A fast wavelet-multipole method for direct BEM

A fast wavelet-multipole method (WMM) has been developed to achieve further speedup for the boundary element method in solving the direct boundary integral equations. The main idea is to compute the right-hand-side vector by the fast multipole method and to solve the linear system by the wavelet compression method. By using the variable order moments, almost linear complexity can be obtained. The primary advantages of the present WMM lie in that it (1) permits efficient implementation; (2) is universal in handling practical problems with complicated geometries. Numerical examples with around 1 million unknowns, performed on nontrivial geometries, clearly show that the WMM can shorten the total computational time by reducing the time for computing the right-hand-side.