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Modified recycling MINRES with application to nonlinear Schrödinger problems

Please always quote using this URN:urn:nbn:de:0296-matheon-11681
  • The authors propose a recycling MINRES scheme for a solution of subsequent self-adjoint linear systems as appearing, for example, in the Newton process for solving nonlinear equations. Ritz vectors are automatically extracted from one MINRES run and then used for self-adjoint deflation in the next. The method is designed to work with a preconditioner and arbitrary inner products. Numerical experiments with nonlinear Schrödinger equations indicate a substantial decrease in computation time when recycling is used.

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Metadaten
Author:André Gaul, Nico Schlömer
URN:urn:nbn:de:0296-matheon-11681
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/08/27
Release Date:2012/08/27
Tag:Ginzburg-Landau equations; Krylov subspace methods; MINRES; Ritz vector recycling; deflation; nonlinear Schrödinger equations
Institute:Research Center Matheon
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q55 NLS-like equations (nonlinear Schrödinger) [See also 37K10]
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q56 Ginzburg-Landau equations
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F08 Preconditioners for iterative methods
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22]
Preprint Number:981
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