SOFTWARE FOR LARGE-SCALE NUMERICAL CALCULATION USING EXTERNAL MEMORY DEVICES

ITERATIVE METHODS FOR SOLVING SPARSE LINEAR SYSTEMS REQUIRE SIGNIFICANTLY FEWER ARITHMETIC OPERATIONS AND LESS MEMORY THAN CURRENTLY POPULAR DIRECT METHODS. HOWEVER, FOR VERY LARGE PROBLEMS, FOR EXAMPLE AS DERIVED FROM DISCRETIZATIONS OF PARTIAL DIFFERENTIAL EQUATIONS IN THREE SPACE VARIABLES, IT IS STILL NECESSARY TO USE SECONDARY STORAGE DEVICES TO STORE THE REQUIRED DATA. WE PROPOSE TO DEVELOP AN EFFICIENTOUT-OF-CORE VERSION OF OUR POWERFUL SPARSE PRECONDITIONED CONJUGATE GRADIENT ITERATIVE METHOD PACKAGE, PCGPAK. THIS WILL INVOLVE THE DEVELOPMENT AND IMPLEMENTATION OF NEW ALGORITHMS WHICH ATTEMPT TO MINIMIZE DISK TRAFFIC AND OVERLAP REQUIRED READS WRITES WITH COMPUTATION AS MUCH AS POSSIBLE. OUR ANALYSIS LEADS US TO BELIEVE THAT WE CAN DEVELOP A PACKAGE WHOSE PERFORMANCE WILL BE CPU BOUND (AS DISTINCT FROM I/O BOUND) ON MOST REASONABLY BALANCED COMPUTER SYSTEMS FOR MOST PROBLEMS OF COMMON INTEREST. AN OUT-OF-CORE PCGPAK WOULD ALLOW USERS TO SOLVE ARBITRARILY LARGE SPARSE LINEAR SYSTEM WITH GREAT SPEED WITHOUT PAYING THE PENALTY OF USING SECONDARY STORAGE DEVICES. FURTHERMORE USERS WOULD NOT HAVE TO CONCERN THEMSELVES WITH THE INTRICATE DETAILS INVOLVED WITH EFFICIENT I/O PROGRAMMING. AN OUT-OF-CORE PCGPAK HAS OUTSTANDING COMMERCIAL POTENTIAL. THE OIL INDUSTRY IS A CONCRETE EXAMPLE OF WHERE SUCH A PACKAGE WOULD BE USED IMMEDIATELY. ALL COMMERCIAL SIMULATE HAVE AN "EVERYTHING BUT THE LINEAR SYSTEM" OUT-OF-CORE OPTION NOW AND WOULD INCLUDE AN OUT-OF-CORE LINEAR SYSTEM SOLVER -- IF AN ADEQUATE ONE EXISTED. OTHER INDUSTRIES WITH A CLEAR NEED FOR SUCH A COMMERCIAL PRODUCT INCLUDE THE AEROSPACE, FLUIDS, AND STRUCTURES INDUSTRIES.