very costly due to expensive simulation processes or manual trials and errors on actual casting processes, this study investigates more efficient methods that will help casting designers utilize their casting experiences systematically to develop good initial casting designs. The objective is to reduce the casting design method iterations; therefore, reducing the cost involved in that design processes. The aim of this research aims at finding a method that can help casting designers design effective risers used in sand casting process of aluminum-silicon alloys by utilizing the analysis of solidification simulation. The analysis focuses on studying the significance of pressure distribution of the liquid metal at the early stage of casting solidification, when heat transfer and convective fluid flow are taken into account in the solidification simulation. The mathematical model of casting solidification was solved using the finite volume method (FVM). This study focuses to improve our
NASA Astrophysics Data System (ADS)
Kramer, Alex; Thumm, Uwe
2016-05-01
We discuss a class of window-transform-based ``virtual detector'' methods for computing momentum-resolved dissociation and ionization spectra by numerically analyzing the motion of nuclear or electronic quantum-mechanical wavepackets at the periphery of their numerical grids. While prior applications of such surface-flux methods considered semi-classical limits to derive ionization and dissociation spectra, we systematically include quantum-mechanical corrections and extensions to higher dimensions, discussing numerical convergence properties and the computational efficiency of our method in comparison with alternative schemes for obtaining momentum distributions. Using the example of atomic ionization by co- and counter-rotating circularly polarized laser pulses, we scrutinize the efficiency of common finite-difference schemes for solving the time-dependent Schrödinger equation in virtual detection and standard Fourier-transformation methods for extracting momentum spectra. Supported by the DoE, NSF, and Alexander von Humboldt foundation.
NASA Astrophysics Data System (ADS)
de La Bernardie, Jérôme; Bour, Olivier; de Dreuzy, Jean-Raynald; Guihéneuf, Nicolas; Chatton, Eliot; Labasque, Thierry; Le Borgne, Tanguy
2017-04-01
Geothermal energy is a renewable energy source particularly attractive due to associated low greenhouse gas emission rates. Crystalline rocks are in general considered of poor interest for geothermal applications at shallow depths (< 100m), because of the low permeability of the medium. In some cases, fractures may enhance permeability, but thermal energy storage at these shallow depths is still remaining very challenging because of the low storativity of the medium. Within this framework, the purpose of this study is to test the possibility of efficient thermal energy storage in shallow fractured rocks. For doing so, several heat tracer tests have been carried on in a single well between two connected fractures. We completed this experimental work with numerical modeling of thermal transport in fractures embedded in an impermeable conductive matrix. The thermal tracer tests were achieved in a crystalline rock aquifer at the experimental site of Ploemeur (H+ observatory network). The experimental setup consists in injecting hot water in a fracture isolated by a double straddle packer in the borehole while pumping and monitoring the temperature in a fracture crossing the same borehole at greater elevation. Several tracer tests were achieved at different pumping and injection rates. This experimental set up allowed to estimate temperature breakthrough for different tracer test durations and hydraulic configurations from fully convergent to perfect dipole tracer tests. Thanks to those tests and numerical modeling of heat transport in fractures, we demonstrate that temperature recovery is highly dependent on flow rate and streamlines shape. Thus, thermal storage rate is inversely proportional to flow and is maximized in perfect dipole configuration. These thermal tracer tests and numerical modeling allow to define the most efficient configuration for optimizing shallow geothermal storage in fractured rock.
Efficient positional misalignment correction method for Fourier ptychographic microscopy
Sun, Jiasong; Chen, Qian; Zhang, Yuzhen; Zuo, Chao
2016-01-01
Fourier ptychographic microscopy (FPM) is a newly developed super-resolution technique, which employs angularly varying illuminations and a phase retrieval algorithm to surpass the diffraction limit of a low numerical aperture (NA) objective lens. In current FPM imaging platforms, accurate knowledge of LED matrix’s position is critical to achieve good recovery quality. Furthermore, considering such a wide field-of-view (FOV) in FPM, different regions in the FOV have different sensitivity of LED positional misalignment. In this work, we introduce an iterative method to correct position errors based on the simulated annealing (SA) algorithm. To improve the efficiency of this correcting process, large number of iterations for several images with low illumination NAs are firstly implemented to estimate the initial values of the global positional misalignment model through non-linear regression. Simulation and experimental results are presented to evaluate the performance of the proposed method and it is demonstrated that this method can both improve the quality of the recovered object image and relax the LED elements’ position accuracy requirement while aligning the FPM imaging platforms. PMID:27446659
Considerations of Methods of Improving Helicopter Efficiency
NASA Technical Reports Server (NTRS)
Dingeldein, Richard C.
1961-01-01
Recent NASA helicopter research indicates that significant improvements in hovering efficiency, up to 7 percent, are available from the use of a special airfoil section formed by combining an NACA 632A015 thickness distribution with an NACA 230 mean line. This airfoil should be considered for flying-crane-type helicopters. Application of standard leading-edge roughness causes a large drop in efficiency; however, the cambered rotor is shown to retain its superiority over a rotor having a symmetrical airfoil when both rotors have leading-edge roughness. A simple analysis of available rotor static-thrust data indicates a greatly reduced effect of compressibility effects on the rotor profile-drag power than predicted from calculations. Preliminary results of an experimental study of helicopter parasite drag indicate the practicability of achieving an equivalent flat-plate parasite-drag area of less than 4 square feet for a rotor-head-pylon-fuselage configuration (landing gear retracted) in the 2,000-pound minimum-flying-weight class. The large drag penalty of a conventional skid-type landing (3.6 square feet) can be reduced by two-thirds by careful design. Clean, fair, and smooth fuselages that tend to have narrow, deep cross sections are shown to have advantages from the standpoint of drag and download. A ferry range of the order of 1,500 miles is indicated to be practicable for the small helicopter considered.
Considerations of Methods of Improving Helicopter Efficiency
NASA Technical Reports Server (NTRS)
Dingeldein, Richard C.
1961-01-01
Recent NASA helicopter research indicates that significant improvements in hovering efficiency, up to 7 percent, are available from the use of a special airfoil section formed by combining an NACA 632A015 thickness distribution with an NACA 230 mean line. This airfoil should be considered for flying-crane-type helicopters. Application of standard leading-edge roughness causes a large drop in efficiency; however, the cambered rotor is shown to retain its superiority over a rotor having a symmetrical airfoil when both rotors have leading-edge roughness. A simple analysis of available rotor static-thrust data indicates a greatly reduced effect of compressibility effects on the rotor profile-drag power than predicted from calculations. Preliminary results of an experimental study of helicopter parasite drag indicate the practicability of achieving an equivalent flat-plate parasite-drag area of less than 4 square feet for a rotor-head-pylon-fuselage configuration (landing gear retracted) in the 2,000-pound minimum-flying-weight class. The large drag penalty of a conventional skid-type landing (3.6 square feet) can be reduced by two-thirds by careful design. Clean, fair, and smooth fuselages that tend to have narrow, deep cross sections are shown to have advantages from the standpoint of drag and download. A ferry range of the order of 1,500 miles is indicated to be practicable for the small helicopter considered.
NASA Astrophysics Data System (ADS)
Luque-Raigon, Jose Miguel; Halme, Janne; Miguez, Hernan
2014-02-01
We design a fully stable numerical solution of the Maxwell's equations with the transfer matrix method (TMM) to understand the interaction between an electromagnetic field and a finite, one-dimensional, non-periodic structure. Such an exact solution can be tailored from a conventional solution by choosing an adequate transformation between its reference systems, which induces a mapping between its associated TMMs. The paper demonstrates theoretically the numerical stability of the TMM for the exact solution within the framework of Maxwell's equations, but the same formalism can efficiently be applied to resolve other classical or quantum linear wave-propagation interaction in one, two, and three dimensions. This is because the formalism is exclusively built up for an in depth analysis of the TMM's symmetries.
NASA Astrophysics Data System (ADS)
Nakamura, Gen; Wang, Haibing
2017-05-01
Consider the problem of reconstructing unknown Robin inclusions inside a heat conductor from boundary measurements. This problem arises from active thermography and is formulated as an inverse boundary value problem for the heat equation. In our previous works, we proposed a sampling-type method for reconstructing the boundary of the Robin inclusion and gave its rigorous mathematical justification. This method is non-iterative and based on the characterization of the solution to the so-called Neumann- to-Dirichlet map gap equation. In this paper, we give a further investigation of the reconstruction method from both the theoretical and numerical points of view. First, we clarify the solvability of the Neumann-to-Dirichlet map gap equation and establish a relation of its solution to the Green function associated with an initial-boundary value problem for the heat equation inside the Robin inclusion. This naturally provides a way of computing this Green function from the Neumann-to-Dirichlet map and explains what is the input for the linear sampling method. Assuming that the Neumann-to-Dirichlet map gap equation has a unique solution, we also show the convergence of our method for noisy measurements. Second, we give the numerical implementation of the reconstruction method for two-dimensional spatial domains. The measurements for our inverse problem are simulated by solving the forward problem via the boundary integral equation method. Numerical results are presented to illustrate the efficiency and stability of the proposed method. By using a finite sequence of transient input over a time interval, we propose a new sampling method over the time interval by single measurement which is most likely to be practical.
Active Problem Solving and Applied Research Methods in a Graduate Course on Numerical Methods
ERIC Educational Resources Information Center
Maase, Eric L.; High, Karen A.
2008-01-01
"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…
Active Problem Solving and Applied Research Methods in a Graduate Course on Numerical Methods
ERIC Educational Resources Information Center
Maase, Eric L.; High, Karen A.
2008-01-01
"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…
Numerical solution of differential algebraic equations (DAEs) by mix-multistep method
NASA Astrophysics Data System (ADS)
Rahim, Yong Faezah; Suleiman, Mohamed; Ibrahim, Zarina Bibi
2014-06-01
Differential Algebraic Equations (DAEs) are regarded as stiff Ordinary Differential Equations (ODEs). Therefore they are solved using implicit method such as Backward Differentiation Formula (BDF) type of methods which require the use of Newton iteration which need much computational effort. However, not all of the ODEs in DAE system are stiff. In this paper, we describe a new technique for solving DAE, where the ODEs are treated as non-stiff at the start of the integration and putting the non-stiff ODEs into stiff subsystem should instability occurs. Adams type of method is used to solve the non-stiff part and BDF method for solving the stiff part. This strategy is shown to be competitive in terms of computational effort and accuracy. Numerical experiments are presented to validate its efficiency.
A method of numerically controlled machine part programming
NASA Technical Reports Server (NTRS)
1970-01-01
Computer program is designed for automatically programmed tools. Preprocessor computes desired tool path and postprocessor computes actual commands causing machine tool to follow specific path. It is used on a Cincinnati ATC-430 numerically controlled machine tool.
Basic numerical methods. [of unsteady and transonic flow
NASA Technical Reports Server (NTRS)
Steger, Joseph L.; Van Dalsem, William R.
