Multigrid Algorithms on the Hypercube Multiprocessor

This paper examines several ways of implementing multigrid algorithms on the hypercube multiprocessor. We consider both the standard multigrid algorithms and a concurrent version proposed by Gannon and Van Rosendale. We present several mappings of the mesh points onto the nodes of the cube. The main property of these mappings, which are based on binary reflected Gray codes, is that the distance between neighboring grid points remains constant from one grid level to another. This results in a communication effective implementation of multigrid algorithms on the hypercube multiprocessor.