A WAVELET ALGORITHM FOR THE BOUNDARY-ELEMENT SOLUTION OF A GEODETIC BOUNDARY-VALUE

In this paper we consider a piecewise bilinear collocation method for the solution of a singular integral equation over a part of the surfac e of the earth. This singular equation is the boundary integral equati on corresponding to the oblique derivative boundary problem for Laplac e's equation. We introduce special wavelet bases for the spaces of tes t and trial functions. Analogously to well-known results on wavelet al gorithms, the stiffness matrices with respect to these bases can be re duced to sparse matrices such that the assembling of the matrices and the iterative solution of the matrix equations quicken. Though the the oretical results apply only to integral equations with 'smooth' soluti ons over 'smooth' manifolds, we present numerical tests for a geometry as difficult as the surface of the earth. (C) 1998 Elsevier Science S .A.