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Relevant bibliographies by topics / Linear equations; Schwarz methods

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Academic literature on the topic 'Linear equations; Schwarz methods'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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Journal articles on the topic "Linear equations; Schwarz methods"

1

Antonietti, Paola F., Blanca Ayuso de Dios, Susanne C. Brenner, and Li-yeng Sung. "Schwarz Methods for a Preconditioned WOPSIP Method for Elliptic Problems." Computational Methods in Applied Mathematics 12, no. 3 (2012): 241–72. http://dx.doi.org/10.2478/cmam-2012-0021.

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Abstract We propose and analyze several two-level non-overlapping Schwarz methods for a preconditioned weakly over-penalized symmetric interior penalty (WOPSIP) discretization of a second order boundary value problem. We show that the preconditioners are scalable and that the condition number of the resulting preconditioned linear systems of equations is independent of the penalty parameter and is of order H/h, where H and h represent the mesh sizes of the coarse and fine partitions, respectively. Numerical experiments that illustrate the performance of the proposed two-level Schwarz methods a

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Nagid, Nabila, and Hassan Belhadj. "New approach for accelerating the nonlinear Schwarz iterations." Boletim da Sociedade Paranaense de Matemática 38, no. 4 (2019): 51–69. http://dx.doi.org/10.5269/bspm.v38i4.37018.

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The vector Epsilon algorithm is an effective extrapolation method used for accelerating the convergence of vector sequences. In this paper, this method is used to accelerate the convergence of Schwarz iterative methods for stationary linear and nonlinear partial differential equations (PDEs). The vector Epsilon algorithm is applied to the vector sequences produced by additive Schwarz (AS) or restricted additive Schwarz (RAS) methods after discretization. Some convergence analysis is presented, and several test-cases of analytical problems are performed in order to illustrate the interest of su

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Antoine, Xavier, Fengji Hou, and Emmanuel Lorin. "Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 4 (2018): 1569–96. http://dx.doi.org/10.1051/m2an/2017048.

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This paper is devoted to the analysis of convergence of Schwarz Waveform Relaxation (SWR) domain decomposition methods (DDM) for solving the stationary linear and nonlinear Schrödinger equations by the imaginary-time method. Although SWR are extensively used for numerically solving high-dimensional quantum and classical wave equations, the analysis of convergence and of the rate of convergence is still largely open for linear equations with variable coefficients and nonlinear equations. The aim of this paper is to tackle this problem for both the linear and nonlinear Schrödinger equations in t

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Wu, Shu-Lin. "Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/474608.

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We are interested in solving heat equations with nonlinear dynamical boundary conditions by using domain decomposition methods. In the classical framework, one first discretizes the time direction and then solves a sequence of state steady problems by the domain decomposition method. In this paper, we consider the heat equations at spacetime continuous level and study a Schwarz waveform relaxation algorithm for parallel computation purpose. We prove the linear convergence of the algorithm on long time intervals and show how the convergence rate depends on the size of overlap and the nonlineari

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Antoine, X., and E. Lorin. "An analysis of Schwarz waveform relaxation domain decomposition methods for the imaginary-time linear Schrödinger and Gross-Pitaevskii equations." Numerische Mathematik 137, no. 4 (2017): 923–58. http://dx.doi.org/10.1007/s00211-017-0897-3.

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Lapenta, Giovanni, and Wei Jiang. "Implicit Temporal Discretization and Exact Energy Conservation for Particle Methods Applied to the Poisson–Boltzmann Equation." Plasma 1, no. 2 (2018): 242–58. http://dx.doi.org/10.3390/plasma1020021.

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We report on a new multiscale method approach for the study of systems with wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson–Boltzmann equation that describes the long-range forces using the Boltzmann formula (i.e., we assume the medium to be in quasi local thermal equilibrium). We develop a new approach where fields and particle information (mediated by the equations for their moments) are solved self-consistently. The new approach is implicit and numerically stable, providing exact energy

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Гурьева, Я. Л., and В. П. Ильин. "On acceleration technologies of parallel decomposition methods." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 1 (April 2, 2015): 146–54. http://dx.doi.org/10.26089/nummet.v16r115.

