Subdomain cluster generation for domain decomposition methods using graph partitioning optimization

Abstract

Balancing and dual domain decomposition methods (DDMs) comprise a family of efficient high performance solution approaches for a large number of problems in computational mechanics. Such DDMs are used in practice on parallel computing environments with the number of generated subdomains being generally larger than the number of available processors. This paper presents an effective heuristic technique for organizing the subdomains into subdomain clusters, in order to assign each cluster to a processor. This task is handled by the proposed approach as a graph partitioning optimization problem using the publicly available software METIS. The objective of the optimization process is to minimize the communication requirements of the DDMs under the constraint of producing balanced processor workloads. This constraint optimization procedure for treating the subdomain cluster generation task leads to increased computational efficiencies for balancing and dual DDMs.