A Direct Adaptive Poisson Solver of Arbitrary Order Accuracy

Abstract

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 requiresO(NK) work, whereNis the number of discretization points andKis the desired order of accuracy.