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Piecewise-constant collocation for first-kind boundary integral equations

Published online by Cambridge University Press:  17 February 2009

I. G. Graham  and
Y. Yan
I. G. Graham
Affiliation:
School of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom.
Y. Yan
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky, U.S.A.
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Abstract

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We examine the piecewise-constant collocation method, with collocation points the mid-points of subintervals, for first-kind integral equations with logarithmic kernels on polygonal boundaries. Previously this method had been shown to converge subject to certain restrictions on the angles at the corners of the polygon. Here, by considering a slightly modified collocation method, we are able to remove any restrictions on these angles, and to generalise slightly the meshes which may be used. Moreover, the modification leads to new results on the convergence of preconditioned two-(or multi-) grid methods for solving the resultant linear systems.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 1 , July 1991 , pp. 39 - 64
Copyright
Copyright © Australian Mathematical Society 1991

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