Hierarchical LU Preconditioning for the Time-Harmonic Maxwell Equations

authored by

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.

Organisation(s)

Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines

Type

Conference contribution

Pages

391-399

No. of pages

9

Publication date

2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Modelling and Simulation, Engineering(all), Discrete Mathematics and Combinatorics, Control and Optimization, Computational Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.2211.11303 (Access: Open)
https://doi.org/10.1007/978-3-031-50769-4_47 (Access: Closed)