SHARED MEMORY IMPLEMENTATION OF A LINEAR SYSTEM SOLVER

SHARED-MEMORY ARCHITECTURES (E.G. THE CRAY-2, THE CRAY-XMP, THE ENCORE MULTIMAX, THE SEQUENT BALANCE SERIES, THE BBN BUTTERFLY, AND THE IBM RP3 PROJECT) ARE ONE OF THE TWO MAJOR APPROACHES TO BUILDING PARALLEL ARCHITECTURES. FOR A LIMITED NUMBER OF PROCESSORS, THE INTERPROCESSOR COMMUNICATION COST (RELATIVE TO THE FLOATING POINT SPEED) IS LOWER FOR SHARED GLOBAL MEMORY MACHINES THAN FOR MESSAGE-PASSING MACHINES. TO DATE, SHARED GLOBAL MEMORY MACHINES HAVE BEEN THE MORE SUCCESSFUL MULTIPROCESSING ARCHITECTURE. BECAUSE SHARED GLOBAL MEMORY MACHINES ARE THEDOMINANT PARALLEL ARCHITECTURE TODAY, IT IS CRITICAL THAT FUNDAMENTAL SCIENTIFIC COMPUTING TOOLS BE DEVELOPED FOR THEM. SCIENTIFIC COMPUTING ASSOCIATES, INC. PROPOSES TO TAKE A STATE-OF-THE-ART SOFTWARE TOOL THAT SOLVES THE COMPUTE-INTENSIVE KERNELS OF MOST LARGE-SCALE COMPUTATIONS FOR SEQUENTIAL PROCESSING ARCHITECTURES AND MODIFY IT FOR SHARED-MEMORY MULTIPROCESSING ENVIRONMENTS. THE TOOL IS PCGPAKTM, THE PRECONDITIONED CONJUGATE GRADIENT PACKAGE OF SUBROUTINES FOR THE ITCRATIVE SOLUTION OF LARGE, SPARSE, NONSYMMETRIC SYSTEMS OF LINEAR EQUATIONS, WHICH ARISE REPEATEDLY IN A VERY WIDE RANGE OF APPLICATION AREAS, PARTICULARLY THOSE AREAS CURRENTLY MAKING THE GREATEST DEMANDS ON LARGE-SCALE COMPUTING RESOURCES. THE PARALLEL IMPLEMENTATION OF PCGPAKTM WILL PERMIT ENGINEERS AND SCIENTISTS TO SOLVE THESE DIFFICULT NUMERICAL PROBLEMS RAPIDLY AND EFFICIENTLY, WITHOUT SPECIALIZED KNOWLEDGE OF ALGORITHMIC OR PROGRAMMING TECHNIQUES. THUS, THEY CAN FULLY USE THE POWER OF SHARED-MEMORY ARCHITECTURES.