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.
Bibliographical noteFunding Information:
* The first author was supported in part by the Department of Energy under Contract DE-AC02-81ER10996 and by the Army Research Office under Contract DAAG-83-0177. The second and third authors were supported in part by the Office of Naval Research under Grant NOOOl4-82-K-0184 and in part by a joint study with IBM/Kingston.