Parallel multigrid algorithms for some specialized computer systems

Abstract

The paper deals with parallelization of multigrid algorithms for some specialized parallel computer systems. These algorithms are optimal because the number of operations that have to be performed linearly depends on the number of discrete unknowns which are to be evaluated. It is shown that for a SIMD-type computer the separate location of grid point values in orthogonal memory blocks and permutation network functions allow to implement the computational phases of the multigrid cycle in parallel. The effective mapping of partitioned grid onto the processors by the Gray code is described for hypercube multiprocessors. Finally, the VLSI design for a multigrid algorithm is presented where the best hitherto known upper bound for solving the model elliptic problem in the area-time complexity is achieved.