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551 results on '"Axelsson, Owe"'

1. A modified version of the PRESB preconditioner for a class of non-Hermitian complex systems of linear equations

Author

Axelsson, Owe and Slakuyeh, Dovod Khojasteh

Subjects
Mathematics - Numerical Analysis, 65F10, 65F50
Abstract

We present a modified version of the PRESB preconditioner for two-by-two block system of linear equations with the coefficient matrix $$\textbf{A}=\left(\begin{array}{cc} F & -G^* G & F \end{array}\right),$$ where $F\in\mathbb{C}^{n\times n}$ is Hermitian positive definite and $G\in\mathbb{C}^{n\times n}$ is positive semidefinite. Spectral analysis of the preconditioned matrix is analyzed. In each iteration of a Krylov subspace method, like GMRES, for solving the preconditioned system in conjunction with proposed preconditioner two subsystems with Hermitian positive definite coefficient matrix should be solved which can be accomplished exactly using the Cholesky factorization or inexactly utilizing the conjugate gradient method. Application of the proposed preconditioner to the systems arising from finite element discretization of PDE-constrained optimization problems is presented. Numerical results are given to demonstrate the efficiency of the preconditioner., Comment: 12 pages, 1 Figure, Submitted

Published
2024

4. Robust iteration methods for complex systems with an indefinite matrix term

Author

Axelsson, Owe, Pourbagher, Maeddeh, and Salkuyeh, Davod Khojasteh

Subjects
Mathematics - Numerical Analysis, 65F10, 65F50
Abstract

Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with symmetric positive definite matrices can be solved readily by rewriting the complex matrix system in two-by-two block matrix form with real matrices which can be efficiently solved by iteration using the preconditioned square block (PRESB) preconditioning method and preferably accelerated by the Chebyshev method. The appearances of an indefinite matrix term causes however some difficulties. To handle this we propose different forms of matrix splitting methods, with or without any parameters involved. A matrix spectral analyses is presented followed by extensive numerical comparisons of various forms of the methods., Comment: 13 pages, submitted

Published
2021

5. An Exact Schur Complement Method for Time-Harmonic Optimal Control Problems

Author

Axelsson, Owe, Lukáš, Dalibor, Neytcheva, Maya, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Lirkov, Ivan, editor, and Margenov, Svetozar, editor

Published
2022
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10. An Introduction and Summary of Use of Optimal Control Methods for PDE’s

Author

Axelsson, Owe, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Lirkov, Ivan, editor, and Margenov, Svetozar, editor

Published
2020
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13. Stage-parallel preconditioners for implicit Runge-Kutta methods of arbitrarily high order, linear problems

Author

Axelsson, Owe, Dravins, Ivo, Neytcheva, Maya, Axelsson, Owe, Dravins, Ivo, and Neytcheva, Maya

Abstract

Fully implicit Runge–Kutta methods offer the possibility to use high order accurate time discretization to match space discretization accuracy, an issue of significant importance for many large scale problems of current interest, where we may have fine space resolution with many millions of spatial degrees of freedom and long time intervals. In this work, we consider strongly A-stable implicit Runge–Kutta methods of arbitrary order of accuracy, based on Radau quadratures. For the arising large algebraic systems we introduce efficient preconditioners, that (1) use only real arithmetic, (2) demonstrate robustness with respect to problem and discretization parameters, and (3) allow for fully stage-parallel solution. The preconditioners are based on the observation that the lower-triangular part of the coefficient matrices in the Butcher tableau has larger in magnitude values, compared to the corresponding strictly upper-triangular part. We analyze the spectrum of the corresponding preconditioned systems and illustrate their performance with numerical experiments. Even though the observation has been made some time ago, its impact on constructing stage-parallel preconditioners has not yet been done and its systematic study constitutes the novelty of this article.

