Partitioning and scheduling algorithms and their implementation in FELISA - An unstructured grid euler solver

Abstract

The numerical solution of partial differential equations with finite element algorithms on distributed memory parallel computers demands that the global mesh be divided into subdomains, the number of which corresponds to the number of processors. The decomposition should be such that the number of elements per subdomain is roughly the same—to ensure global load balancing—and the number of shared faces between the two subdomains are minimized—to reduce the communication costs. This chapter compares a number of established grid partitioning algorithms. A new hybrid algorithm that is found to be highly competitive on small to medium size meshes is proposed in the chapter. Once a partitioning has been established for an irregular grid, a communication scheme needs to be devised to organize the communication among processors. A message passing scheme using blocked pairwise exchange in a number of stages is described in the chapter. The chapter develops algorithms to deal with non-uniform message lengths. The algorithms attempt to minimize the communication time by scheduling messages of similar lengths in the same stage of the message passing scheme. It is found that the load balancing of communication can reduce the communication costs by up to 30%. The partitioning and scheduling algorithms are used as a preprocessor in a parallel version of the unstructured grid finite element 3D explicit Euler equation solver FELISA. The results for a parallel implementation of FELISA code using the most efficient grid decomposition and message scheduling algorithms are presented in the chapter.