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Одним из главных препятствий масштабированному распараллеливанию алгебраических методов декомпозиции для решения сверхбольших разреженных систем линейных алгебраических уравнений (СЛАУ) является замедление скорости сходимости аддитивного итерационного алгоритма Шварца в подпространствах Крылова при увеличении количества подобластей. Целью настоящей статьи является сравнительный экспериментальный анализ различных приeмов ускорения итераций: параметризованное пересечение подобластей, использование специальных интерфейсных условий на границах смежных подобластей, а также применение грубосеточной

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Zhou, H., and H. A. A. Tchelepi. "Two-Stage Algebraic Multiscale Linear Solver for Highly Heterogeneous Reservoir Models." SPE Journal 17, no. 02 (2012): 523–39. http://dx.doi.org/10.2118/141473-pa.

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Summary An efficient Two-Stage Algebraic Multiscale Solver (TAMS) that converges to the fine-scale solution is described. The first (global) stage is a multiscale solution obtained algebraically for the given fine-scale problem. In the second stage, a local preconditioner, such as the Block ILU (BILU), or the Additive Schwarz (AS) method is used. Spectral analysis shows that the multiscale solution step captures the low-frequency parts of the error spectrum quite well, while the local preconditioner represents the high-frequency components accurately. Combining the two stages in an iterative s

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Kong, Fande, and Xiao-Chuan Cai. "Scalability study of an implicit solver for coupled fluid-structure interaction problems on unstructured meshes in 3D." International Journal of High Performance Computing Applications 32, no. 2 (2016): 207–19. http://dx.doi.org/10.1177/1094342016646437.

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Fluid-structure interaction (FSI) problems are computationally very challenging. In this paper we consider the monolithic approach for solving the fully coupled FSI problem. Most existing techniques, such as multigrid methods, do not work well for the coupled system since the system consists of elliptic, parabolic and hyperbolic components all together. Other approaches based on direct solvers do not scale to large numbers of processors. In this paper, we introduce a multilevel unstructured mesh Schwarz preconditioned Newton–Krylov method for the implicitly discretized, fully coupled system of

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Phillips, Peter C. B., and Werner Ploberger. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection." Econometric Theory 10, no. 3-4 (1994): 774–808. http://dx.doi.org/10.1017/s026646660000877x.

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The Kalman filter is used to derive updating equations for the Bayesian data density in discrete time linear regression models with stochastic regressors. The implied “Bayes model” has time varying parameters and conditionally heterogeneous error variances. A σ-finite Bayes model measure is given and used to produce a new-model-selection criterion (PIC) and objective posterior odds tests for sharp null hypotheses like the presence of a unit root. This extends earlier work by Phillips and Ploberger [18]. Autoregressive-moving average (ARMA) models are considered, and a general test of trend-sta

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Dissertations / Theses on the topic "Linear equations; Schwarz methods"

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Terkhova, Karina. "Capacitance matrix preconditioning." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244593.

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Garay, Jose. "Asynchronous Optimized Schwarz Methods for Partial Differential Equations in Rectangular Domains." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/510451.

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Mathematics<br>Ph.D.<br>Asynchronous iterative algorithms are parallel iterative algorithms in which communications and iterations are not synchronized among processors. Thus, as soon as a processing unit finishes its own calculations, it starts the next cycle with the latest data received during a previous cycle, without waiting for any other processing unit to complete its own calculation. These algorithms increase the number of updates in some processors (as compared to the synchronous case) but suppress most idle times. This usually results in a reduction of the (execution) time to achieve

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Tang, Wei-pai. "Schwarz splitting and template operators." Stanford, CA : Dept. of Computer Science, Stanford University, 1987. http://doi.library.cmu.edu/10.1184/OCLC/19643650.

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Thesis (Ph. D.)--Stanford University, 1987.<br>"June 1987." "Also numbered Classic-87-03"--Cover. "This research was supported by NASA Ames Consortium Agreement NASA NCA2-150 and Office of Naval Research Contracts N00014-86-K-0565, N00014-82-K-0335, N00014-75-C-1132"--P. vi. Includes bibliographical references (p. 125-129).

