PRELIMINARIES Poisson’s Equation

Current and future accelerator design requires efficient 3D space charge computations for high brightness bunches which should be as precise and fast as possible. One possible approach for space charge calculations is the particle-mesh-method, where the potential is calculated in the rest frame of the bunch by means of Poisson’s equation. For an efficient solution of this elliptic PDE an appropri-ate adaptive discretization of the domain is required. Es-pecially it has to take into account discontinuities in the distribution of the particles. The solution method we investigate in this paper is a self-adaptive multigrid method applying composite grids. To accomplish this, we use the library Chombo which is be-ing developed as a framework for adaptive multiresolution solvers for elliptic and hyperbolic partial differential equa-tions