A Mixed Tree-Cotree Gauge for the Reduced Basis Approximation of Maxwell's Eigenvalue Problem

TL;DR

This paper introduces a mixed tree-cotree gauge approach to improve reduced basis methods for Maxwell's eigenvalue problem, effectively removing spurious solutions and enhancing computational efficiency.

Contribution

It presents two novel tree-cotree gauge-based techniques for eliminating spurious eigenmodes in reduced basis approximations of Maxwell's eigenvalue problem.

Findings

Effective removal of spurious eigenmodes

Enhanced accuracy of reduced basis solutions

Reduced computational effort

Abstract

Model order reduction methods are a powerful tool to drastically reduce the computational effort of problems which need to be evaluated repeatedly, i.e., when computing the same system for various parameter values. When applying a reduced basis approximation algorithm to the Maxwell eigenvalue problem, we encounter spurious solutions in the reduced system which hence need to be removed during the basis construction. In this paper, we discuss two tree-cotree gauge-based methods for the removal of the spurious eigenmodes.