A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions: beyond the minimum interface size criterion

Abstract

Mesh partitioning is often the preferred approach for solving unstructured computational mechanics problems on massively parallel processors. Research in this area has focused so far on the automatic generation of subdomains with minimum interface points. In this paper, we address this issue and emphasize other aspects of the partitioning problem including the fast generation of large-scale mesh decompositions on conventional workstations, the optimization of initial decompositions for specific kernels such as parallel frontal solvers and domain decomposition based iterative methods, and parallel adaptive refinement. More specifically, we discuss a two-step partitioning paradigm for tailoring generated mesh partitions to specific applications, and propose a simple mesh contraction procedure for speeding up the optimization of initial mesh decompositions. We discuss what defines a good mesh partition for a given problem, and show that the methodology proposed herein can produce better mesh partitions than the well celebrated multilevel Recursive Spectral Bisection algorithm, and yet be an order of magnitude faster. We illustrate the combined two-step partitioning and contraction methodology with several examples from structural mechanics and fluid dynamics problems, and highlight its impact on the total solution time of realistic applications on current massively parallel processors. In particular, we show that the minimum interface size criterion does not have a significant impact on a reasonably well parallelized application, and highlight other criterion which can have a significant impact.