1989-01-01
Some of the basic finite-difference schemes that can be used to solve the nonlinear equations that describe unsteady inviscid and viscous transonic flow are reviewed. Numerical schemes for solving the unsteady Euler and Navier-Stokes, boundary-layer, and nonlinear potential equations are described. Emphasis is given to the elementary ideas used in constructing various numerical procedures, not specific details of any one procedure.
Analysis of coupling efficiency on hemispherical fiber lens by method of lines.
Lambak, Zainuddin; Abdul Rahman, Faidz; Mokhtar, Mohd Ridzuan; Tengku, Imran A
2009-02-16
The method of lines (MoL) has been developed to study coupling efficiency on hemispherical lens. In this paper, the physical shape of the lens is approximated by cascading a number of straight waveguide segments. The perfectly matched layer (PML) is applied as an absorber for the MoL to reduce numerical reflection in the simulation region. Analysis is done by calculating coupling efficiency at the plane of integration where the coupling efficiency is an overlap integral between laser diode field and fiber field. The result of coupling efficiency in this analysis is compared to the experiment and ABCD matrix. It is found that MoL gives good result accuracy.
NASA Technical Reports Server (NTRS)
Wright, William B.
1988-01-01
Transient, numerical simulations of the deicing of composite aircraft components by electrothermal heating have been performed in a 2-D rectangular geometry. Seven numerical schemes and four solution methods were used to find the most efficient numerical procedure for this problem. The phase change in the ice was simulated using the Enthalpy method along with the Method for Assumed States. Numerical solutions illustrating deicer performance for various conditions are presented. Comparisons are made with previous numerical models and with experimental data. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.
Review of Methods and Approaches for Deriving Numeric ...
EPA will propose numeric criteria for nitrogen/phosphorus pollution to protect estuaries, coastal areas and South Florida inland flowing waters that have been designated Class I, II and III , as well as downstream protective values (DPVs) to protect estuarine and marine waters. In accordance with the formal determination and pursuant to a subsequent consent decree, these numeric criteria are being developed to translate and implement Florida’s existing narrative nutrient criterion, to protect the designated use that Florida has previously set for these waters, at Rule 62-302.530(47)(b), F.A.C. which provides that “In no case shall nutrient concentrations of a body of water be altered so as to cause an imbalance in natural populations of aquatic flora or fauna.” Under the Clean Water Act and EPA’s implementing regulations, these numeric criteria must be based on sound scientific rationale and reflect the best available scientific knowledge. EPA has previously published a series of peer reviewed technical guidance documents to develop numeric criteria to address nitrogen/phosphorus pollution in different water body types. EPA recognizes that available and reliable data sources for use in numeric criteria development vary across estuarine and coastal waters in Florida and flowing waters in South Florida. In addition, scientifically defensible approaches for numeric criteria development have different requirements that must be taken into consider
Numerical tracing of energetic electron microsignatures: methods and applications
NASA Astrophysics Data System (ADS)
Andriopoulou, M.; Roussos, E.; Krupp, N.; Paranicas, C.; Thomsen, M. F.; Krimigis, S. M.; Dougherty, M. K.
2012-12-01
One of the most sensitive methods to measure weak, non-corotational velocity components in Saturn's magnetosphere is the detection and analysis of the energetic electron microsignature locations. Microsignatures are typically very sharp and narrow energetic electron flux dropouts observed in the inner saturnian magnetosphere and at locations that map magnetically close to the orbits of the planet's icy moons. Microsignatures form after the drifting electrons encounter one of these moons and get absorbed. Since the resulting cavities cannot refill within the local, moon-magnetosphere interaction region, they propagate in the magnetosphere with the properties of the pre-depleted energetic electrons. Microsignatures may survive up to 1.5 rotations around the planet, and for that reason they are excellent tools for tracing the shape of the magnetospheric particle drift shells. In all tracing studies up to now, however, calculations were performed assuming a dipole field configuration and corotation-driven azimuthal electric fields. These assumptions allow for straightforward, analytical solutions of the equations of motion. Aspects that are usually neglected are related to the detection of the microsignatures, such as the finite energy width and complex response of the detector channels that record the relevant signals. Furthermore, the role of the weak, non-corotational and/or non-dipolar drift components becomes important as the energy of the electrons increases, since corotation and magnetic drifts tend to cancel out between about 400 keV and few MeV. Neglecting these weak drifts at high energies can be a source of large systematic errors in the tracing procedure. In this study we demonstrate how all these assumptions and simplifications may affect the quality and the outcome of the microsignature analysis. We then show how the use of the correct system of equations and numerical tracing helps to understand all major observational aspects of microsignatures (e
On Efficient Multigrid Methods for Materials Processing Flows with Small Particles
NASA Technical Reports Server (NTRS)
Thomas, James (Technical Monitor); Diskin, Boris; Harik, VasylMichael
2004-01-01
Multiscale modeling of materials requires simulations of multiple levels of structural hierarchy. The computational efficiency of numerical methods becomes a critical factor for simulating large physical systems with highly desperate length scales. Multigrid methods are known for their superior efficiency in representing/resolving different levels of physical details. The efficiency is achieved by employing interactively different discretizations on different scales (grids). To assist optimization of manufacturing conditions for materials processing with numerous particles (e.g., dispersion of particles, controlling flow viscosity and clusters), a new multigrid algorithm has been developed for a case of multiscale modeling of flows with small particles that have various length scales. The optimal efficiency of the algorithm is crucial for accurate predictions of the effect of processing conditions (e.g., pressure and velocity gradients) on the local flow fields that control the formation of various microstructures or clusters.
Methods used to improve gamete efficiency.
Marrs, R P; Serafini, P C; Kerin, J F; Batzofin, J; Stone, B A; Brown, J; Wilson, L; Quinn, P
1988-01-01
Male factor infertility accounts for a significant percentage of problems in infertile couples. With clinical utilization of the technologies for selection of good-quality spermatozoa from the ejaculate, our ability to successfully treat the severely affected male factor couple has improved. However, it must be remembered that even with current technologies, fertilization success is reduced in these patients but remains above a 50% level. Other factors that can be used in the future to improve on these statistics are being investigated in regard to the in vitro environment for gametes, that is, the type of culture medium, the methods of coincubation of the sperm and egg, and other methods of enhancement of sperm fertilizing potential. However, methods of sperm preparation will achieve improvement in a percentage of these males treated, and can be used to improve fertilization and pregnancy success. It is important to understand the limitations of the zona-free hamster test, but it is also important to use that test as a screening method for sperm handling. By utilizing the SPA to select out the optimal method of sperm preparation, the fertilization and pregnancy outcome can be improved. Overall, the live-birth rate in male factor infertile couples is lower than non-male-factor couples treated by IVF and GIFT. Until more is known about basic spermatozoal function, and the ability to improve that function in affected males, the live-birth rate should not be expected to change substantially.
An Efficient Method for Transferring Adult Mosquitoes during Field Tests,
CULICIDAE, *COLLECTING METHODS, REPRINTS, BLOOD SUCKING INSECTS, FIELD TESTS, HAND HELD, EFFICIENCY, LABORATORY EQUIPMENT, MORTALITY RATES , ADULTS, AEDES, ASPIRATORS, CULICIDAE, TEST AND EVALUATION, REPRINTS
Atzberger, Paul J.
2010-05-01
Stochastic partial differential equations are introduced for the continuum concentration fields of reaction-diffusion systems. The stochastic partial differential equations account for fluctuations arising from the finite number of molecules which diffusively migrate and react. Spatially adaptive stochastic numerical methods are developed for approximation of the stochastic partial differential equations. The methods allow for adaptive meshes with multiple levels of resolution, Neumann and Dirichlet boundary conditions, and domains having geometries with curved boundaries. A key issue addressed by the methods is the formulation of consistent discretizations for the stochastic driving fields at coarse-refined interfaces of the mesh and at boundaries. Methods are also introduced for the efficient generation of the required stochastic driving fields on such meshes. As a demonstration of the methods, investigations are made of the role of fluctuations in a biological model for microorganism direction sensing based on concentration gradients. Also investigated, a mechanism for spatial pattern formation induced by fluctuations. The discretization approaches introduced for SPDEs have the potential to be widely applicable in the development of numerical methods for the study of spatially extended stochastic systems.
Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.
Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing
2016-10-01
The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.
An efficient method for multiple sequence alignment
Kim, J.; Pramanik, S.
1994-12-31
Multiple sequence alignment has been a useful method in the study of molecular evolution and sequence-structure relationships. This paper presents a new method for multiple sequence alignment based on simulated annealing technique. Dynamic programming has been widely used to find an optimal alignment. However, dynamic programming has several limitations to obtain optimal alignment. It requires long computation time and cannot apply certain types of cost functions. We describe detail mechanisms of simulated annealing for multiple sequence alignment problem. It is shown that simulated annealing can be an effective approach to overcome the limitations of dynamic programming in multiple sequence alignment problem.
Efficient protein structure search using indexing methods
2013-01-01
Understanding functions of proteins is one of the most important challenges in many studies of biological processes. The function of a protein can be predicted by analyzing the functions of structurally similar proteins, thus finding structurally similar proteins accurately and efficiently from a large set of proteins is crucial. A protein structure can be represented as a vector by 3D-Zernike Descriptor (3DZD) which compactly represents the surface shape of the protein tertiary structure. This simplified representation accelerates the searching process. However, computing the similarity of two protein structures is still computationally expensive, thus it is hard to efficiently process many simultaneous requests of structurally similar protein search. This paper proposes indexing techniques which substantially reduce the search time to find structurally similar proteins. In particular, we first exploit two indexing techniques, i.e., iDistance and iKernel, on the 3DZDs. After that, we extend the techniques to further improve the search speed for protein structures. The extended indexing techniques build and utilize an reduced index constructed from the first few attributes of 3DZDs of protein structures. To retrieve top-k similar structures, top-10 × k similar structures are first found using the reduced index, and top-k structures are selected among them. We also modify the indexing techniques to support θ-based nearest neighbor search, which returns data points less than θ to the query point. The results show that both iDistance and iKernel significantly enhance the searching speed. In top-k nearest neighbor search, the searching time is reduced 69.6%, 77%, 77.4% and 87.9%, respectively using iDistance, iKernel, the extended iDistance, and the extended iKernel. In θ-based nearest neighbor serach, the searching time is reduced 80%, 81%, 95.6% and 95.6% using iDistance, iKernel, the extended iDistance, and the extended iKernel, respectively. PMID:23691543
Efficient protein structure search using indexing methods.
