Some multigrid algorithms for elliptic problems on data parallel machines

Previously a semicoarsening multigrid algorithm suitable for use on data parallel architectures was investigated. Through the use of new software tools, the performance of this algorithm has been considerably improved. The method has also been extended to three space dimensions. The method performs well for strongly anisotropic problems and for problems with coefficients jumping by orders of magnitude across internal interfaces. The parallel efficiency of this method is analyzed, and its actual performance on the CM-5 is compared with its performance on the CRAY Y-MP and the Sparc-5. A standard coarsening multigrid algorithm is also considered, and we compare its performance on these three platforms as well.