Parallel Performance of a Preconditioned CG Solver for Unstructured Finite Element Applications

John N. Shadid, Scott A. Hutchinson and Harry K. Moffat

Sandia National Laboratories
Albuquerque, New Mexico 87185


A parallel unstructured finite element (FE) implementation designed for message passing MIMD machines is described. This implementation employs automated problem partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global finite element equations and a parallel conjugate gradient (CG) solver. In this paper a number of issues related to the efficient implementation of parallel unstructured mesh applications are pre sented. These include the differences between structured and unstructured mesh parallel applica tions, major communication kernels for unstructured CG solvers, automatic mesh partitioning algorithms, and the influence of mesh partitioning metrics on parallel performance. Initial results are presented for example finite element (FE) heat transfer analysis applications on a 1024 proces sor nCUBE 2 hypercube. Results indicate over 95% scaled efficiencies are obtained for some large problems despite the required unstructured data communication.