Hierarchical LU Preconditioning for the Time-Harmonic Maxwell Equations

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OriginalspracheEnglisch
Titel des SammelwerksDomain Decomposition Methods in Science and Engineering XXVII
Herausgeber/-innenZdenek Dostal, Tomas Kozubek, Axel Klawonn, Luca F. Pavarino, Olof B. Widlund, Ulrich Langer, Jakub Sístek
Herausgeber (Verlag)Springer Science and Business Media Deutschland GmbH
Seiten391-399
Seitenumfang9
ISBN (Print)9783031507687
PublikationsstatusVeröffentlicht - 2024
Veranstaltung27th International Conference on Domain Decomposition Methods in Science and Engineering, DD 2022 - Prague, Tschechische Republik
Dauer: 25 Juli 202229 Juli 2022

Publikationsreihe

NameLecture Notes in Computational Science and Engineering
Band149
ISSN (Print)1439-7358
ISSN (elektronisch)2197-7100

Abstract

The time-harmonic Maxwell equations are used to study the effect of electric and magnetic fields on each other. Although the linear systems resulting from solving this system using FEMs are sparse, direct solvers cannot reach the linear complexity. In fact, due to the indefinite system matrix, iterative solvers suffer from slow convergence. In this work, we study the effect of using the inverse of \(\mathcal{H}\)-matrix approximations of the Galerkin matrices arising from Nédélec's edge FEM discretization to solve the linear system directly. We also investigate the impact of applying an \(\mathcal{H}-LU\) factorization as a preconditioner and we study the number of iterations to solve the linear system using iterative solvers.

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Hierarchical LU Preconditioning for the Time-Harmonic Maxwell Equations. / Parvizi, Maryam; Khodadadian, Amirreza; Beuchler, Sven et al.
Domain Decomposition Methods in Science and Engineering XXVII. Hrsg. / Zdenek Dostal; Tomas Kozubek; Axel Klawonn; Luca F. Pavarino; Olof B. Widlund; Ulrich Langer; Jakub Sístek. Springer Science and Business Media Deutschland GmbH, 2024. S. 391-399 (Lecture Notes in Computational Science and Engineering; Band 149).

Publikation: Beitrag in Buch/Bericht/Sammelwerk/KonferenzbandAufsatz in KonferenzbandForschungPeer-Review

Parvizi, M, Khodadadian, A, Beuchler, S & Wick, T 2024, Hierarchical LU Preconditioning for the Time-Harmonic Maxwell Equations. in Z Dostal, T Kozubek, A Klawonn, LF Pavarino, OB Widlund, U Langer & J Sístek (Hrsg.), Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, Bd. 149, Springer Science and Business Media Deutschland GmbH, S. 391-399, 27th International Conference on Domain Decomposition Methods in Science and Engineering, DD 2022, Prague, Tschechische Republik, 25 Juli 2022. https://doi.org/10.48550/arXiv.2211.11303, https://doi.org/10.1007/978-3-031-50769-4_47
Parvizi, M., Khodadadian, A., Beuchler, S., & Wick, T. (2024). Hierarchical LU Preconditioning for the Time-Harmonic Maxwell Equations. In Z. Dostal, T. Kozubek, A. Klawonn, L. F. Pavarino, O. B. Widlund, U. Langer, & J. Sístek (Hrsg.), Domain Decomposition Methods in Science and Engineering XXVII (S. 391-399). (Lecture Notes in Computational Science and Engineering; Band 149). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.48550/arXiv.2211.11303, https://doi.org/10.1007/978-3-031-50769-4_47
Parvizi M, Khodadadian A, Beuchler S, Wick T. Hierarchical LU Preconditioning for the Time-Harmonic Maxwell Equations. in Dostal Z, Kozubek T, Klawonn A, Pavarino LF, Widlund OB, Langer U, Sístek J, Hrsg., Domain Decomposition Methods in Science and Engineering XXVII. Springer Science and Business Media Deutschland GmbH. 2024. S. 391-399. (Lecture Notes in Computational Science and Engineering). doi: 10.48550/arXiv.2211.11303, 10.1007/978-3-031-50769-4_47
Parvizi, Maryam ; Khodadadian, Amirreza ; Beuchler, Sven et al. / Hierarchical LU Preconditioning for the Time-Harmonic Maxwell Equations. Domain Decomposition Methods in Science and Engineering XXVII. Hrsg. / Zdenek Dostal ; Tomas Kozubek ; Axel Klawonn ; Luca F. Pavarino ; Olof B. Widlund ; Ulrich Langer ; Jakub Sístek. Springer Science and Business Media Deutschland GmbH, 2024. S. 391-399 (Lecture Notes in Computational Science and Engineering).
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abstract = "The time-harmonic Maxwell equations are used to study the effect of electric and magnetic fields on each other. Although the linear systems resulting from solving this system using FEMs are sparse, direct solvers cannot reach the linear complexity. In fact, due to the indefinite system matrix, iterative solvers suffer from slow convergence. In this work, we study the effect of using the inverse of \(\mathcal{H}\)-matrix approximations of the Galerkin matrices arising from N{\'e}d{\'e}lec's edge FEM discretization to solve the linear system directly. We also investigate the impact of applying an \(\mathcal{H}-LU\) factorization as a preconditioner and we study the number of iterations to solve the linear system using iterative solvers. ",
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