Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems-Reference-Cited by-同舟云学术

Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems

Published:2021-03-12 Issue:2 Volume:21 Page:385-405
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Giani Stefano¹^ORCID,Grubišić Luka²^ORCID,Heltai Luca³^ORCID,Mulita Ornela⁴

Affiliation:

1. Durham University , Stockton Road , Durham , DH1 3LE , United Kingdom

2. Department of Mathematics , Faculty of Science , University of Zagreb , Bijenička 30, 10000 Zagreb , Croatia

3. Scuola Internazionale Superiore di Studi Avanzati , Via Bonomea 265, 34136 Trieste , Italy

4. Institut für Mathematik , Humboldt-Universität zu Berlin , Unter den Linden 6, 10099 Berlin , Germany

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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