J Austral Math Soc Ser B 33 pp39--64, 1991.

Piecewise-constant collocation for first-kind boundary integral equations

I. G. Graham and Y. Yan

Abstract

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.

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Authors

I. G. Graham

School of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom.

Y. Yan

Department of Mathematics, University of Kentucky, Lexington, Kentucky, U.S.A.