Hierarchical LU Preconditioning for the Time-Harmonic Maxwell Equations

verfasst von

Maryam Parvizi, Amirreza Khodadadian, Sven Beuchler, Thomas Wick

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.

Organisationseinheit(en)

Institut für Angewandte Mathematik
PhoenixD: Simulation, Fabrikation und Anwendung optischer Systeme

Typ

Aufsatz in Konferenzband

Seiten

391-399

Anzahl der Seiten

9

Publikationsdatum

2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Modellierung und Simulation, Ingenieurwesen (insg.), Diskrete Mathematik und Kombinatorik, Steuerung und Optimierung, Computational Mathematics

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2211.11303 (Zugang: Offen)
https://doi.org/10.1007/978-3-031-50769-4_47 (Zugang: Geschlossen)