Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems

Giani, S.; Grubišić, L.; Heltai, L.; Mulita, O.

doi:10.1515/cmam-2020-0027

Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems

Giani, S.; Grubišić, L.; Heltai, L.; Mulita, O.

Authors

Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor

L. Grubišić

L. Heltai

O. 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.

Citation

Giani, S., Grubišić, L., Heltai, L., & Mulita, O. (2021). Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems. Computational Methods in Applied Mathematics, 21(2), 385-405. https://doi.org/10.1515/cmam-2020-0027

Journal Article Type	Article
Acceptance Date	Feb 16, 2021
Online Publication Date	Mar 12, 2021
Publication Date	2021
Deposit Date	Feb 23, 2021
Publicly Available Date	Mar 12, 2022
Journal	Computational Methods in Applied Mathematics
Print ISSN	1609-4840
Electronic ISSN	1609-9389
Publisher	De Gruyter
Peer Reviewed	Peer Reviewed
Volume	21
Issue	2
Pages	385-405
DOI	https://doi.org/10.1515/cmam-2020-0027