Details
| Original language | English |
|---|---|
| Title of host publication | Domain Decomposition Methods in Science and Engineering XXVII |
| Editors | Zdenek Dostal, Tomas Kozubek, Axel Klawonn, Luca F. Pavarino, Olof B. Widlund, Ulrich Langer, Jakub Sístek |
| Publisher | Springer Science and Business Media Deutschland GmbH |
| Pages | 391-399 |
| Number of pages | 9 |
| ISBN (print) | 9783031507687 |
| Publication status | Published - 2024 |
| Event | 27th International Conference on Domain Decomposition Methods in Science and Engineering, DD 2022 - Prague, Czech Republic Duration: 25 Jul 2022 → 29 Jul 2022 |
Publication series
| Name | Lecture Notes in Computational Science and Engineering |
|---|---|
| Volume | 149 |
| ISSN (Print) | 1439-7358 |
| ISSN (electronic) | 2197-7100 |
Abstract
Keywords
- math.NA, cs.NA
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Computational Mathematics
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Domain Decomposition Methods in Science and Engineering XXVII. ed. / Zdenek Dostal; Tomas Kozubek; Axel Klawonn; Luca F. Pavarino; Olof B. Widlund; Ulrich Langer; Jakub Sístek. Springer Science and Business Media Deutschland GmbH, 2024. p. 391-399 (Lecture Notes in Computational Science and Engineering; Vol. 149).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Hierarchical LU Preconditioning for the Time-Harmonic Maxwell Equations
AU - Parvizi, Maryam
AU - Khodadadian, Amirreza
AU - Beuchler, Sven
AU - Wick, Thomas
N1 - Funding Information: Acknowledgements The authors acknowledge the Deutsche Forschungsgemeinschaft (DFG) under Germany Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). Maryam Parvizi is funded by Alexander von Humboldt Foundation project named H-matrix approximability of the inverses for FEM, BEM and FEM-BEM coupling of the electromagnetic problems. Finally, the authors thank Sebastian Kinnewig for fruitful discussions.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - math.NA
KW - cs.NA
UR - http://www.scopus.com/inward/record.url?scp=85184280379&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2211.11303
DO - 10.48550/arXiv.2211.11303
M3 - Conference contribution
SN - 9783031507687
T3 - Lecture Notes in Computational Science and Engineering
SP - 391
EP - 399
BT - Domain Decomposition Methods in Science and Engineering XXVII
A2 - Dostal, Zdenek
A2 - Kozubek, Tomas
A2 - Klawonn, Axel
A2 - Pavarino, Luca F.
A2 - Widlund, Olof B.
A2 - Langer, Ulrich
A2 - Sístek, Jakub
PB - Springer Science and Business Media Deutschland GmbH
T2 - 27th International Conference on Domain Decomposition Methods in Science and Engineering, DD 2022
Y2 - 25 July 2022 through 29 July 2022
ER -