Jacobi-type Gauss-Seidel Smoother with Error Compensation for Parallel Multigrid ⋆

Smoother is the most important component of parallel multigrid methods, however, the widely used Gauss-Seidel smoother is difficult to be parallelized. This paper proposes a new parallel smoother, Jacobi-type Gauss-Seidel with error compensa-tion(JGSEC), by compensating the error caused by Jacobi-type Gauss-Seidel(JGS) smoother. Requiring no more inter-processor communication than JGS, JGSEC can eliminate the main part (more than ninety-five percent) of error arising from JGS at cost of a little more work amount. Numerical experiment has verified the good performance of JGSEC