Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
[1] F. Koster. Preconditioners for sparse grid discretizations. Technical Report No. 746, SFB 256, Universität Bonn, Germany, 2001.
bib | .ps.gz 1 ]
In this paper we deal with preconditioners for sparse grid finite-difference- and Petrov-Galerkin-discretizations of the Poisson equation. We analyse the Jacobi-preconditioner for the simple setting of non-adaptive grids and periodic boundary conditions. The analysis shows that the resulting condition numbers mainly depend on the underlying tensor product Wavelets. For example, high order Lifting-Interpolets lead to l2-condition numbers which are essentially independent of the finest mesh size. Based on this observation we introduce a so-called Lifting-preconditioner for discretizations which use Interpolets as trial-functions. Numerical examples show the efficiency of the preconditioners for cases which are not covered by our analysis, e.g., adaptive grids.