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Smith, James A. "“Looking for nothing" : Bayes linear methods for solving equations." Thesis, Durham University, 1993. http://etheses.dur.ac.uk/2207/.

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Here I will describe and implement Bayes linear methods for finding zeros of deterministic functions. We assume that the zero is known to be unique. Initially, the value of the function is modelled simply as the product of two independent factors, the position of the point from the zero and a "slope" which is assumed to vary "smoothly” with position. Additional prior information specifies first and second order properties of the slopes and the position of the zero: in particular, smoothness is specified by modelling the slope process to be stationary with a decreasing correlation function. Thi

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Elmikkawy, M. E. A. "Embedded Runge-Kutta-Nystrom methods." Thesis, Teesside University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371400.

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Saravi, Masoud. "Numerical solution of linear ordinary differential equations and differential-algebraic equations by spectral methods." Thesis, Open University, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446280.

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This thesis involves the implementation of spectral methods, for numerical solution of linear Ordinary Differential Equations (ODEs) and linear Differential-Algebraic Equations (DAEs). First we consider ODEs with some ordinary problems, and then, focus on those problems in which the solution function or some coefficient functions have singularities. Then, by expressing weak and strong aspects of spectral methods to solve these kinds of problems, a modified pseudospectral method which is more efficient than other spectral methods is suggested and tested on some examples. We extend the pseudo-sp

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Campos, Frederico Ferreira. "Analysis of conjugate gradients-type methods for solving linear equations." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282319.

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Blake, Kenneth William. "Moving mesh methods for non-linear parabolic partial differential equations." Thesis, University of Reading, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369545.

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9

Shank, Stephen David. "Low-rank solution methods for large-scale linear matrix equations." Diss., Temple University Libraries, 2014. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/273331.

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Mathematics<br>Ph.D.<br>We consider low-rank solution methods for certain classes of large-scale linear matrix equations. Our aim is to adapt existing low-rank solution methods based on standard, extended and rational Krylov subspaces to solve equations which may viewed as extensions of the classical Lyapunov and Sylvester equations. The first class of matrix equations that we consider are constrained Sylvester equations, which essentially consist of Sylvester's equation along with a constraint on the solution matrix. These therefore constitute a system of matrix equations. The second are gene

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Fischer, Rainer. "Multigrid methods for anisotropic and indefinite structured linear systems of equations." [S.l.] : [s.n.], 2006. http://mediatum2.ub.tum.de/doc/601806/document.pdf.

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Books on the topic "Linear equations; Schwarz methods"

1

Kythe, Prem K. Computational Methods for Linear Integral Equations. Birkhäuser Boston, 2002.

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Kythe, Prem K., and Pratap Puri. Computational Methods for Linear Integral Equations. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0101-4.

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Laflin, S. Numerical methods of linear algebra. Chartwell-Brat, 1988.

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Yoshida, Masaaki. Fuchsian differential equations, with special emphasis on the Gauss-Schwarz theory. Vieweg, 1987.

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5

Greenbaum, Anne. Iterative methods for solving linear systems. Society for Industrial and Applied Mathematics, 1997.

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6

General linear methods for ordinary differential equations. Wiley, 2009.

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Jackiewicz, Zdzisław. General Linear Methods for Ordinary Differential Equations. John Wiley & Sons, Inc., 2009. http://dx.doi.org/10.1002/9780470522165.

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8

Jerri, Abdul J. Linear Difference Equations with Discrete Transform Methods. Springer US, 1996. http://dx.doi.org/10.1007/978-1-4757-5657-9.

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9

Kelley, C. T. Iterative methods for linear and nonlinear equations. Society for Industrial and Applied Mathematics, 1995.

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10

Jerri, Abdul J. Linear difference equations with discrete transform methods. Kluwer Academic, 1996.

