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An adaptive homotopy approach for non-selfadjoint eigenvalue problems

Please always quote using this URN:urn:nbn:de:0296-matheon-7058
  • This paper presents three different adaptive algorithms for eigenvalue problems associated with non-selfadjoint partial differential operators. The basis for the developed algorithms is a homotopy method. The homotopy method starts from a well-understood selfadjoint problem, for which well-established adaptive methods are available. Apart from the adaptive grid refinement, the progress of the homotopy as well as the solution of the iterative method are adapted to balance the contributions of the different error sources. The first algorithm balances the homotopy, discretization and approximation errors with respect to a fixed step-size $\tau$ in the homotopy. The second algorithm combines the adaptive step-size control for the homotopy with an adaptation in space that ensures an error below a fixed tolerance $\varepsilon$. The third algorithm allows the complete adaptivity in space, homotopy step-size as well as the iterative algebraic eigenvalue solver. All three algorithms are compared in numerical examples.

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Metadaten
Author:Carsten Carstensen, Joscha Gedicke, Volker Mehrmann, Agnieszka Miedlar
URN:urn:nbn:de:0296-matheon-7058
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/03/09
Release Date:2010/03/09
Tag:
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
65-XX NUMERICAL ANALYSIS / 65Hxx Nonlinear algebraic or transcendental equations / 65H20 Global methods, including homotopy approaches [See also 58C30, 90C30]
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N15 Error bounds
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N25 Eigenvalue problems
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N50 Mesh generation and refinement
Preprint Number:718
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