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An extended basis inexact shift–invert Lanczos for the efficient solution of large-scale generalized eigenproblems

Abstract

This paper proposes a technique, based on the Inexact Shift–Invert Lanczos (ISIL) method with Inexact Jacobi Orthogonal Component Correction (IJOCC) refinement, and a preconditioned conjugate-gradient (PCG) linear solver with multilevel preconditioner, for finding several eigenvalues for generalized symmetric eigenproblems. Several eigenvalues are found by constructing (with the ISIL process) an extended projection basis. Presented results of numerical experiments confirm the technique can be effectively applied to challenging, large-scale problems characterized by very dense spectra, such as resonant cavities with spatial dimensions which are large with respect to wavelengths of the resonating electromagnetic fields. It is also shown that the proposed scheme based on inexact linear solves delivers superior performance, as compared to methods which rely on exact linear solves, indicating tremendous potential of the ‘inexact solve’ concept. Finally, the scheme which generates an extended projection basis is found to provide a cost-efficient alternative to classical deflation schemes when several eigenvalues are computed.

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Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
COMPUTER PHYSICS COMMUNICATIONS no. 184, edition 9, pages 2127 - 2135,
ISSN: 0010-4655
Language:
English
Publication year:
2013
Bibliographic description:
Rewieński M., Lamęcki A., Mrozowski M.: An extended basis inexact shift–invert Lanczos for the efficient solution of large-scale generalized eigenproblems// COMPUTER PHYSICS COMMUNICATIONS. -Vol. 184, iss. 9 (2013), s.2127-2135
DOI:
Digital Object Identifier (open in new tab) 10.1016/j.cpc.2013.04.006
Verified by:
Gdańsk University of Technology

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