Kim, Sungchul; Sael, Lee; Yu, Hwanjo
2013-01-01
Understanding functions of proteins is one of the most important challenges in many studies of biological processes. The function of a protein can be predicted by analyzing the functions of structurally similar proteins, thus finding structurally similar proteins accurately and efficiently from a large set of proteins is crucial. A protein structure can be represented as a vector by 3D-Zernike Descriptor (3DZD) which compactly represents the surface shape of the protein tertiary structure. This simplified representation accelerates the searching process. However, computing the similarity of two protein structures is still computationally expensive, thus it is hard to efficiently process many simultaneous requests of structurally similar protein search. This paper proposes indexing techniques which substantially reduce the search time to find structurally similar proteins. In particular, we first exploit two indexing techniques, i.e., iDistance and iKernel, on the 3DZDs. After that, we extend the techniques to further improve the search speed for protein structures. The extended indexing techniques build and utilize an reduced index constructed from the first few attributes of 3DZDs of protein structures. To retrieve top-k similar structures, top-10 × k similar structures are first found using the reduced index, and top-k structures are selected among them. We also modify the indexing techniques to support θ-based nearest neighbor search, which returns data points less than θ to the query point. The results show that both iDistance and iKernel significantly enhance the searching speed. In top-k nearest neighbor search, the searching time is reduced 69.6%, 77%, 77.4% and 87.9%, respectively using iDistance, iKernel, the extended iDistance, and the extended iKernel. In θ-based nearest neighbor serach, the searching time is reduced 80%, 81%, 95.6% and 95.6% using iDistance, iKernel, the extended iDistance, and the extended iKernel, respectively.
NASA Astrophysics Data System (ADS)
Lewis, R. W.; Johnson, J. A.; Smith, W. R.
Aspects of heat conduction are discussed, taking into account the numerical solution of steady periodic problems in heat conduction, partially discontinuous boundary elements for heat conduction, the numerical solution of heat conduction in a nonhomogeneous infinite domain by coupling the finite difference method and the boundary element method, and a method for efficiently incorporating radiative boundaries in finite element programs. Other subjects explored are related to phase change, heat and mass transfer in porous bodies, thermal and drying stresses, mathematical and computational techniques, free and forced convection, coupled conduction and convection, turbulent heat transfer, fire and combustion simulation, nuclear waste disposal, solar energy, and industrial and scientific applications. Attention is given to the dynamics of heat exchangers, temperature fields of burnt-up nuclear fuel elements in dry-storage containers, a numerical analysis of solar convective dryers, and a numerical solution by digital computer of optimum thermochemical parameters for the rocket thrust chamber.
Numerical simulations of multicomponent ecological models with adaptive methods.
Owolabi, Kolade M; Patidar, Kailash C
2016-01-08
The study of dynamic relationship between a multi-species models has gained a huge amount of scientific interest over the years and will continue to maintain its dominance in both ecology and mathematical ecology in the years to come due to its practical relevance and universal existence. Some of its emergence phenomena include spatiotemporal patterns, oscillating solutions, multiple steady states and spatial pattern formation. Many time-dependent partial differential equations are found combining low-order nonlinear with higher-order linear terms. In attempt to obtain a reliable results of such problems, it is desirable to use higher-order methods in both space and time. Most computations heretofore are restricted to second order in time due to some difficulties introduced by the combination of stiffness and nonlinearity. Hence, the dynamics of a reaction-diffusion models considered in this paper permit the use of two classic mathematical ideas. As a result, we introduce higher order finite difference approximation for the spatial discretization, and advance the resulting system of ODE with a family of exponential time differencing schemes. We present the stability properties of these methods along with the extensive numerical simulations for a number of multi-species models. When the diffusivity is small many of the models considered in this paper are found to exhibit a form of localized spatiotemporal patterns. Such patterns are correctly captured in the local analysis of the model equations. An extended 2D results that are in agreement with Turing typical patterns such as stripes and spots, as well as irregular snakelike structures are presented. We finally show that the designed schemes are dynamically consistent. The dynamic complexities of some ecological models are studied by considering their linear stability analysis. Based on the choices of parameters in transforming the system into a dimensionless form, we were able to obtain a well-balanced system that
Numerical Simulation of Antennas with Improved Integral Equation Method
NASA Astrophysics Data System (ADS)
Ma, Ji; Fang, Guang-You; Lu, Wei
2015-08-01
Simulating antennas around a conducting object is a challenge task in computational electromagnetism, which is concerned with the behaviour of electromagnetic fields. To analyze this model efficiently, an improved integral equation-fast Fourier transform (IE-FFT) algorithm is presented in this paper. The proposed scheme employs two Cartesian grids with different size and location to enclose the antenna and the other object, respectively. On the one hand, IE-FFT technique is used to store matrix in a sparse form and accelerate the matrix-vector multiplication for each sub-domain independently. On the other hand, the mutual interaction between sub-domains is taken as the additional exciting voltage in each matrix equation. By updating integral equations several times, the whole electromagnetic system can achieve a stable status. Finally, the validity of the presented method is verified through the analysis of typical antennas in the presence of a conducting object. Supported by in part China Postdoctoral Science Foundation under Grant No. 2014M550839, and in part by the Key Research Program of the Chinese Academy of Sciences under Grant No. KGZD-EW-603
Graphical method for analyzing digital computer efficiency
NASA Technical Reports Server (NTRS)
Chan, S. P.; Munoz, R. M.
1971-01-01
Analysis method utilizes graph-theoretic approach for evaluating computation cost and makes logical distinction between linear graph of a computation and linear graph of a program. It applies equally well to other processes which depend on quatitative edge nomenclature and precedence relationships between edges.
New efficient optimizing techniques for Kalman filters and numerical weather prediction models
NASA Astrophysics Data System (ADS)
Famelis, Ioannis; Galanis, George; Liakatas, Aristotelis
2016-06-01
The need for accurate local environmental predictions and simulations beyond the classical meteorological forecasts are increasing the last years due to the great number of applications that are directly or not affected: renewable energy resource assessment, natural hazards early warning systems, global warming and questions on the climate change can be listed among them. Within this framework the utilization of numerical weather and wave prediction systems in conjunction with advanced statistical techniques that support the elimination of the model bias and the reduction of the error variability may successfully address the above issues. In the present work, new optimization methods are studied and tested in selected areas of Greece where the use of renewable energy sources is of critical. The added value of the proposed work is due to the solid mathematical background adopted making use of Information Geometry and Statistical techniques, new versions of Kalman filters and state of the art numerical analysis tools.
A Fast Numerical Method for a Nonlinear Black-Scholes Equation
NASA Astrophysics Data System (ADS)
Koleva, Miglena N.; Vulkov, Lubin G.
2009-11-01
In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed.
NASA Astrophysics Data System (ADS)
Wang, Lesong
The objective of the present research is to investigate the recent development of the vorticity confinement method. First, a new formulation of the vorticity confinement term is studied. Advantages of the new formulation over the original one include the ability to conserve the momentum, and the ability to preserve the centroid motion of some flow properties such as the vorticity magnitude. Next, new difference schemes, which are simpler and more efficient than the old schemes, are discussed. At last, two computational models based on the vorticity confinement method are investigated. One of the models is devised to simulate inviscid flows over bodies with surfaces not aligned with the grid. The other is a surface boundary layer model, which is intended for efficiently simulating viscous flows with separations from the body surfaces. To validate the computational models, numerical simulations of three-dimensional flows over a 6:1 ellipsoid at incidence are performed. Comparisons have been made with exact solutions for inviscid simulations or experimental data for viscous simulations, and data obtained with conventional CFD methods. It is observed that both the inviscid and the viscous solutions with the new models exhibit good agreement with the exact solutions or the experiment data. The new models can have much higher efficiency than conventional CFD methods, and are able to obtain solutions with comparable accuracy.
A numerical analysis method for evaluating rod lenses using the Monte Carlo method.
Yoshida, Shuhei; Horiuchi, Shuma; Ushiyama, Zenta; Yamamoto, Manabu
2010-12-20
We propose a numerical analysis method for evaluating GRIN lenses using the Monte Carlo method. Actual measurements of the modulation transfer function (MTF) of a GRIN lens using this method closely match those made by conventional methods. Experimentally, the MTF is measured using a square wave chart, and is then calculated based on the distribution of output strength on the chart. In contrast, the general method using computers evaluates the MTF based on a spot diagram made by an incident point light source. However the results differ greatly from those from experiments. We therefore developed an evaluation method similar to the experimental system based on the Monte Carlo method and verified that it more closely matches the experimental results than the conventional method.
An efficient method for solving fractional Hodgkin-Huxley model
NASA Astrophysics Data System (ADS)
Nagy, A. M.; Sweilam, N. H.
2014-06-01
In this paper, we present an accurate numerical method for solving fractional Hodgkin-Huxley model. A non-standard finite difference method (NSFDM) is implemented to study the dynamic behaviors of the proposed model. The Grünwald-Letinkov definition is used to approximate the fractional derivatives. Numerical results are presented graphically reveal that NSFDM is easy to implement, effective and convenient for solving the proposed model.
NASA Astrophysics Data System (ADS)
Álvaro, M.; Carretero, M.; Bonilla, L. L.
2012-05-01
We present a finite difference method to solve a new type of nonlocal hydrodynamic equations that arise in the theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices. The hydrodynamic equations describe the evolution of the electron density, electric field and the complex amplitude of the Bloch oscillations for the electron current density and the mean energy density. These equations contain averages over the Bloch phase which are integrals of the unknown electric field and are derived by singular perturbation methods. Among the solutions of the hydrodynamic equations, at a 70 K lattice temperature, there are spatially inhomogeneous Bloch oscillations coexisting with moving electric field domains and Gunn-type oscillations of the current. At higher temperature (300 K) only Bloch oscillations remain. These novel solutions are found for restitution coefficients in a narrow interval below their critical values and disappear for larger values. We use an efficient numerical method based on an implicit second-order finite difference scheme for both the electric field equation (of drift-diffusion type) and the parabolic equation for the complex amplitude. Double integrals appearing in the nonlocal hydrodynamic equations are calculated by means of expansions in modified Bessel functions. We use numerical simulations to ascertain the convergence of the method. If the complex amplitude equation is solved using a first order scheme for restitution coefficients near their critical values, a spurious convection arises that annihilates the complex amplitude in the part of the superlattice that is closer to the cathode. This numerical artifact disappears if the space step is appropriately reduced or we use the second-order numerical scheme.
SAMSAN- MODERN NUMERICAL METHODS FOR CLASSICAL SAMPLED SYSTEM ANALYSIS
NASA Technical Reports Server (NTRS)
Frisch, H. P.
1994-01-01
SAMSAN was developed to aid the control system analyst by providing a self consistent set of computer algorithms that support large order control system design and evaluation studies, with an emphasis placed on sampled system analysis. Control system analysts have access to a vast array of published algorithms to solve an equally large spectrum of controls related computational problems. The analyst usually spends considerable time and effort bringing these published algorithms to an integrated operational status and often finds them less general than desired. SAMSAN reduces the burden on the analyst by providing a set of algorithms that have been well tested and documented, and that can be readily integrated for solving control system problems. Algorithm selection for SAMSAN has been biased toward numerical accuracy for large order systems with computational speed and portability being considered important but not paramount. In addition to containing relevant subroutines from EISPAK for eigen-analysis and from LINPAK for the solution of linear systems and related problems, SAMSAN contains the following not so generally available capabilities: 1) Reduction of a real non-symmetric matrix to block diagonal form via a real similarity transformation matrix which is well conditioned with respect to inversion, 2) Solution of the generalized eigenvalue problem with balancing and grading, 3) Computation of all zeros of the determinant of a matrix of polynomials, 4) Matrix exponentiation and the evaluation of integrals involving the matrix exponential, with option to first block diagonalize, 5) Root locus and frequency response for single variable transfer functions in the S, Z, and W domains, 6) Several methods of computing zeros for linear systems, and 7) The ability to generate documentation "on demand". All matrix operations in the SAMSAN algorithms assume non-symmetric matrices with real double precision elements. There is no fixed size limit on any matrix in any
SAMSAN- MODERN NUMERICAL METHODS FOR CLASSICAL SAMPLED SYSTEM ANALYSIS
NASA Technical Reports Server (NTRS)
Frisch, H. P.
