Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems
- Resource Type
- Authors
- Ornela Mulita; Luca Heltai; Luka Grubišić; Stefano Giani
- Source
- Computational methods in applied mathematics, 2021, Vol.21(2), pp.385-405 [Peer Reviewed Journal]
- Subject
- Inverse iteration
Mesh Adaptation
MathematicsofComputing_NUMERICALANALYSIS
Mesh Construction
Residual
computer.software_genre
Domain (mathematical analysis)
Settore MAT/08 - Analisi Numerica
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
Elliptic Eigenvalue Problem
FOS: Mathematics
Applied mathematics
Inexact Perturbed Inverse Iteration
Mathematics - Numerical Analysis
Eigenvalues and eigenvectors
Mathematics
Numerical Analysis
Numerical linear algebra
Laplace transform
Applied Mathematics
Estimator
Numerical Analysis (math.NA)
Mathematics::Spectral Theory
Computational Mathematics
Laplace Operator
computer
Inexact Solve
Subspace topology
- Language
- ISSN
- 1609-9389
1609-4840
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.
Comment: 30 pages, 15 figures