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Book chapters on the topic "Linear equations; Schwarz methods"

1

Descombes, Stéphane, Victorita Dolean, and Martin J. Gander. "Schwarz Waveform Relaxation Methods for Systems of Semi-Linear Reaction-Diffusion Equations." In Lecture Notes in Computational Science and Engineering. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11304-8_49.

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Kress, Rainer. "Quadrature Methods." In Linear Integral Equations. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9593-2_12.

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Kress, Rainer. "Projection Methods." In Linear Integral Equations. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9593-2_13.

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Kress, Rainer. "Quadrature Methods." In Linear Integral Equations. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-97146-4_12.

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Kress, Rainer. "Projection Methods." In Linear Integral Equations. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-97146-4_13.

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Kress, Rainer. "Quadrature Methods." In Linear Integral Equations. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0559-3_12.

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Kress, Rainer. "Projection Methods." In Linear Integral Equations. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0559-3_13.

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Woodford, C., and C. Phillips. "Linear Equations." In Numerical Methods with Worked Examples: Matlab Edition. Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-1366-6_2.

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Kanwal, Ram P. "Integral Transform Methods." In Linear Integral Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-6012-1_9.

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Kanwal, Ram P. "Integral Transform Methods." In Linear Integral Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-0765-8_9.

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Conference papers on the topic "Linear equations; Schwarz methods"

1

Wang, Guangbin, Hao Wen, and Fuping Tan. "Synchronous Multi-splitting and Schwarz Methods for Solving Linear Complementarity Problems." In 2008 International Symposium on Computer Science and Computational Technology. IEEE, 2008. http://dx.doi.org/10.1109/iscsct.2008.145.

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2

Svetlichny, George, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "Constant modulus solutions of linear and nonlinear Schrödinger equations." In GEOMETRIC METHODS IN PHYSICS. AIP, 2008. http://dx.doi.org/10.1063/1.3043857.

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Ponting, David Kenneth, and Richard Hammersley. "Solving Linear Equations In Reservoir Simulation Using Multigrid Methods." In SPE Russian Oil and Gas Technical Conference and Exhibition. Society of Petroleum Engineers, 2008. http://dx.doi.org/10.2118/115017-ms.

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Borawski, Kamil. "Characteristic equations for descriptor linear electrical circuits." In 2017 22nd International Conference on Methods and Models in Automation and Robotics (MMAR). IEEE, 2017. http://dx.doi.org/10.1109/mmar.2017.8046952.

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Hammersley, R. P., and D. K. Ponting. "Solving Linear Equations In Reservoir Simulation Using Multigrid Methods (Russian)." In SPE Russian Oil and Gas Technical Conference and Exhibition. Society of Petroleum Engineers, 2008. http://dx.doi.org/10.2118/115017-ru.

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Swanson, Charles D., and Anthony T. Chronopoulos. "Orthogonal s-step methods for nonsymmetric linear systems of equations." In the 6th international conference. ACM Press, 1992. http://dx.doi.org/10.1145/143369.143450.

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Barkatou, Moulay A. "Symbolic methods for solving systems of linear ordinary differential equations." In the 2010 International Symposium. ACM Press, 2010. http://dx.doi.org/10.1145/1837934.1837940.

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Lai, Siyan. "GPU-Based Monte Carlo Methods for Solving Linear Algebraic Equations." In The fourth International Conference on Information Science and Cloud Computing. Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.264.0047.

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Abe, Kuniyoshi, and Kensuke Aihara. "Hybrid BiCR methods with a stabilization strategy for solving linear equations." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912917.

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Zhang, Hong, Adrian Sandu, Zdzisław Jackiewicz, and Angelamaria Cardone. "Construction of highly stable implicit-explicit general linear methods." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.0185.

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Reports on the topic "Linear equations; Schwarz methods"

1

Varga, Richard S. Investigation on Improved Iterative Methods for Solving Sparse Systems of Linear Equations. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada187046.

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Varga, Richard S. Investigations on Improved Iterative Methods for Solving Sparse Systems of Linear Equations. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada166170.

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Hesthaven, Jan. Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences. Office of Scientific and Technical Information (OSTI), 2012. http://dx.doi.org/10.2172/1034525.

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