1994-01-01
SAMSAN was developed to aid the control system analyst by providing a self consistent set of computer algorithms that support large order control system design and evaluation studies, with an emphasis placed on sampled system analysis. Control system analysts have access to a vast array of published algorithms to solve an equally large spectrum of controls related computational problems. The analyst usually spends considerable time and effort bringing these published algorithms to an integrated operational status and often finds them less general than desired. SAMSAN reduces the burden on the analyst by providing a set of algorithms that have been well tested and documented, and that can be readily integrated for solving control system problems. Algorithm selection for SAMSAN has been biased toward numerical accuracy for large order systems with computational speed and portability being considered important but not paramount. In addition to containing relevant subroutines from EISPAK for eigen-analysis and from LINPAK for the solution of linear systems and related problems, SAMSAN contains the following not so generally available capabilities: 1) Reduction of a real non-symmetric matrix to block diagonal form via a real similarity transformation matrix which is well conditioned with respect to inversion, 2) Solution of the generalized eigenvalue problem with balancing and grading, 3) Computation of all zeros of the determinant of a matrix of polynomials, 4) Matrix exponentiation and the evaluation of integrals involving the matrix exponential, with option to first block diagonalize, 5) Root locus and frequency response for single variable transfer functions in the S, Z, and W domains, 6) Several methods of computing zeros for linear systems, and 7) The ability to generate documentation "on demand". All matrix operations in the SAMSAN algorithms assume non-symmetric matrices with real double precision elements. There is no fixed size limit on any matrix in any
Method and apparatus for energy efficient comminution
Karra, V.K.; Magerowski, A.J.
1987-06-09
This patent describes a method of crushing minerals by means of a cone crusher having a specified maximum head diameter and comprising a material inlet, a conical head of corresponding maximum head diameter, an annular inner bowl liner against which an annular outer mantle on the head crushes incoming material in a gyrating cycle, the bowl liner and mantle having a circumferential gap or cavity therebetween, the crusher having specified head throw and gyrating speed characteristics.
Efficient solution on solving 3D Maxwell equations using stable semi-implicit splitting method
NASA Astrophysics Data System (ADS)
Cen, Wei; Gu, Ning
2016-05-01
In this paper, we propose an efficient solution on solving 3-dimensional (3D) time-domain Maxwell equations using the semi-implicit Crank-Nicholson (CN) method for time domain discretization with advantage of unconditional time stability. By applying the idea of fractional steps method (FSM) to the CN scheme, the proposed method provides a much simpler and efficient implementation than a direct implementation of the CN scheme. Compared with the alternating-direction implicit (ADI) method and explicit finite-difference time-domain approach (FDTD), it significantly saves the computational resource like memory and CPU time while remains similar numerical accuracy.
Modeling supersonic combustion using a fully-implicit numerical method
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Wilson, Gregory J.
1990-01-01
A fully-implicit finite-volume algorithm for two-dimensional axisymmetric flows has been coupled to a detailed hydrogen-air reaction mechanism (13 species and 33 reactions) so that supersonic combustion phenomena may be investigated. Numerical computations are compared with ballistic-range shadowgraphs of Lehr (1972) that exhibit two discontinuities caused by a blunt body as it passes through a premixed stoichiometric hydrogen-air mixture. The suitability of the numerical procedure for simulating these double-front flows is shown. The requirements for the physical formulation and the numerical modeling of these flowfields are discussed. Finally, the sensitivity of these external flowfields to changes in certain key reaction rate constants is examined.
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.
2010-01-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward-difference-formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications. PMID:20577570
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H; Miller, Cass T
2010-07-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward-difference-formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.
Bu Sunyoung Huang Jingfang Boyer, Treavor H. Miller, Cass T.
2010-07-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.
Efficient discretization in finite difference method
NASA Astrophysics Data System (ADS)
Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris
2015-04-01
Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.
Application of numerical methods to planetary radiowave scattering
NASA Technical Reports Server (NTRS)
Simpson, Richard A.; Tyler, G. Leonard
1987-01-01
Existing numerical techniques for the solution of scattering problems were investigated to determine those which might be applicable to planetary surface studies, with the goal of improving the interpretation of radar data from Venus, Mars, the Moon, and icy satellites. The general characteristics of the models are described along with computational concerns. In particular, the Numerical Electrogmatics Code (NEC) developed at the Lawrence Livermore Laboratory is discussed. Though not developed for random rough surfaces, the NEC contains elements which may be generalized and which could be valuable in the study of scattering by planetary surfaces.
A numerical method for the nonlinear oscillator problem
NASA Astrophysics Data System (ADS)
Killingbeck, J.; Jolicard, G.
1998-03-01
The treatment of a nonlinear Schrödinger equation with power law potential terms by means of hypervirial perturbation theory (HVPT) is considered. Previous workers have tried to handle the nonlinearity by constructing an HVPT which also contains a nonlinear term. We show that higher numerical accuracy can be obtained by reverting to the usual linear HVPT in combination with a simple numerical procedure. The procedure also works with finite-difference shooting calculations, which would permit the calculations to be extended to handle more general potentials.
Tournament Methods for WLAN: Analysis and Efficiency
NASA Astrophysics Data System (ADS)
Galtier, Jérôme
In the context of radio distributed networks, we present a generalized approach for Medium Access Control (MAC) with a fixed congestion window. Our protocol is quite simple to analyze and can be used in a lot of different situations. We give mathematical evidence showing that our performance is asymptotically tight. We also place ourselves in the WiFi and WiMAX frameworks, and discuss experimental results showing acollision reduction of 14% to 21% compared to the best-known methods. We discuss channel capacity improvement and fairness considerations.
Numerical algorithms for highly oscillatory dynamic system based on commutator-free method
NASA Astrophysics Data System (ADS)
Li, Wencheng; Deng, Zichen; Zhang, Suying
2007-04-01
In the present paper, an efficiently improved modified Magnus integrator algorithm based on commutator-free method is proposed for the second-order dynamic systems with time-dependent high frequencies. Firstly, the second-order dynamic systems are transferred to the frame of reference by introducing new variable so that highly oscillatory behaviour inherited from the entries. Then the modified Magnus integrator method based on local linearization is appropriately designed for solving the above new form. And some optimized strategies for reducing the number of function evaluations and matrix operations are also suggested. Finally, several numerical examples for highly oscillatory dynamic systems, such as Airy equation, Bessel equation, Mathieu equation, are presented to demonstrate the validity and effectiveness of the proposed method.
NASA Technical Reports Server (NTRS)
Rosenfeld, Moshe; Israeli, Moshe; Wolfshtein, Micha
1987-01-01
A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.
NASA Technical Reports Server (NTRS)
Rosenfeld, Moshe; Israeli, Moshe; Wolfshtein, Micha
1987-01-01
A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.
Properties-preserving high order numerical methods for a kinetic eikonal equation
NASA Astrophysics Data System (ADS)
Luo, Songting; Payne, Nicholas
2017-02-01
For the BGK (Bhatnagar-Gross-Krook) equation in the large scale hyperbolic limit, the density of particles can be transformed as the Hopf-Cole transformation, where the phase function converges uniformly to the viscosity solution of an effective Hamilton-Jacobi equation, referred to as the kinetic eikonal equation. In this work, we present efficient high order finite difference methods for numerically solving the kinetic eikonal equation. The methods are based on monotone schemes such as the Godunov scheme. High order weighted essentially non-oscillatory techniques and Runge-Kutta procedures are used to obtain high order accuracy in both space and time. The effective Hamiltonian is determined implicitly by a nonlinear equation given as integrals with respect to the velocity variable. Newton's method is applied to solve the nonlinear equation, where integrals with respect to the velocity variable are evaluated either by a Gauss quadrature formula or as expansions with respect to moments of the Maxwellian. The methods are designed such that several key properties such as the positivity of the viscosity solution and the positivity of the effective Hamiltonian are preserved. Numerical experiments are presented to demonstrate the effectiveness of the methods.
Stress analysis and damage evaluation of flawed composite laminates by hybrid-numerical methods
NASA Technical Reports Server (NTRS)
Yang, Yii-Ching
1992-01-01
Structural components in flight vehicles is often inherited flaws, such as microcracks, voids, holes, and delamination. These defects will degrade structures the same as that due to damages in service, such as impact, corrosion, and erosion. It is very important to know how a structural component can be useful and survive after these flaws and damages. To understand the behavior and limitation of these structural components researchers usually do experimental tests or theoretical analyses on structures with simulated flaws. However, neither approach has been completely successful. As Durelli states that 'Seldom does one method give a complete solution, with the most efficiency'. Examples of this principle is seen in photomechanics which additional strain-gage testing can only average stresses at locations of high concentration. On the other hand, theoretical analyses including numerical analyses are implemented with simplified assumptions which may not reflect actual boundary conditions. Hybrid-Numerical methods which combine photomechanics and numerical analysis have been used to correct this inefficiency since 1950's. But its application is limited until 1970's when modern computer codes became available. In recent years, researchers have enhanced the data obtained from photoelasticity, laser speckle, holography and moire' interferometry for input of finite element analysis on metals. Nevertheless, there is only few of literature being done on composite laminates. Therefore, this research is dedicated to this highly anisotropic material.
Numerical study of insulator-based dielectrophoresis method for circulating tumor cell separation
NASA Astrophysics Data System (ADS)
Aghaamoo, Mohammad; Aghilinejad, Arian; Chen, Xiaolin
2017-02-01
Insulator-based dielectrophoresis (iDEP) is known as a powerful technique for separation and manipulation of bioparticles. In recent years, iDEP designs using arrays of insulating posts have shown promising results towards reaching high-efficient bioparticles manipulation. However, there is still an essential need for providing comprehensive design guidelines and further optimizing such devices. In this research, we utilized numerical simulation to study, in detail, insulating posts iDEP technique with the specific application of bioparticles separation. To achieve this, we first developed a robust numerical model to predict the electric and fluid flow fields' distribution, and how bioparticles are being manipulated inside the system. This enabled us to study the fundamental principles of such an iDEP method. In the next step, different design aspects of insulating posts iDEP were investigated. Specifically, we focused on the effect of posts geometry and configuration on the systems' key operation criteria such as the effectiveness of the electric field non-uniformity, the flow velocity distribution and shear stress rates. Furthermore, we studied how different electrodes' setup may affect the electric field distribution and consequently the device performance. Finally, the developed numerical tool was used to demonstrate separation of circulating tumor cells (CTCs) from white blood cells (WBCs). For this purpose, MDA-231 breast cancer cells and Granulocytes were chosen as an indicator of CTCs ad WBCs. Our developed numerical model and presented results lay the groundwork for design and fabrication of high-efficient insulating posts iDEP microchips.
