Stable Computation of Laplacian Eigenfunctions Corresponding to Clustered Eigenvalues

TL;DR

This paper introduces a stable method for computing Laplacian eigenfunctions associated with tightly clustered eigenvalues, addressing the challenge of domain perturbation effects on eigenfunction accuracy.

Contribution

It proposes a novel approach using shape difference quotients to improve the stability of eigenfunction computation for clustered eigenvalues.

Findings

Enhanced stability in eigenfunction computation

Effective handling of domain perturbations

Applicable to tightly clustered eigenvalues

Abstract

The accurate computation of eigenfunctions corresponding to tightly clustered Laplacian eigenvalues remains an extremely difficult problem. In this paper, using the shape difference quotient of eigenvalues, we propose a stable computation method for the eigenfunctions of clustered eigenvalues caused by domain perturbation.