On the creation of sparse boundary element matrices for two dimensional electrostatics problems using the orthogonal Haar wavelet

This paper describes the creation of sparse boundary element matrices arising from Laplace's equation with mixed boundary conditions using an orthogonal wavelet basis. In contrast to previous work which employed a similarity transform that changed the finite dimensional basis a posteriori, the method described here can produce the sparse matrix directly. This has obvious advantages for large problems, where quadratic growth of the storage space required for the matrix coefficients can be prohibitively expensive.