Efficient high-order analysis of bowtie nanoantennas using the locally corrected Nyström method.
Chorsi, Hamid T; Gedney, Stephen D
2015-11-30
It is demonstrated that the Locally Corrected Nyström (LCN) method is a versatile and numerically efficient computational method for the modeling of scattering from plasmonic bowtie nanoantennas. The LCN method is a high-order analysis method that can provide exponential convergence. It is straightforward to implement, accurate and computationally efficient. To the best of the author's knowledge, the high-order LCN is here applied for the first time to 3D nanostructures. Numerical results show the accuracy and efficiency of the LCN applied to the electromagnetic analysis of nanostructures.
Bahşı, Ayşe Kurt; Yalçınbaş, Salih
2016-01-01
In this study, the Fibonacci collocation method based on the Fibonacci polynomials are presented to solve for the fractional diffusion equations with variable coefficients. The fractional derivatives are described in the Caputo sense. This method is derived by expanding the approximate solution with Fibonacci polynomials. Using this method of the fractional derivative this equation can be reduced to a set of linear algebraic equations. Also, an error estimation algorithm which is based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation algorithm. If the exact solution of the problem is not known, the absolute error function of the problems can be approximately computed by using the Fibonacci polynomial solution. By using this error estimation function, we can find improved solutions which are more efficient than direct numerical solutions. Numerical examples, figures, tables are comparisons have been presented to show efficiency and usable of proposed method.
Aviles, B.N.; Sutton, T.M.; Kelly, D.J. III.
1991-09-01
A generalized Runge-Kutta method has been employed in the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic timestep control. The efficiency of the Runge-Kutta method is enhanced by a block-factorization technique that exploits the sparse structure of the matrix system resulting from the space and energy discretized form of the time-dependent neutron diffusion equations. Preliminary numerical evaluation using a one-dimensional finite difference code shows the sparse matrix implementation of the generalized Runge-Kutta method to be highly accurate and efficient when compared to an optimized iterative theta method. 12 refs., 5 figs., 4 tabs.
The Design of CAL Packages for Teaching Numerical Methods to Chemistry Students.
ERIC Educational Resources Information Center
Norris, A. C.
1979-01-01
Discusses the design of computational exercises useful for a course in numerical methods for chemists. Some of the exercises make use of available programs while others require the student to write programs incorporating numerical routines. The emphasis throughout is on the use of numerical methods to solve chemical problems. (Author)
Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids
2006-12-01
numerical solution dictate the practical choice of t∆ 10 ( Chapra and Canale, 1998). Let /B RD dk θ ξ= , where Rξ is a reference concentration per unit...H. A.; Wilkes, J. O. Applied Numerical Methods; Wiley: New York, 1969. Chapra , S. C.; Canale, R. P. Numerical Methods for Engineers with
Taylor, G.; Dong, C.; Sun, S.
2010-03-18
A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods, i.e. mixed finite element (MFE) and the finite volume methods. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocities field for both the fractures and matrix which are crucial to the convection part of the transport equation. The finite volume method and the standard MFE method are used to approximate the convection and dispersion terms respectively. The model is used to investigate the interaction of adsorption with transport and to extract information on effective adsorption distribution coefficients. Numerical examples in different fractured media illustrate the robustness and efficiency of the proposed numerical model.
Numerical modeling of shallow magma intrusions with finite element method
NASA Astrophysics Data System (ADS)
Chen, Tielin; Cheng, Shaozhen; Fang, Qian; Zhou, Cheng
2017-03-01
A numerical approach for simulation of magma intrusion process, considering the couplings of the stress distribution, the viscous fluid flow of magma, and the fracturing of host rock, has been developed to investigate the mechanisms of fracture initiation and propagation in host rock during magma intrusion without pre-placing a set of fractures. The study focused on the dike intrusions filled with injected viscous magma in shallow sediments. A series of numerical modellings were carried out to simulate the process of magma intrusion in host rocks, with particular attention on the magma propagation processes and the formation of intrusion shapes. The model materials were Mohr-Coulomb materials with tension failure and shear failure. The scenarios of both stochastically heterogeneous host rocks and layered host rocks were analyzed. The injected magma formed intrusions shapes of (a) dyke, (b) sill, (c) cup-shaped intrusion, (d) saucer-shaped intrusion. The numerical results were in agreement with the experimental and field observed results, which confirmed the adequacy and the power of the numerical approach.
Numerical Simulation of Turbulent Combustion Using Vortex Methods
1990-01-08
Electric Co., Schenectady, October 1988. 2. DOD and EPA Tyndall Conference on Halon, the Ozone Layer and Research on Alternative Chemicals, Tyndall...26th Aerospace Sciences Meetin , January 11-14, Reno, Nevada, AIAA-88-0729. 13. Ghoniem A.F., and Ng K.K., Numerical study of a forced shear layet
IMPROVED NUMERICAL METHODS FOR MODELING RIVER-AQUIFER INTERACTION.
Tidwell, Vincent Carroll; Sue Tillery; Phillip King
2008-09-01
A new option for Local Time-Stepping (LTS) was developed to use in conjunction with the multiple-refined-area grid capability of the U.S. Geological Survey's (USGS) groundwater modeling program, MODFLOW-LGR (MF-LGR). The LTS option allows each local, refined-area grid to simulate multiple stress periods within each stress period of a coarser, regional grid. This option is an alternative to the current method of MF-LGR whereby the refined grids are required to have the same stress period and time-step structure as the coarse grid. The MF-LGR method for simulating multiple-refined grids essentially defines each grid as a complete model, then for each coarse grid time-step, iteratively runs each model until the head and flux changes at the interfacing boundaries of the models are less than some specified tolerances. Use of the LTS option is illustrated in two hypothetical test cases consisting of a dual well pumping system and a hydraulically connected stream-aquifer system, and one field application. Each of the hypothetical test cases was simulated with multiple scenarios including an LTS scenario, which combined a monthly stress period for a coarse grid model with a daily stress period for a refined grid model. The other scenarios simulated various combinations of grid spacing and temporal refinement using standard MODFLOW model constructs. The field application simulated an irrigated corridor along the Lower Rio Grande River in New Mexico, with refinement of a small agricultural area in the irrigated corridor.The results from the LTS scenarios for the hypothetical test cases closely replicated the results from the true scenarios in the refined areas of interest. The head errors of the LTS scenarios were much smaller than from the other scenarios in relation to the true solution, and the run times for the LTS models were three to six times faster than the true models for the dual well and stream-aquifer test cases, respectively. The results of the field application
An efficient numerical progressive diagonalization scheme for the quantum Rabi model revisited
NASA Astrophysics Data System (ADS)
Pan, Feng; Bao, Lina; Dai, Lianrong; Draayer, Jerry P.
2017-02-01
An efficient numerical progressive diagonalization scheme for the quantum Rabi model is revisited. The advantage of the scheme lies in the fact that the quantum Rabi model can be solved almost exactly by using the scheme that only involves a finite set of one variable polynomial equations. The scheme is especially efficient for a specified eigenstate of the model, for example, the ground state. Some low-lying level energies of the model for several sets of parameters are calculated, of which one set of the results is compared to that obtained from the Braak’s exact solution proposed recently. It is shown that the derivative of the entanglement measure defined in terms of the reduced von Neumann entropy with respect to the coupling parameter does reach the maximum near the critical point deduced from the classical limit of the Dicke model, which may provide a probe of the critical point of the crossover in finite quantum many-body systems, such as that in the quantum Rabi model.
Efficient or inaccurate? Analytical and numerical modelling of random search strategies.
James, Alex; Pitchford, Jonathan W; Plank, Michael J
2010-05-01
A large number of observational and theoretical studies have investigated animal movement strategies for finding randomly located food items. Many of these studies have claimed that a particular strategy is advantageous over other strategies or that the spatial distribution of the food items affects the search efficiency. Here, we study a deliberately idealised problem, in which a blind forager searches for re-visitable food items. We show analytically that the forager's efficiency is completely independent of both its movement strategy and the spatial pattern of the food items and depends only on the density of food in the environment. However, in some cases, apparent optima in search strategies can arise as artefacts of inappropriate and inaccurate numerical simulations. We discuss modifications to the idealised foraging problem that can confer an advantage on certain strategies, including when the forager has some memory or knowledge of the environment; when the food items are non-revisitable; and when the problem is viewed in an evolutionary context.
NASA Astrophysics Data System (ADS)
Bury, Tomasz; Składzień, Jan; Widziewicz, Katarzyna
2010-10-01
The work deals with experimental and numerical thermodynamic analyses of cross-flow finned tube heat exchangers of the gas-liquid type. The aim of the work is to determine an impact of the gas non-uniform inlet on the heat exchangers performance. The measurements have been carried out on a special testing rig and own numerical code has been used for numerical simulations. Analysis of the experimental and numerical results has shown that the range of the non-uniform air inlet to the considered heat exchangers may be significant and it can significantly affect the heat exchanger efficiency.
Botello-Smith, Wesley M; Luo, Ray
2015-10-26
Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membranes into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multigrid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations.
Botello-Smith, Wesley M.; Luo, Ray
2016-01-01
Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966
Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications
2015-06-24
AFRL-AFOSR-VA-TR-2015-0281 Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications Hans Mittelmann...2012 - March 2015 4. TITLE AND SUBTITLE Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications 5a...problems. The size 16 three-dimensional quadratic assignment problem Q3AP from wireless communications was solved using a sophisticated approach
Efficient implementation of minimal polynomial and reduced rank extrapolation methods
NASA Technical Reports Server (NTRS)
Sidi, Avram
1990-01-01
The minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are two effective techniques that have been used in accelerating the convergence of vector sequences, such as those that are obtained from iterative solution of linear and nonlinear systems of equation. Their definitions involve some linear least squares problems, and this causes difficulties in their numerical implementation. Timewise efficient and numerically stable implementations for MPE and RRE are developed. A computer program written in FORTRAN 77 is also appended and applied to some model problems.
Numerical study of reflectance imaging using a parallel Monte Carlo method.
