Reduced Basis Approximation for Maxwell's Eigenvalue Problem and Parameter-Dependent Domains

TL;DR

This paper introduces a reduced basis method to efficiently solve Maxwell's eigenvalue problems on parameter-dependent domains, enabling faster eigenvalue tracking in high-frequency simulations.

Contribution

It extends existing greedy algorithms to handle Maxwell eigenvalue problems with parameter-dependent domains, addressing spurious eigenmodes and improving computational efficiency.

Findings

Effective eigenvalue tracking demonstrated on parameter-dependent Maxwell problems.

Algorithm reduces computational costs significantly.

Addresses spurious eigenmodes in reduced basis methods.

Abstract

In many high-frequency simulation workflows, eigenvalue tracking along a parameter variation is necessary. This can become computationally prohibitive when repeated time-consuming eigenvalue problems must be solved. Therefore, we employ a reduced basis approximation to bring down the computational costs. It is based on the greedy strategy from Horger et al. 2017 which considers multiple eigenvalues for elliptic eigenvalue problems. We extend this algorithm to deal with parameter-dependent domains and the Maxwell eigenvalue problem. In this setting, the reduced basis may contain spurious eigenmodes, which require special treatment. We demonstrate our algorithm in an eigenvalue tracking application for an eigenmode classification.