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.
Bibliographical noteFunding Information:
* The authors were supported by the Applied Mathematical Sciences Program of the U.S. Department of Energy under Contract DEFGO288ER25053, by the Office of Naval Research under Contract N00014-91-J-1312, by a NSF Presidential Young Investigator Award to L.G. and by a Packard Foundation Fellowship to L.G.