Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems

TL;DR

This paper introduces a perturbed subspace iteration algorithm combined with mesh refinement to efficiently approximate the lowest eigenvalues of elliptic problems, demonstrated on polygonal domains in 2D and 3D.

Contribution

It develops a novel perturbed inverse iteration method integrated with residual-based mesh refinement for elliptic eigenvalue problems.

Findings

Effective approximation of lowermost eigenvalues in polygonal domains.

Successful application to 2D and 3D model problems.

Demonstrates convergence and efficiency of the proposed method.

Abstract

We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigenvalue problem posed in a polygonal domain. The algorithm is motivated by the analysis of inexact (perturbed) inverse iteration algorithms in numerical linear algebra. We couple the perturbed inverse iteration approach with mesh refinement strategy based on residual estimators. We demonstrate our approach on model problems in two and three dimensions.