A Cache-Efficient Parallel Gauss-Seidel Solver with Alternating Tiling

We present a new cache-efficient parallel multilayer Gauss-Seidel algorithm to solve 2D diffusion equations on distributed memory machines, by focusing on improving its cache behaviour and parallelism simultaneously. The novelty of our parallel multi-layer algorithm lies in performing Gauss-Seidel in two alternating sweeping directions (with multiple layers, i.e., iterations per direction) and applying alternating tiling strategies in two opposite sweeping directions to the subdomain allocated to every processor. As a result, its efficiency comes from a significant reduction in two sources of overhead: data cache misses and communication costs. In comparison with two commonly used parallel Gauss-Seidel algorithms, our algorithm has good performance and scalability in a cluster computing environment.