Fully discrete Alpert multiwavelet Galerkin BEM in 2D

A fully discrete Galerkin boundary element method (BEM) based on Alpert multiwavelets is proposed for fast solution of Laplace's boundary integral equations in two dimensions. To make it more suitable for practical use, the highest resolution levels in the boundary patches are allowed to be different from each other. New patch and level dependent cut-off parameters which can compress the nonzero entries to at most O(NlogN)O(NlogN) (where N   is the degrees of freedom) are presented. A diagonal preconditioner is utilized to improve the system matrix. To evaluate the logarithmic singular double integrals more efficiently, coordinate transformations are introduced to remove the singularities. Numerical results show that the method can achieve O(NlogN)O(NlogN) complexity.