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 θ(n log n). We also develop a block diagonal preconditioner for the discrete single layer potential which reduces the condition number of the matrix from θ(n) to θ(log2n). We provide numerical results supporting our theory