Analysis of the Multigrid FMV Cycle on Large-Scale Parallel Machines
Ray S. Tuminaro, David E. Womble · SIAM Journal on Scientific Computing · 1993
On serial computers it is well known that the multigrid FMV cycle is preferable to the V cycle both asymptotically and in practical use over a wide range of applications. However, on massively parallel machines, the parallel efficiency of the FMV (full multigrid V cycle) scheme is noticeably lower than that of the V cycle due to a large percentage of time spent on coarse grids. Thus the question arises: are the additional coarse grid computations within the FMV cycle warranted on massively parallel machines? To answer this, a number of issues are addressed regarding parallel FMV cycles: what efficiencies can be achieved; how do these compare with V cycle efficiencies; are FMV cycles still preferable to V cycles in a massively parallel environment? A model is used to analyze the efficiency of both FMV and V cycles as a function of relaxation efficiency. Using this model, the standard FMV grid-switching criterion is modified to incorporate the efficiency of the coarse grid processing. Numerical results obtained from a multigrid implementation on a 1024-processor nCUBE 2 are used in conjunction with the model to quantify the performance and efficiency of the FMV cycle. Finally, comments are made regarding limitations of parallel processors based on FMV efficiencies.