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arXiv · 2102.06818

Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems

Stefano Giani·Luka Grubišić·Luca Heltai·Ornela Mulita
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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.

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Stefano Giani, Luka Grubišić, Luca Heltai, Ornela Mulita. 2021-02-12. Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems. https://doi.org/10.1515/cmam-2020-0027

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