并行多重网格光滑子JGS与PGS的性能比较

Parallel Mulitgrid Smoothing:JGS vs. PGS

研究两个并行多重网格光滑子JGS和PGS,它们都是串行的GS光滑子的并行化。研究表明:JGS和PGS的光滑效果,在并行子网格内部与GS相近,而在子网格交界处附近很差。为衡量并行光滑子在子网格交界处的光滑性能,文中首次引入并行收敛速度的概念。数值结果显示,在光滑一到三次时,JGS的并行收敛速度总体优于PGS。最后结论是:JGS和PGS都算不上好的并行光滑子,设计新的并行光滑子应着眼于寻找子网格交界处误差的产生原因。

The two parapllel multigrid smoothers, JGS and PGS, were studied. They are all parallelization of the sequential Gauss-Seidel （GS） smoother. It is shown that their smoothing performances are similar to GS in the interior of parallel subgrids, however the performances are bad in the neighborhood of the interfaces of subgrids for JGS and PGS. A new notion of parallel convergence rate is introduced to express the performances of the parallel smoothers on the interfaces of subgrids Numerical results indicate that, for smoothing from one to three times, JGS is better than PGS on parallel convergence rate generally. Finally, the conclusion is gained that either JGS or PGS is not good parallel smoother and the design of new parallel smoothers depends on finding out the reason of error on the interfaces of subgrids.