Creation of sparse boundary element matrices for 2-D and axi-symmetric electrostatics problems using the bi-orthogonal Haar wavelet

In our previous paper we described the creation of sparse boundary element matrices that arise from Laplace´s equation with mixed boundary conditions using an orthogonal wavelet basis. In this paper we examine the properties of wavelet expansions, and propose a way to construct even sparser matrices than the ones we obtained using the conventional Haar wavelet. We observe that the number of ´vanishing moments´ of a wavelet qualitatively determines the density of BEM matrices. Then we introduce a way of constructing a wavelet that has more vanishing moments than Haar´s wavelet, but still retains a form that is very simple to implement. The time to solution employing the new wavelet is comparable to the Haar wavelet; both are faster than algorithms that rely on a conventional piecewise constant basis. However the quality of the solution is much better, for a given sparsity, the L/sub 2/ error of the source distribution is as much as an order of magnitude lower with the new bi-orthogonal wavelet.