Solving elliptic partial differential equations on the hypercube multiprocessor

We discuss the implementation of several classical methods for solving elliptic partial differential equations on the hypercube multiprocessor. The methods considered are the alternating directions implicit (ADI) algorithm, a direct banded Gaussian elimination method and multigrid methods. The complexity analysis of these algorithms shows that high efficiencies can be achieved by carefully assigning the data to the processors and (sometimes) resorting to more parallellizable methods. The binary reflected Gray code plays an important role for both the multigrid and the ADI algorithms.