Chen, Cheng; Lu, Jun Q; Li, Kai; Zhao, Suisheng; Brock, R Scott; Hu, Xin-Hua
2007-07-01
Reflectance imaging of biological tissues with visible and near-infrared light has the significant potential to provide a noninvasive and safe imaging modality for diagnosis of dysplastic and malignant lesions in the superficial tissue layers. The difficulty in the extraction of optical and structural parameters lies in the lack of efficient methods for accurate modeling of light scattering in biological tissues of turbid nature. We present a parallel Monte Carlo method for accurate and efficient modeling of reflectance images from turbid tissue phantoms. A parallel Monte Carlo code has been developed with the message passing interface and evaluated on a computing cluster with 16 processing elements. The code was validated against the solutions of the radiative transfer equation on the bidirectional reflection and transmission functions. With this code we investigated numerically the dependence of reflectance image on the imaging system and phantom parameters. The contrasts of reflectance images were found to be nearly independent of the numerical aperture (NA) of the imaging camera despite the fact that reflectance depends on the NA. This enables efficient simulations of the reflectance images using an NA at 1.00. Using heterogeneous tissue phantoms with an embedded region simulating a lesion, we investigated the correlation between the reflectance image profile or contrast and the phantom parameters. It has been shown that the image contrast approaches 0 when the single-scattering albedos of the two regions in the heterogeneous phantoms become matched. Furthermore, a zone of detection has been demonstrated for determination of the thickness of the embedded region and optical parameters from the reflectance image profile and contrast. Therefore, the utility of the reflectance imaging method with visible and near-infrared light has been firmly established. We conclude from these results that the optical parameters of the embedded region can be determined inversely
Papadopoulos, D F; Anastassi, Z A; Simos, T E
2010-08-01
A new Runge-Kutta-Nyström method, with phase-lag and amplification error of order infinity, for the numerical solution of the Schrödinger equation is developed in this paper. The new method is based on the Runge-Kutta-Nyström method with fourth algebraic order, developed by Dormand, El-Mikkawy and Prince. Numerical illustrations indicate that the new method is much more efficient than other methods derived for the same purpose.
Method for computationally efficient design of dielectric laser accelerator structures
Hughes, Tyler; Veronis, Georgios; Wootton, Kent P.; ...
2017-06-22
Here, dielectric microstructures have generated much interest in recent years as a means of accelerating charged particles when powered by solid state lasers. The acceleration gradient (or particle energy gain per unit length) is an important figure of merit. To design structures with high acceleration gradients, we explore the adjoint variable method, a highly efficient technique used to compute the sensitivity of an objective with respect to a large number of parameters. With this formalism, the sensitivity of the acceleration gradient of a dielectric structure with respect to its entire spatial permittivity distribution is calculated by the use of onlymore » two full-field electromagnetic simulations, the original and ‘adjoint’. The adjoint simulation corresponds physically to the reciprocal situation of a point charge moving through the accelerator gap and radiating. Using this formalism, we perform numerical optimizations aimed at maximizing acceleration gradients, which generate fabricable structures of greatly improved performance in comparison to previously examined geometries.« less
NASA Technical Reports Server (NTRS)
Thompson, J. F.; Mcwhorter, J. C.; Siddiqi, S. A.; Shanks, S. P.
1973-01-01
Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.
Simulation of intra-aneurysmal blood flow by different numerical methods.
Weichert, Frank; Walczak, Lars; Fisseler, Denis; Opfermann, Tobias; Razzaq, Mudassar; Münster, Raphael; Turek, Stefan; Grunwald, Iris; Roth, Christian; Veith, Christian; Wagner, Mathias
2013-01-01
The occlusional performance of sole endoluminal stenting of intracranial aneurysms is controversially discussed in the literature. Simulation of blood flow has been studied to shed light on possible causal attributions. The outcome, however, largely depends on the numerical method and various free parameters. The present study is therefore conducted to find ways to define parameters and efficiently explore the huge parameter space with finite element methods (FEMs) and lattice Boltzmann methods (LBMs). The goal is to identify both the impact of different parameters on the results of computational fluid dynamics (CFD) and their advantages and disadvantages. CFD is applied to assess flow and aneurysmal vorticity in 2D and 3D models. To assess and compare initial simulation results, simplified 2D and 3D models based on key features of real geometries and medical expert knowledge were used. A result obtained from this analysis indicates that a combined use of the different numerical methods, LBM for fast exploration and FEM for a more in-depth look, may result in a better understanding of blood flow and may also lead to more accurate information about factors that influence conditions for stenting of intracranial aneurysms.
Simulation of Intra-Aneurysmal Blood Flow by Different Numerical Methods
Weichert, Frank; Walczak, Lars; Fisseler, Denis; Opfermann, Tobias; Münster, Raphael; Grunwald, Iris; Roth, Christian; Veith, Christian; Wagner, Mathias
2013-01-01
The occlusional performance of sole endoluminal stenting of intracranial aneurysms is controversially discussed in the literature. Simulation of blood flow has been studied to shed light on possible causal attributions. The outcome, however, largely depends on the numerical method and various free parameters. The present study is therefore conducted to find ways to define parameters and efficiently explore the huge parameter space with finite element methods (FEMs) and lattice Boltzmann methods (LBMs). The goal is to identify both the impact of different parameters on the results of computational fluid dynamics (CFD) and their advantages and disadvantages. CFD is applied to assess flow and aneurysmal vorticity in 2D and 3D models. To assess and compare initial simulation results, simplified 2D and 3D models based on key features of real geometries and medical expert knowledge were used. A result obtained from this analysis indicates that a combined use of the different numerical methods, LBM for fast exploration and FEM for a more in-depth look, may result in a better understanding of blood flow and may also lead to more accurate information about factors that influence conditions for stenting of intracranial aneurysms. PMID:23662158
Numerical methods for multiphysics, multiphase, and multicomponent models for fuel cells
NASA Astrophysics Data System (ADS)
Xue, Guangri
In this dissertation, we design and analyze efficient numerical methods for obtaining accurate solutions to model problems arising in fuel cells. A basic fuel cell model consists of five principles of conservation, namely, mass, momentum, species, charges (electrons and ions), and thermal energy. Overall, transport equations couple with electrochemical processes through source terms to describe reaction kinetics and electro-osmotic drag in the polymer electrolyte. To model multiphase species transport in the porous media and the gas channel of fuel cells, we consider a multiphase mixture model framework. The diffusivity of the two-phase mixture water conservation equation in this model is nonlinear, discontinuous, and degenerate. To handle this difficulty, we developed efficient and fast nonlinear iterative solvers based on the Kirchhoff transformation and nonlinear Dirichlet-Neumann domain decomposition methods. To model the coupling between the multiphase flow in the porous media and the viscous flow in the gas channel of fuel cells, we consider the Darcy-Stokes-Brinkman model, which treats both the Darcy equation and the Stokes equation in a single form of partial differential equation (PDE) but with strongly discontinuous viscosity and permeability coefficients. For this model, we develop robust finite element methods that are uniformly stable with respect to the highly discontinuous coefficients and their jumps. Finally, we develop new numerical methods for the full steady-state 3D multi-physics simulation of liquid-feed direct methanol fuel cells (DMFC), consisting of five fundamental conservation equations: mass, momentum, species, charges, and thermal energy. Fast convergence of nonlinear iteration is achieved in our method.
Advanced Numerical Methods for Three-Dimensional Parallel Hybrid MHD/PIC.
1996-10-31
energy density plasmas . Prototype problems include studies of physical systems encountered in advanced weapons, space propulsion thrusters, pulsed power...We have developed, implemented, and applied coupled Eulerican/Lagrangian computational models for efficient parallel numerical simulation of high
Subleading poles in the numerical unitarity method at two loops
NASA Astrophysics Data System (ADS)
Abreu, S.; Febres Cordero, F.; Ita, H.; Jaquier, M.; Page, B.
2017-05-01
We describe the unitarity approach for the numerical computation of two-loop integral coefficients of scattering amplitudes. It is well known that the leading propagator singularities of an amplitude's integrand are related to products of tree amplitudes. At two loops, Feynman diagrams with doubled propagators appear naturally, which lead to subleading pole contributions. In general, it is not known how these contributions can be directly expressed in terms of a product of on-shell tree amplitudes. We present a universal algorithm to extract these subleading pole terms by releasing some of the on-shell conditions. We demonstrate the new approach by numerically computing two-loop four-gluon integral coefficients.
A method for direct numerical integration of the Boltzmann equation
NASA Technical Reports Server (NTRS)
Cheremisin, F. G.
1972-01-01
The principal difficulties in numerical solution of the Boltzmann equation are considered. The study is aimed at formulating a numerical solution in such a manner that it contains a minimum amount of excess information at the distribution function level. It is pointed out that the accurate calculation of the distribution function at each point in phase space requires a tremendous number of operations, due to the necessity of solving five-fold quadratures in the collision integral. This results in the operational memory of the digital computer being insufficient to store all the data on the distribution functions at the necessary points in phase space. An algorithm is constructed involving successive iterations of the Boltzmann equation which does not require storage of each step of the new distribution function.
Some variance reduction methods for numerical stochastic homogenization.
Blanc, X; Le Bris, C; Legoll, F
2016-04-28
We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here.
Efficient hybrid-symbolic methods for quantum mechanical calculations
NASA Astrophysics Data System (ADS)
Scott, T. C.; Zhang, Wenxing
2015-06-01
We present hybrid symbolic-numerical tools to generate optimized numerical code for rapid prototyping and fast numerical computation starting from a computer algebra system (CAS) and tailored to any given quantum mechanical problem. Although a major focus concerns the quantum chemistry methods of H. Nakatsuji which has yielded successful and very accurate eigensolutions for small atoms and molecules, the tools are general and may be applied to any basis set calculation with a variational principle applied to its linear and non-linear parameters.
Variable inertia method: A novel numerical method for mantle convection simulation
NASA Astrophysics Data System (ADS)
Takeyama, Kosuke; Saitoh, Takayuki R.; Makino, Junichiro
2017-01-01
3D numerical simulations have been very useful for the understanding of mantle convection of the earth. In almost all previous simulations of mantle convection, the (extended) Boussinesq approximation has been used. This method is implicit in the sense that buoyancy force and viscosity are balanced, and allows the use of long timesteps that are not limited by the CFL condition. However, the resulting matrix is ill-conditioned, in particular since the viscosity strongly depends on the temperature. It is not well-suited to modern large-scale parallel machines. In this paper, we propose an explicit method which can be used to solve the mantle convection problem. If we can reduce the sound speed without changing the characteristics of the flow, we can increase the timestep and thus can use the explicit method. In order to reduce the sound speed, we multiplied the inertia term of the equation of motion by a large and viscosity-dependent coefficient. Theoretically, we can expect that this modification would not change the flow as long as the Reynolds number and the Mach number are sufficiently smaller than unity. We call this method the variable inertia method (VIM). We have performed an extensive set of numerical tests of the proposed method for thermal convection, and concluded that it works well. In particular, it can handle differences in viscosity of more than five orders of magnitude.
Methods, Software and Tools for Three Numerical Applications. Final report
E. R. Jessup
2000-03-01
This is a report of the results of the authors work supported by DOE contract DE-FG03-97ER25325. They proposed to study three numerical problems. They are: (1) the extension of the PMESC parallel programming library; (2) the development of algorithms and software for certain generalized eigenvalue and singular value (SVD) problems, and (3) the application of techniques of linear algebra to an information retrieval technique known as latent semantic indexing (LSI).
