Volume 29, pp. 70-80, 2007-2008.
Hierarchical grid coarsening for the solution of the Poisson equation in free space
Matthias Bolten
Abstract
In many applications the solution of PDEs in infinite domains with
vanishing boundary conditions at infinity is of interest. If the
Green's function of the particular PDE is known, the solution can
easily be obtained by folding it with the right hand side in a finite
subvolume. Unfortunately this requires
operations. Washio and Oosterlee presented an algorithm that rather
than that uses hierarchically coarsened grids in order to solve the
problem (Numer. Math. (2000) 86: 539–563). They use infinitely
many grid levels for the error analysis. In this paper we present an
extension of their work. Instead of continuing the refinement process
up to infinitely many grid levels, we stop the refinement process at an
arbitrary level and impose the Dirichlet boundary conditions of the
original problem there. The error analysis shows that the proposed
method still is of order , as the original method with infinitely
many refinements.
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Key words
the Poisson equation, free boundary problems for PDE, multigrid method
AMS subject classifications
35J05, 35R35, 65N55
