Fast computation of volume potentials on structured grids
Phillip Colella, LBNL

In this talk, we will describe a method for computing solutions to Poisson's equation on locally-refined grids in three dimensions. It is based on the Method of Local Corrections, first developed for fast particle methods by Chris Anderson, and uses a combination of fast Fourier transforms,  fast multipole methods, and multigrid. The resulting method has a cost per grid point of less than three times that of a uniform grid FFT at a comparable resolution, and runs efficiently on up to 1024 processors. We will also discuss the error analysis of this method, which is based on a combination of discrete and continuous potential theory.