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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.
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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) |
|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
| Divisions: | Faculty of Science > Physics Faculty of Science > Centre for Scientific Computing |
| 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 |
| Date: | 2007 |
| Volume: | Vol.7 |
| Number: | No.1 |
| Page Range: | pp. 1021003-1021004 |
| Identification Number: | 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 |
| Related URLs: | |
| URI: | http://wrap.warwick.ac.uk/id/eprint/40148 |
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