Parallel Multigrid Methods on Sparse Grids

Abstract

This paper deals with multigrid methods on two-dimensional sparse grids and their vectorization. First we will introduce sparse grids and discuss briefly their properties. Sparse grids contain only O(n ld n) grid points in contrast to the usually used O(n²)-grids whereas, for a sufficiently smooth function, the accuracy of the representation is only slightly deteriorated from O(n⁻²) to O(n⁻² ld n). We sketch the main features of a multigrid method that works on these sparse grids and discuss its vectorization and parallelization aspects. Additionally, we present the results of numerical experiments for an implementation of this algorithm on the CRAY-Y-MP.