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On large-scale diagonalization techniques for the Anderson model of localization
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Schenk, Olaf, Bollhofer, Matthias and Roemer, Rudolf A. (2007) On large-scale diagonalization techniques for the Anderson model of localization. In: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zurich, Germany. Published in: Proceedings in Applied Mathematics and Mechanics, Vol.7 (No.1). pp. 1021003-1021004. doi:10.1002/pamm.200700768 ISSN 1617-7061.
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Official URL: http://dx.doi.org/10.1002/pamm.200700768
Abstract
We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for large-scale sparse real and symmetric indefinite matrices of the Anderson model of localization. Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multi-level incomplete LDLT factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly ill-conditioned symmetric indefinite Anderson matrices. Our numerical examples reveal that recent algebraic multi-level preconditioning solvers can accelerate the computation of a large-scale eigenvalue problem corresponding to the Anderson model of localization by several orders of magnitude. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Item Type: | Conference Item (Paper) | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics Faculty of Science, Engineering and Medicine > Science > Centre for Scientific Computing |
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Library of Congress Subject Headings (LCSH): | Anderson model, Eigenvalues, Algorithms, Matrices | ||||
Journal or Publication Title: | Proceedings in Applied Mathematics and Mechanics | ||||
Publisher: | Wiley - V C H Verlag GmbH & Co. KGaA | ||||
ISSN: | 1617-7061 | ||||
Official Date: | 2007 | ||||
Dates: |
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Volume: | Vol.7 | ||||
Number: | No.1 | ||||
Page Range: | pp. 1021003-1021004 | ||||
DOI: | 10.1002/pamm.200700768 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Version or Related Resource: | Schenk, O., et al. (2008). On large-scale diagonalization techniques for the Anderson model of localization. Siam Review, 50(1), pp. 91-112. ; Schenk, O., Bollhöfer, M. and Römer R.A. (2006). On large-scale diagonalization techniques for the Anderson model of localization. SIAM Journal on Scientific Computing, 28(3), pp.963-983 | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting | ||||
Type of Event: | Conference | ||||
Location of Event: | Zurich, Germany | ||||
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