Solving Elliptic Partial Differential Equations on the Hypercube Multiprocessor

...-I I for public release and 'sa le;its " La _ L ditribution is unlimited. DEPARMENTOF COMPUTER SCIENCE UNVRIT.. I-F t, Abstract. We-ie ~ the implementation of several classical methods for solving elliptic partial differential equations on the hypercube multiprocessor. The method.s considered are the Alternating Directions Implicit (AD!) algorithm, a direct banded Gaussian elimination method and multigrid methods. The complexityv analyvsis of these algorithms shows that high effciencies can be achieved by carefully assigning the data to the processors and (sometimes) resorting to more parallelizable methods. The binaryv reflected Gray code plays an important role for both the multigrid and the AD! algorithms