Semicoarsening Multigrid on a Hypercube

A semicoarsening multigrid algorithm suitable for the kinds of problems arising in reservoir simulation has been implemented on the Intel iPSC/2 hypercube. The method is an extension to nonsymmetric problems of a method in [Dendy et al., Paper SPE 18409, presented at Society of Petroleum Engineers Symposium on Reservoir Simulation, Houston, TX, 1989]. It performs well for strongly anisotropic problems and problems with strongly discontinuous coefficients. For a test set of reservoir simulation problems, residual reduction factors for a full-multigrid V-cycle range from 0.0022 to 0.19. The current codes achieve about 50 percent parallel efficiency in two dimensions and about 30 percent parallel efficiency in three dimensions with about $\sqrt{N} /8$ processors for a grid with N unknowns.