Preconditioned multiwavelet Galerkin boundary element solution of Laplace's equation

In this paper, we study the boundary element solution of Laplace's equation using a Galerkin method with multiwavelet basis functions. This leads to significant matrix compression, requiring computation of only O(nlogn) elements. We also develop a block diagonal preconditioner for the discrete single layer potential which reduces the condition number of the matrix from O(n)O(n) to O(log2n)O(log2n). We provide numerical results supporting our theory.