Parallel Smoother Based on Block Red-Black Ordering for Multigrid Poisson Solver

摘要

This paper describes parallelization techniques for a multi-grid solver for finite difference analysis of three-dimensional Poisson equations. We first apply our block red-black ordering for parallelization of a Gauss-Seidel (GS) smoother, whose sequentiality is often problematic in parallelization of multigrid methods. Furthermore, we introduce a new multiplicative Schwarz smoother, in which multiple GS iterations are performed in each of red-black ordered blocks. Numerical tests are conducted on a cluster of multi-processor nodes comprising four quad-core AMD Opteron processors to examine the effectiveness of these parallel smoothers. The multi-process test using 216 processes in flat-MPI model shows that the block red-black GS smoother and its multiplicative Schwarz variant achieve 1.3 and 1.8 times better performance than the conventional red-black GS smoother, respectively.