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Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems

Giani, S. and Grubišić, L. and Heltai, L. and Mulita, O. (2021) 'Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems.', Computational methods in applied mathematics., 21 (2). pp. 385-405.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1515/cmam-2020-0027
Date accepted:16 February 2021
Date deposited:23 February 2021
Date of first online publication:12 March 2021
Date first made open access:12 March 2022

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