A multigrid algorithm for parallel computers: CPMG

Abstract

In this article, we present a multigrid algorithm for parallel computers, the chopped parallel multigrid (CPMG) algorithm. The CPMG algorithm improves the processor utilization by reducing the work load on coarse grids without affecting the convergence rate of the algorithm. This is in contrast to earlier approaches (Gannon and van Rosendale, 1986; Frederickson and McBryan, 1989), where unutilized processors are used to improve the convergence rate. The CPMG algorithm reduces the coarse grid work bychopping the alternate cycles of multigrid. Using analytical results and simulations on sequential machines we show that the CPMG can achieve almost the same convergence rate as standard MG for many cases. Analytically we show that the advantage gained by CPMG over standard MG on a mesh connected massively parallel machine is 33% in hardware utilization, 50% in communication overheads and 38% in overall execution time. We have also evaluated the performance of CPMG on an actual massively parallel machine, the DAP-510. The advantage gained by CPMG over standard MG is 35% in overall execution time. Moreover, the CPMG can be integrated with other parallel multigrid algorithms, such as the PSMG algorithm (Frederickson and McBryan, 1989) and Decker's algorithm (Decker, 1990).