A direct adaptive Poisson solver of arbitrary order accuracy

We present a direct, adaptive solver for the Poisson equation which can achieve any prescribed order of accuracy. It is based on a domain decomposition approach using local spectral approximation, as well as potential theory and the fast multipole method. In two space dimensions, the algorithm requires O(NK) work, where N is the number of discretization points and K is the desired order Of accuracy. (C) 1996 Academic Press, Inc.