Efficient Trefftz collocation algorithms for elliptic problems in circular domains

Authors:
A. Karageorghis
Affiliations:
Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus 1678
Venue:
Numerical Algorithms
Year:
2013

Citing 4
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Abstract

We consider the numerical solution of certain elliptic boundary value problems in disks and annuli using the Trefftz collocation method. In particular we examine boundary value problems for the Laplace, Helmholtz, modified Helmholtz and biharmonic equations in such domains. It is shown that this approach leads to systems in which the matrices possess specific structures. By exploiting these structures we propose efficient algorithms for the solution of the systems. The proposed algorithms are applied to standard test problems.