Multiwavelet solutions to the boundary integral equations

We solve the boundary integral equation on an open wedge using multiwavelet based Galerkin and collocation methods. When the solution to the BIE possess singular derivatives at the comer, we regain the optimal convergent rate O(hm) and obtain a sparse stiffness matrix by introducing a parameter to the original BIE and by using wavelet as basis. Numerical examples on how the convergent rate varies with the different parameter values and with different levels of splitting for the BIE on an open wedge are given. The sparse pattern of the stiffness matrix is observed and there are only at most O( n) significant entries for matrix results from Galerkin method and O&parl0;n1+12m+1 logn&parr0; for the collocation method respectively. We also obtain optimal convergent rate and sparse stiffness matrix theoretically when we apply the method to a polygon.