Published
2024
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18. Preconditioners for Time-Harmonic Optimal Control Eddy-Current Problems

Author

Axelsson, Owe, Lukáš, Dalibor, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Lirkov, Ivan, editor, and Margenov, Svetozar, editor

Published
2018
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26. A Comparison of Preconditioning Methods for Saddle Point Problems with an Application to Porous Media Flow Problems

Author

Axelsson, Owe, Blaheta, Radim, Hasal, Martin, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Josef, Kittler, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Kozubek, Tomáš, editor, Blaheta, Radim, editor, Šístek, Jakub, editor, Rozložník, Miroslav, editor, and Čermák, Martin, editor

Published
2016
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28. Preconditioners for Mixed FEM Solution of Stationary and Nonstationary Porous Media Flow Problems

Author

Axelsson, Owe, Blaheta, Radim, Luber, Tomáš, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Lirkov, Ivan, editor, Margenov, Svetozar D., editor, and Waśniewski, Jerzy, editor

Published
2015
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31. Stage-parallel preconditioners for implicit Runge-Kutta methods of arbitrarily high order, linear problems

Author

Axelsson, Owe, Dravins, Ivo, Neytcheva, Maya, Axelsson, Owe, Dravins, Ivo, and Neytcheva, Maya

Abstract

Fully implicit Runge–Kutta methods offer the possibility to use high order accurate time discretization to match space discretization accuracy, an issue of significant importance for many large scale problems of current interest, where we may have fine space resolution with many millions of spatial degrees of freedom and long time intervals. In this work, we consider strongly A-stable implicit Runge–Kutta methods of arbitrary order of accuracy, based on Radau quadratures. For the arising large algebraic systems we introduce efficient preconditioners, that (1) use only real arithmetic, (2) demonstrate robustness with respect to problem and discretization parameters, and (3) allow for fully stage-parallel solution. The preconditioners are based on the observation that the lower-triangular part of the coefficient matrices in the Butcher tableau has larger in magnitude values, compared to the corresponding strictly upper-triangular part. We analyze the spectrum of the corresponding preconditioned systems and illustrate their performance with numerical experiments. Even though the observation has been made some time ago, its impact on constructing stage-parallel preconditioners has not yet been done and its systematic study constitutes the novelty of this article.

Published
2023
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37. Material Parameter Identification with Parallel Processing and Geo-applications

Author

Blaheta, Radim, Hrtus, Rostislav, Kohut, Roman, Axelsson, Owe, Jakl, Ondřej, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Wyrzykowski, Roman, editor, Dongarra, Jack, editor, Karczewski, Konrad, editor, and Waśniewski, Jerzy, editor

Published
2012
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38. An Additive Matrix Preconditioning Method with Application for Domain Decomposition and Two-Level Matrix Partitionings

Author

Axelsson, Owe, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Lirkov, Ivan, editor, Margenov, Svetozar, editor, and Waśniewski, Jerzy, editor

Published
2010
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40. Mesh Independent Convergence Rates Via Differential Operator Pairs

Author

Axelsson, Owe, Karátson, János, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Lirkov, Ivan, editor, Margenov, Svetozar, editor, and Waśniewski, Jerzy, editor

Published
2008
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48. Stage-Parallel Preconditioners for Implicit Runge-Kutta Methods of Arbitrary High Order. Linear problems

Author

Axelsson, Owe, Dravins, Ivo, Neytcheva, Maya, Axelsson, Owe, Dravins, Ivo, and Neytcheva, Maya

Abstract

Fully implicit Runge-Kutta methods offer the possibility to use high order accurate time discretization to match space discretization accuracy, an issue of significant importance for many large scale problems of current interest, where we may have fine space resolution with many millions of spatial degrees of freedom and long time intervals. In this work we consider strongly A-stable implicit Runge-Kutta methods of arbitrary order of accuracy, based on Radau quadratures. For the arising large algebraic systems we introduce an efficient preconditioner, that allows for fully stage-parallel solution. We analyse the spectrum of the corresponding preconditioned system and illustrate the performance of the solution method with numerical experiments using MPI. In this work we consider only linear problems.

Published
2022

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