HIGHLY PARALLEL INTERATIVE METHODS FOR MASSIVELY PARALLEL MULTIPROCESSORS

FOR THE REST OF THIS CENTURY, TWO OF THE POTENTIALLY MOST IMPORTANT ADVANCES IN THE "TECHNOLOGY" OF LARGE SCALE SCIENTIFIC COMPUTING ARE SPARSE MATRIX (ITERATIVE) ALGORITHMS AND MASSIVELY PARALLEL PROCESSING. IN THIS PROPOSAL, WE OUTLINE OUR PLANS TO BUILD A SOFTWARE PACKAGE FOR THE CONNECTION MACHINE CM-2 THAT WILL BRING THE POWER OF BOTH ADVANCES TO THE AID OF THE SCIENTIFIC COMMUNITY WITHOUT FORCING THAT COMMUNITY TO BECOME EXPERT IN EITHER TECHNOLOGY. WE PROPOSE TO DEVELOP EFFICIENT MASSIVELY PARALLEL ALGORITHMS FOR THE ITERATIVE SOLUTION OF LARGE SPARSE LINEAR SYSTEMS OF EQUATIONS. WE WILL IMPLEMENT THESE ALGORITHMS IN A PACKAGE PCGPAK/CM EXPLICITLY DESIGNED AND OPTIMIZED FOR THE CONNECTION MACHINE. PCGPAK/CM WILL BE BASED ON OUR EXISTING PROPRIETARY PACKAGE PCGPAK(TM), THE PRECONDITIONED CONJUGATE GRADIENT PACKAGE OF SUBROUTINES FOR THE ITERATIVE SOLUTION OF LARGE, SPARSE NONSYMMETRIC SYSTEMS OF LINEAR EQUATIONS. PCGPAK IS A STATEOF-THE-ART SOLVER FOR UNIPROCESSOR ARCHITECTURES. IT WAS DESIGNED AND DEVELOPED BY SCIENTIFIC COMPUTING ASSOCIATES AND IS CURRENTLY MARKETED IN A HIGHLY-PORTABLE SEQUENTIAL PROCESSOR FORTRAN IMPLEMENTATION AND A HIGHLY VECTORIZED IMPLEMENTATION FOR THE CRAY-X/MP. PCGPAK IS CURRENTLY BEING USED AT MANY SITES INCLUDING SEVERAL OF THE NSF NATIONAL SUPERCOMPUTER CENTERS. WE BELIEVE THAT COMBINATION OF THE CM-2 AND PCGPAK/CM WILL BE SO MUCH FASTER THAN EXISTING SOLUTION TECHNOLOGIES SO AS TO COMPLETELY REVOLUTIONIZE THE STATE-OF-THE-ART IN COMPUTER SIMULATION.