Solution of Boundary Integral Equations Using Wavelet Bases
John S. Kot, D. Glenn Geers, Nasiha Nikolic · 1996
The wavelet bases considered in this paper are orthonormal bases. The basis functions have vanishing moments up to some order, and are defined recursively, usually as the translations and dilations of a single function. The wavelet basis and the closely related scaling function basis can be used to build a multiresolution analysis of a function or operator. This analysis can be applied to a class of singular integral operators arising in elliptic boundary-value problems to give a sparse matrix representation of these operators. This in turn leads to fast numerical methods for solving the resulting matrix equations. As an example, a 2-dimensional Dirichlet problem is solved numerically using a Galerkin method with a wavelet basis.