Numerical conformal mapping: Methods, applications, and theory. Final report
DeLillo, T.K.
1995-11-01
Section 1 of this report, briefly summarizes research performed under this grant during the first two years 1992 to 1994 and makes some overall remarks. Section 2, summarizes research performed during the final year from September, 1994 through May 31, 1995, more fully. The main achievement of the last period has been the application of numerical conformed mapping to the solution of the biharmonic equation. Section 3, summarizes travel, meetings, and other expenses supported by this grant during the final year.
Improved numerical methods for turbulent viscous recirculating flows
NASA Technical Reports Server (NTRS)
Turan, A.
1985-01-01
The hybrid-upwind finite difference schemes employed in generally available combustor codes possess excessive numerical diffusion errors which preclude accurate quantative calculations. The present study has as its primary objective the identification and assessment of an improved solution algorithm as well as discretization schemes applicable to analysis of turbulent viscous recirculating flows. The assessment is carried out primarily in two dimensional/axisymetric geometries with a view to identifying an appropriate technique to be incorporated in a three-dimensional code.
Mapping methods for computationally efficient and accurate structural reliability
NASA Technical Reports Server (NTRS)
Shiao, Michael C.; Chamis, Christos C.
1992-01-01
Mapping methods are developed to improve the accuracy and efficiency of probabilistic structural analyses with coarse finite element meshes. The mapping methods consist of the following: (1) deterministic structural analyses with fine (convergent) finite element meshes; (2) probabilistic structural analyses with coarse finite element meshes; (3) the relationship between the probabilistic structural responses from the coarse and fine finite element meshes; and (4) a probabilistic mapping. The results show that the scatter in the probabilistic structural responses and structural reliability can be efficiently predicted using a coarse finite element model and proper mapping methods with good accuracy. Therefore, large structures can be efficiently analyzed probabilistically using finite element methods.
An efficient method for computation of the manipulator inertia matrix
NASA Technical Reports Server (NTRS)
Fijany, Amir; Bejczy, Antal K.
1989-01-01
An efficient method of computation of the manipulator inertia matrix is presented. Using spatial notations, the method leads to the definition of the composite rigid-body spatial inertia, which is a spatial representation of the notion of augmented body. The previously proposed methods, the physical interpretations leading to their derivation, and their redundancies are analyzed. The proposed method achieves a greater efficiency by eliminating the redundancy in the intrinsic equations as well as by a better choice of coordinate frame for their projection. In this case, removing the redundancy leads to greater efficiency of the computation in both serial and parallel senses.
Overview: Applications of numerical optimization methods to helicopter design problems
NASA Technical Reports Server (NTRS)
Miura, H.
1984-01-01
There are a number of helicopter design problems that are well suited to applications of numerical design optimization techniques. Adequate implementation of this technology will provide high pay-offs. There are a number of numerical optimization programs available, and there are many excellent response/performance analysis programs developed or being developed. But integration of these programs in a form that is usable in the design phase should be recognized as important. It is also necessary to attract the attention of engineers engaged in the development of analysis capabilities and to make them aware that analysis capabilities are much more powerful if integrated into design oriented codes. Frequently, the shortcoming of analysis capabilities are revealed by coupling them with an optimization code. Most of the published work has addressed problems in preliminary system design, rotor system/blade design or airframe design. Very few published results were found in acoustics, aerodynamics and control system design. Currently major efforts are focused on vibration reduction, and aerodynamics/acoustics applications appear to be growing fast. The development of a computer program system to integrate the multiple disciplines required in helicopter design with numerical optimization technique is needed. Activities in Britain, Germany and Poland are identified, but no published results from France, Italy, the USSR or Japan were found.
Numerical simulations of non-equilibrium shock layers with efficient implicit schemes
NASA Technical Reports Server (NTRS)
Cambier, Jean-Luc; Prabhu, Dinesh K.
1992-01-01
Current and future calculations of nonequilibrium shock layers require the use of a very large number of equations, due to a multiplicity of chemical species, excited states, and internal energy modes. The computational cost associated with the use of standard implicit methods becomes prohibitive; it is therefore desirable to examine the potential of several methods and determine if any can be projected to be more efficient and accurate for large systems of equations. Here, the performance of several implicit schemes on several simple practical examples of reacting flows is examined. The Euler equations are solved by three different implicit methods, and two methods of coupling between the fluid dynamics and the chemistry are studied. Several cases of stiffness are considered and both 1D and 2D examples are computed.
Vernekar, R; Krüger, T
2015-09-01
We investigate the effect of particle volume fraction on the efficiency of deterministic lateral displacement (DLD) devices. DLD is a popular passive sorting technique for microfluidic applications. Yet, it has been designed for treating dilute suspensions, and its efficiency for denser samples is not well known. We perform 3D simulations based on the immersed-boundary, lattice-Boltzmann and finite-element methods to model the flow of red blood cells (RBCs) in different DLD devices. We quantify the DLD efficiency in terms of appropriate "failure" probabilities and RBC counts in designated device outlets. Our main result is that the displacement mode breaks down upon an increase of RBC volume fraction, while the zigzag mode remains relatively robust. This suggests that the separation of larger particles (such as white blood cells) from a dense RBC background is simpler than separating smaller particles (such as platelets) from the same background. The observed breakdown stems from non-deterministic particle collisions interfering with the designed deterministic nature of DLD devices. Therefore, we postulate that dense suspension effects generally hamper efficient particle separation in devices based on deterministic principles.
Numerical simulation of diffusion MRI signals using an adaptive time-stepping method
NASA Astrophysics Data System (ADS)
Li, Jing-Rebecca; Calhoun, Donna; Poupon, Cyril; Le Bihan, Denis
2014-01-01
The effect on the MRI signal of water diffusion in biological tissues in the presence of applied magnetic field gradient pulses can be modelled by a multiple compartment Bloch-Torrey partial differential equation. We present a method for the numerical solution of this equation by coupling a standard Cartesian spatial discretization with an adaptive time discretization. The time discretization is done using the explicit Runge-Kutta-Chebyshev method, which is more efficient than the forward Euler time discretization for diffusive-type problems. We use this approach to simulate the diffusion MRI signal from the extra-cylindrical compartment in a tissue model of the brain gray matter consisting of cylindrical and spherical cells and illustrate the effect of cell membrane permeability.
Numerical simulation of diffusion MRI signals using an adaptive time-stepping method.
Li, Jing-Rebecca; Calhoun, Donna; Poupon, Cyril; Le Bihan, Denis
2014-01-20
The effect on the MRI signal of water diffusion in biological tissues in the presence of applied magnetic field gradient pulses can be modelled by a multiple compartment Bloch-Torrey partial differential equation. We present a method for the numerical solution of this equation by coupling a standard Cartesian spatial discretization with an adaptive time discretization. The time discretization is done using the explicit Runge-Kutta-Chebyshev method, which is more efficient than the forward Euler time discretization for diffusive-type problems. We use this approach to simulate the diffusion MRI signal from the extra-cylindrical compartment in a tissue model of the brain gray matter consisting of cylindrical and spherical cells and illustrate the effect of cell membrane permeability.
Sun, Jiasong; Chen, Qian; Zhang, Yuzhen; Zuo, Chao
2016-03-15
In this Letter, an accurate and highly efficient numerical phase aberration compensation method is proposed for digital holographic microscopy. Considering that most parts of the phase aberration resides in the low spatial frequency domain, a Fourier-domain mask is introduced to extract the aberrated frequency components, while rejecting components that are unrelated to the phase aberration estimation. Principal component analysis (PCA) is then performed only on the reduced-sized spectrum, and the aberration terms can be extracted from the first principal component obtained. Finally, by oversampling the reduced-sized aberration terms, the precise phase aberration map is obtained and thus can be compensated by multiplying with its conjugation. Because the phase aberration is estimated from the limited but more relevant raw data, the compensation precision is improved and meanwhile the computation time can be significantly reduced. Experimental results demonstrate that our proposed technique could achieve both high compensating accuracy and robustness compared with other developed compensation methods.
NASA Astrophysics Data System (ADS)
Mittal, R. C.; Jiwari, Ram
2011-01-01
In this paper, a rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical study of a two-dimensional reaction-diffusion Brusselator system. In the Brusselator system the reaction terms arise from the mathematical modeling of chemical systems such as in enzymatic reactions, and in plasma and laser physics in multiple coupling between modes. By employing DQM, accurate results can be obtained using fewer grid points in spatial domain for a large value of T = 50. We also found that Chebyshev-Gauss-Lobatto grid points give excellent results in comparison to other grid points such as uniform grid points. Three examples are solved to illustrate the accuracy and efficiency of the DQM. Convergence and stability of the method is also examined.
NASA Astrophysics Data System (ADS)
Varado, N.; Braud, I.; Ross, P. J.
2003-04-01
5; but was generally less than 10%. The study also showed that the Lai and Katul (2000) model formulation was not adapted for sandy soils. Twice less water than the Li model could be extracted on sandy soils. The comparison of the two root modules with the initial version of SiSPAT shows that the Lai model was unable to extract as water as the initial SiSPAT or the Li model, even when changing the sensitive parameters. As a conclusion the new numerical method coupled with the Li et al. (2001) model provides an efficient and accurate solution for inclusion of a physically-based infiltration-evapotranspiration module into larger scale watershed models.
NASA Astrophysics Data System (ADS)
Nagel, T.; Böttcher, N.; Görke, U. J.; Kolditz, O.
2014-12-01
The design process of geotechnical installations includes the application of numerical simulation tools for safety assessment, dimensioning and long term effectiveness estimations. Underground salt caverns can be used for the storage of natural gas, hydrogen, oil, waste or compressed air. For their design one has to take into account fluctuating internal pressures due to different levels of filling, the stresses imposed by the surrounding rock mass, irregular geometries and possibly heterogeneous material properties [3] in order to estimate long term cavern convergence as well as locally critical wall stresses. Constitutive models applied to rock salt are usually viscoplastic in nature and most often based on a Burgers-type rheological model extended by non-linear viscosity functions and/or plastic friction elements. Besides plastic dilatation, healing and damage are sometimes accounted for as well [2]. The scales of the geotechnical system to be simulated and the laboratory tests from which material parameters are determined are vastly different. The most common material testing modalities to determine material parameters in geoengineering are the uniaxial and the triaxial compression tests. Some constitutive formulations in widespread use are formulated based on equivalent rather than tensorial quantities valid under these specific test conditions and are subsequently applied to heterogeneous underground systems and complex 3D load cases. We show here that this procedure is inappropriate and can lead to erroneous results. We further propose alternative formulations of the constitutive models in question that restore their validity under arbitrary loading conditions. For an efficient numerical simulation, the discussed constitutive models are integrated locally with a Newton-Raphson algorithm that directly provides the algorithmically consistent tangent matrix for the global Newton iteration of the displacement based finite element formulation. Finally, the finite
Numerical Study of Boundary Layer Interaction with Shocks: Method Improvement and Test Computation
NASA Technical Reports Server (NTRS)
Adams, N. A.
