Parallel Dense Gauss-Seidel Algorithm on Many-Core Processors

Abstract

The Gauss-Seidel method is very efficient for solving problems such as tightly-coupled constraints with possible redundancies. However, the underlying algorithm is inherently sequential. Previous works have exploited sparsity in the system matrix to extract parallelism. In this paper, we propose to study several parallelization schemes for fully-coupled systems, unable to be parallelized by existing methods, taking advantage of recent many-cores architectures offering fast synchronization primitives. Experimental results on both multi-core CPUs and recent GPUs show that our proposed method is able to fully exploit the available units, whereas trivial parallel algorithms often fail. This method is illustrated by an application in medical intervention planning, where it is used to solve a linear complementary problem (LCP) expressing the contacts applied to a deformable body.