Wavelet Galerkin BEM on unstructured meshes

Abstact The present paper is devoted to the fast solution of boundary integral equations on unstructured meshes by the Galerkin scheme. On the given mesh we construct a wavelet basis providing vanishing moments with respect to the traces of polynomials in the space. With this basis at hand, the system matrix in wavelet coordinates can be compressed to O(Nlog N) relevant matrix coefficients, where N denotes the number of unknowns. The compressed system matrix can be computed within suboptimal complexity by using techniques from the fast multipole method or panel clustering. Numerical results prove that we succeeded in developing a fast wavelet Galerkin scheme for solving the considered class of problems. Mathematics Subject Classification (2000) 47A20; 65F50; 65N38; 65R20; 65T60 This work is supported in part by the SFB 393 Numerical Simulation on Massive Parallel Computers funded by the Deutsche Forschungsgemeinschaft. Dedicated to George C. Hsiao on the occasion of his 70th birthday.