A Local Corrections Algorithm for Solving Poisson's Equation inThree Dimensions

We present a second-order accurate algorithm for solving thefree-space Poisson's equation on a locally-refined nested grid hierarchyin three dimensions. Our approach is based on linear superposition oflocal convolutions of localized charge distributions, with the nonlocalcoupling represented on coarser grids. There presentation of the nonlocalcoupling on the local solutions is based on Anderson's Method of LocalCorrections and does not require iteration between different resolutions.A distributed-memory parallel implementation of this method is observedto have a computational cost per grid point less than three times that ofa standard FFT-based method on a uniform grid of the same resolution, andscales well up to 1024 processors