WIAS Preprint No. 106, (1994)

A wavelet algorithm for the solution of the double layer potential equation over polygonal boundaries


Authors

  • Rathsfeld, Andreas
    ORCID: 0000-0002-2029-5761

2010 Mathematics Subject Classification

  • 45L10 65R20

Keywords

  • potential equation, collocation, wavelet algorithm

DOI

10.20347/WIAS.PREPRINT.106

Abstract

In this paper we consider a piecewise linear collocation method for the solution of the double layer potential equation corresponding to Laplace's equation over polygonal domains. We give a wavelet algorithm for the computation of the corresponding stiffness matrix and for the solution of the arising matrix equation with no more than O(N·[log N]8) arithmetic operations. The error of the resulting approximate solution is of order O(N-2·[log N]6).Finally, we give some remarks on the generalization of the algorithm to the piecewise cubic collocation and present numerical tests.

Appeared in

  • J. Integral Equations Appl. 7 (1995) pp. 47--98

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