Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems

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

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
• Public URL: https://durham-repository.worktribe.com/output/1246203