NOTE ON THE PARALLEL EFFICIENCY OF THE FREDERICKSON-MCBRYAN MULTIGRID ALGORITHM

作     者：DECKER, NH 

出 版 物：《SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING》 (工业与应用数学会科学计算杂志)

年 卷 期：1991年第12卷第1期

页      面：208-220页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：PARALLEL MULTIGRID PARALLEL MULTILEVEL ALGORITHMS MULTIGRID 

摘      要：Standard multigrid algorithms must lead to processor idle time on large-scale parallel computers because the coarsest grids have fewer points than processors. In some cases, this may be considered to be a disadvantage. Frederickson and McBryan [Multigrid Methods, Marcel Dekker, New York, 1988] show that retaining all points on all grid levels (using all processors) can lead to a superconvergent algorithm in that a very good convergence rate is obtained. Has the parallel superconvergent multigrid algorithm (PSMG) of Frederickson and McBryan solved the problem of implementing multigrid on a massively parallel single-instruction-multiple-data (SIMD) architecture? How much can be gained by retaining all points on all grid levels, keeping all processors busy? The purpose of this note is to compare the parallel efficiency of the PSMG algorithm to a standard multigrid algorithm. It is shown that the perfect processor utilization and the good convergence rates of the PSMG algorithm do lead to a more efficient algorithm for the special case of one (or fewer) grid points per processor. Normalized computation and communication requirements are given, so that the two types of algorithms can be compared directly.