1995-01-01
The objective is the development of a high-order and high-resolution method for the direct numerical simulation of shock turbulent-boundary-layer interaction. Details concerning the spatial discretization of the convective terms can be found in Adams and Shariff (1995). The computer code based on this method as introduced in Adams (1994) was formulated in Cartesian coordinates and thus has been limited to simple rectangular domains. For more general two-dimensional geometries, as a compression corner, an extension to generalized coordinates is necessary. To keep the requirements or limitations for grid generation low, the extended formulation should allow for non-orthogonal grids. Still, for simplicity and cost efficiency, periodicity can be assumed in one cross-flow direction. For easy vectorization, the compact-ENO coupling algorithm as used in Adams (1994) treated whole planes normal to the derivative direction with the ENO scheme whenever at least one point of this plane satisfied the detection criterion. This is apparently too restrictive for more general geometries and more complex shock patterns. Here we introduce a localized compact-ENO coupling algorithm, which is efficient as long as the overall number of grid points treated by the ENO scheme is small compared to the total number of grid points. Validation and test computations with the final code are performed to assess the efficiency and suitability of the computer code for the problems of interest. We define a set of parameters where a direct numerical simulation of a turbulent boundary layer along a compression corner with reasonably fine resolution is affordable.
Efficient modelling of gravity effects due to topographic masses using the Gauss-FFT method
NASA Astrophysics Data System (ADS)
Wu, Leyuan
2016-04-01
We present efficient Fourier-domain algorithms for modelling gravity effects due to topographic masses. The well-known Parker's formula originally based on the standard fast Fourier transform (FFT) algorithm is modified by applying the Gauss-FFT method instead. Numerical precision of the forward and inverse Fourier transforms embedded in Parker's formula and its extended forms are significantly improved by the Gauss-FFT method. The topographic model is composed of two major aspects, the geometry and the density. Versatile geometric representations, including the mass line model, the mass prism model, the polyhedron model and smoother topographic models interpolated from discrete data sets using high-order splines or pre-defined by analytical functions, in combination with density distributions that vary both laterally and vertically in rather arbitrary ways following exponential or general polynomial functions, now can be treated in a consistent framework by applying the Gauss-FFT method. The method presented has been numerically checked by space-domain analytical and hybrid analytical/numerical solutions already established in the literature. Synthetic and real model tests show that both the Gauss-FFT method and the standard FFT method run much faster than space-domain solutions, with the Gauss-FFT method being superior in numerical accuracy. When truncation errors are negligible, the Gauss-FFT method can provide forward results almost identical to space-domain analytical or semi-numerical solutions in much less time.
NASA Astrophysics Data System (ADS)
Chen, Jiefu
2015-03-01
A discontinuous Galerkin finite element method is employed to study the responses of microresistivity imaging tools used in the oil and gas exploration industry. The multiscale structure of an imaging problem is decomposed into several nested subdomains based on its geometric characteristics. Each subdomain is discretized independently, and numerical flux is used to couple all subdomains together. The nested domain decomposition scheme will lead to a block tridiagonal linear system, and the block Thomas algorithm is utilized here to eliminate the subdomain based iteration in the step of solving the linear system. Numerical results demonstrate the validity and efficiency of this method.
Sources of Chaos in Planetary Systems Formed Through Numerical Methods
NASA Astrophysics Data System (ADS)
Clement, Matthew S.
2017-01-01
The formation of the solar system’s terrestrial planets has been numerically modeled in countless works, and many other studies have been devoted to char- acterizing our modern planets’ chaotic dynamical state. However, it is still not known whether our planets fragile chaotic state is an expected outcome of terrestrial planet accretion. We use a large suite of numerical simulations to present a detailed analysis and characterization of the dynamical chaos in 145 different systems produced via terrestrial planet formation in Kaib & Cowan (2015). These systems were created in the presence of a fully formed Jupiter and Saturn, using a variety of different initial conditions. We provide the first analysis of the dynamical states of fully evolved (4.5 Gyr) planetary systems formed using numerical simulations. We find that dynamical chaos is preva- lent in roughly half of the systems, with the largest source of the chaos being perturbations from Jupiter. Chaos is most prevalent in systems that form 4 or 5 terrestrial planets. Additionally, an eccentric Jupiter and Saturn is shown to enhance the prevalence of chaos in systems. Furthermore, systems with a center of mass highly concentrated between 0.8-1.2 AU generally prove to be less chaotic than systems with more exotic mass distributions. Through the process of evolving systems to the current epoch, we show that late instabilities are quite common in our systems. Of greatest interest, many of the sources of chaos observed in our own solar system (such as the secularly driven chaos between Mercury and Jupiter) are shown to be common outcomes of terrestrial planetary formation. Thus, the solar system’s marginally stable, chaotic state may naturally arise from the process of terrestrial planet formation.
Numerical methods for a general class of porous medium equations
Rose, M. E.
1980-03-01
The partial differential equation par. deltau/par. deltat + par. delta(f(u))/par. deltax = par. delta(g(u)par. deltau/par. deltax)/par. deltax, where g(u) is a non-negative diffusion coefficient that may vanish for one or more values of u, was used to model fluid flow through a porous medium. Error estimates for a numerical procedure to approximate the solution are derived. A revised version of this report will appear in Computers and Mathematics with Applications.
Magnetohydrodynamic (MHD) modelling of solar active phenomena via numerical methods
NASA Technical Reports Server (NTRS)
Wu, S. T.
1988-01-01
Numerical ideal MHD models for the study of solar active phenomena are summarized. Particular attention is given to the following physical phenomena: (1) local heating of a coronal loop in an isothermal and stratified atmosphere, and (2) the coronal dynamic responses due to magnetic field movement. The results suggest that local heating of a magnetic loop will lead to the enhancement of the density of the neighboring loops through MHD wave compression. It is noted that field lines can be pinched off and may form a self-contained magnetized plasma blob that may move outward into interplanetary space.
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Rashidi, Mohammad Mehdi
2016-04-01
In this paper, we propose a modified cubic B-spline differential quadrature method (MCB-DQM) to solve three-dimensional (3D) coupled viscous Burger equation with appropriate initial and boundary conditions. In this method, modified cubic B-spline is treated as a basis function in the differential quadrature method (DQM) to compute the weighting coefficients. In this way, the Burger equation is reduced into a system of ordinary differential equations. An optimal strong stability-preserving Runge-Kutta (SSP-RK) method is employed to solve the resulting system of ordinary differential equations. In order to illustrate the accuracy and efficiency of the proposed method, a numerical problem is considered. From the numerical experiment, it is found that the computed result is in good agreement with the exact solution. Stability analysis of the method is also carried out using the matrix stability analysis method and found to be unconditionally stable.
Comparison of induction motor field efficiency evaluation methods
Hsu, J.S.; Kueck, J.D.; Olszewski, M.; Casada, D.A.; Otaduy, P.J.; Tolbert, L.M.
1996-10-01
Unlike testing motor efficiency in a laboratory, certain methods given in the IEEE-Std 112 cannot be used for motor efficiency in the field. For example, it is difficult to load a motor in the field with a dynamometer when the motor is already coupled to driven equipment. The motor efficiency field evaluation faces a different environment from that for which the IEEE-Std 112 is chiefly written. A field evaluation method consists of one or several basic methods according to their physical natures. Their intrusivenesses and accuracies are also discussed. This study is useful for field engineers to select or to establish a proper efficiency evaluation method by understanding the theories and error sources of the methods.
Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case
Fernández-Nieto, Enrique D.
2014-05-01
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.
An efficient numerical technique for the solution of the monodomain and bidomain equations.
Whiteley, Jonathan P
2006-11-01
Most numerical schemes for solving the monodomain or bidomain equations use a forward approximation to some or all of the time derivatives. This approach, however, constrains the maximum timestep that may be used by stability considerations as well as accuracy considerations. Stability may be ensured by using a backward approximation to all time derivatives, although this approach requires the solution of a very large system of nonlinear equations at each timestep which is computationally prohibitive. In this paper we propose a semi-implicit algorithm that ensures stability. A linear system is solved on each timestep to update the transmembrane potential and, if the bidomain equations are being used, the extracellular potential. The remainder of the equations to be solved uncouple into small systems of ordinary differential equations. The backward Euler method may be used to solve these systems and guarantee numerical stability: as these systems are small, only the solution of small nonlinear systems are required. Simulations are carried out to show that the use of this algorithm allows much larger timesteps to be used with only a minimal loss of accuracy. As a result of using these longer timesteps the computation time may be reduced substantially.
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.
2003-01-01
The generalization of a class of low-dissipative high order filter finite difference schemes for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been developed. The new scheme consists of a divergence free preserving high order spatial base scheme with a filter approach which can be divergence-free preserving depending on the type of filter operator being used, the method of applying the filter step, and the type of flow problem to be considered. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field (Delta * B) numerical error in the sense that no standard divergence cleaning is required. Performance evaluation of these variants, and the key role that the proper treatment of their corresponding numerical boundary conditions can play will be illustrated. Many levels of grid refinement and detailed comparison with several commonly used compressible MHD shock-capturing schemes will be sought. For certain MHD 2-D test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.
A 2D strain estimator with numerical optimization method for soft-tissue elastography.
Liu, Ke; Zhang, Pengfei; Shao, Jinhua; Zhu, Xinjian; Zhang, Yun; Bai, Jing
2009-12-01
Elastography is a bioelasticity-based imaging modality which has been proved to be a potential evaluation tool to detect the tissue abnormalities. Conventional method for elastography is to estimate the displacement based on cross-correlation technique firstly, then strain profile is calculated as the gradient of the displacement. The main problem of this method arises from the fact that the cross-correlation between pre- and post-compression signals will be decreased because of the signal's compression-to-deformation. It may constrain the estimation of the displacement. Numerical optimization, as an efficient tool to estimate the non-rigid deformation in image registration, has its potential to achieve the elastogram. This paper incorporates the idea of image registration into elastography and proposes a radio frequency (RF) signal registration strain estimator based on the minimization of a cost function using numerical optimization method with Powell algorithm (NOMPA). To evaluate the proposed scheme, the simulation data with a hard inclusion embedded in the homogeneous background is produced for analysis. NOMPA can obtain the displacement profiles and strain profiles simultaneously. When compared with the cross-correlation based method, NOMPA presents better signal-to-noise ratio (SNR, 32.6+/-1.5 dB vs. 23.8+/-1.1 dB) and contrast-to-noise ratio (CNR, 28.8+/-1.8 dB vs. 21.7+/-0.9 dB) in axial normal strain estimation. The in vitro experiment of porcine liver with ethanol-induced lesion is also studied. The statistic results of SNR and CNR indicate that strain profiles by NOMPA performs better anti-noise and target detectability than that by cross-correlation based method. Though NOMPA carry a heavier computational burden than cross-correlation based method, it may be an useful method to obtain 2D strains in elastography.