Heuristics for Domain Decomposition

Abstract

The domain decomposition method embodies large potentials for a parallelization of FEM methods. In this data-parallel approach, the domain of interest is partitioned into smaller subdomains, either before the mesh generation or afterwards (mesh partitioning). The subdomains are assigned to processors that calculate the corresponding part of the approximation. The mesh decomposition and assignments of subdomains to processors can be modeled as graph embedding problem where a large graph (the mesh) has to be mapped onto a smaller one (the processor network). Unfortunately, this mapping problem is NP-complete and there exist almost no efficient sequential or parallel heuristics that solve this problem sufficiently [1]. With growing performance of interconnection networks and especially with the establishment of independent routing networks, it is appropriate to reduce the mapping problem to the task of partitioning the graph (the FEM-mesh) into as many equal sized (or weighted) clusters a..