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An iterative adaptive hp-FEM method for non-symmetric elliptic eigenvalue problems

Solin, P.; Giani, S.

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Authors

P. Solin



Abstract

We present a novel adaptive higher-order finite element (hp-FEM) algorithm to solve non-symmetric elliptic eigenvalue problems. This is an extension of our prior work on symmetric elliptic eigenvalue problems. The method only needs to make one call to a generalized eigensolver on the coarse mesh, and then it employs Newton’s or Picard’s methods to resolve adaptively a selected eigenvalue–eigenvector pair. The fact that the method does not need to make repeated calls to a generalized eigensolver not only makes it very efficient, but it also eliminates problems that pose great complications to adaptive algorithms, such as eigenvalue reordering or returning arbitrary linear combinations of eigenvectors associated with the same eigenvalue. New theoretical and numerical results for the non-symmetric case are presented.

Citation

Solin, P., & Giani, S. (2013). An iterative adaptive hp-FEM method for non-symmetric elliptic eigenvalue problems. Computing, 95(1 Supplement), S183-S213. https://doi.org/10.1007/s00607-012-0251-7

Journal Article Type Article
Acceptance Date Dec 3, 2012
Publication Date May 1, 2013
Deposit Date Feb 12, 2013
Publicly Available Date Oct 13, 2015
Journal Computing
Print ISSN 0010-485X
Electronic ISSN 1436-5057
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 95
Issue 1 Supplement
Pages S183-S213
DOI https://doi.org/10.1007/s00607-012-0251-7
Keywords Partial differential equation, Non-symmetric eigenvalue problem, Iterative method, Adaptive higher-order finite element method, hp-FEM.

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