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Licensed Unlicensed Requires Authentication Published by De Gruyter March 12, 2021

Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems

Stefano Giani ORCID logo, Luka Grubišić ORCID logo, Luca Heltai ORCID logo and Ornela Mulita

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.

MSC 2010: 65N25; 65N30; 65N50

Funding source: Hrvatska Zaklada za Znanost

Award Identifier / Grant number: IP-2019-04-6268

Funding statement: Luka Grubišić was supported by the Croatian Science Foundation grant HRZZ IP-2019-04-6268. Luka Grubišić is also thankful to the hospitality of the research visit to Scuola Internazionale Superiore di Studi Avanzati where the work has started. Ornela Mulita is thankful to the University of Zagreb for the hospitality during her collaborative research visit there. Luca Heltai was partially supported by the National Research Projects (PRIN 2017) “Numerical Analysis for Full and Reduced Order Methods for the efficient and accurate solution of complex systems governed by Partial Differential Equations”, funded by the Italian Ministry of Education, University, and Research.

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Received: 2020-03-02
Revised: 2021-02-13
Accepted: 2021-02-16
Published Online: 2021-03-12
Published in Print: 2021-04-01

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