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IMA Journal of Numerical Analysis Advance Access originally published online on October 27, 2006
IMA Journal of Numerical Analysis 2007 27(3):451-478; doi:10.1093/imanum/drl030
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A GSVD formulation of a domain decomposition method forplanar eigenvalue problems

Timo Betcke{dagger}

School of Mathematics, The University of Manchester, Sackville Street, Manchester, M60 1QD, UK

{dagger} Email: timo.betcke{at}maths.man.ac.uk

Received on 12 April 2006. Revised on 1 October 2006.


  Abstract

In this article, we present a modification of the domain decomposition method of Descloux and Tolley for planar eigenvalue problems. Instead of formulating a generalized eigenvalue problem, our method is based on the generalized singular value decomposition. This approach is robust and at the same time highly accurate. Furthermore, we give an improved convergence analysis based on results from complex approximation theory. Several examples show the effectiveness of our method.

Key Words: eigenvalues; domain decomposition; generalized singular values; method of particular solutions; conformal maps


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