Parallel Smoothers for Matrix-Based Geometric Multigrid Methods on Locally Refined Meshes Using Multicore CPUs and GPUs

Abstract

Multigrid methods are efficient and fast solvers for problems typically modeled by partial differential equations of elliptic type. We use the approach of matrix-based geometric multigrid that has high flexibility with respect to complex geometries and local singularities. Furthermore, it adapts well to the exigences of modern computing platforms. In this work we investigate multi-colored Gauß-Seidel type smoothers, the power(q)-pattern enhanced multi-colored ILU(p,q) smoothers with fill-ins, and factorized sparse approximate inverse (FSAI) smoothers. These approaches provide efficient smoothers with a high degree of parallelism. We describe the configuration of our smoothers in the context of the portable lmpLAtoolbox and the HiFlow3 parallel finite element package. In our approach, a single source code can be used across diverse platforms including multicore CPUs and GPUs. Highly optimized implementations are hidden behind a unified user interface. Efficiency and scalability of our multigrid solvers are demonstrated by means of a comprehensive performance analysis on multicore CPUs and GPUs.KeywordsParallel smoothersmatrix-based geometric multigridmulti-coloringpower(q)-pattern methodFSAImulti-coreGPUs