A two-level domain-decomposition preconditioner for the time-harmonic Maxwell's equations

TL;DR

This paper explores the effectiveness of a two-level domain-decomposition preconditioner for solving the indefinite time-harmonic Maxwell's equations efficiently at mid- to high-frequency ranges, addressing computational challenges similar to those in Helmholtz problems.

Contribution

It extends the application of domain-decomposition preconditioners from Helmholtz equations to Maxwell's equations, providing both theoretical analysis and numerical validation.

Findings

Preconditioner improves convergence for Maxwell's equations.

Theoretical insights support numerical results.

Effective at mid- to high-frequency regimes.

Abstract

The construction of fast iterative solvers for the indefinite time-harmonic Maxwell's system at mid- to high-frequency is a problem of great current interest. Some of the difficulties that arise are similar to those encountered in the case of the mid- to high-frequency Helmholtz equation. Here we investigate how two-level domain-decomposition preconditioners recently proposed for the Helmholtz equation work in the Maxwell case, both from the theoretical and numerical points of view.