ASYNCHRONOUS MULTILEVEL ADAPTIVE METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS ON THE NAVIER-STOKES COMPUTER

NASA IS CURRENTLY SUPPORTING A VERY PROMISING PROJECT FOR DEVELOPMENT OF A HIGH-POWERED MULTIPROCESSOR SYSTEM, THE NAVIER-STOKES COMPUTER (NSC). WHILE MULTILEVEL ALGORITHMS ARE BEING STUDIED IN THE NSC ENVIRONMENT FOR SOLVING THE ELLIPTIC EQUATIONS THAT ARISE IN DISCRETIZING INCOMPRESSIBLENAVIER-STOKES EQUATIONS, NO RESEARCH HAS YET FOCUSED ON LOCAL ADAPTIVE SCHEMES FOR THIS PURPOSE. THIS IS IMPORTANT BECAUSE VERY LARGE SCALE PHYSICAL PROBLEMS USUALLY DEMAND LOCAL RESOLUTION TO ACCOUNT FOR SUCH THINGS AS BOUNDARY SINGULARITIES, SHOCKS, AND TRANSITION REGIONS. THE PROJECT PLAN IS TO STUDY SOME VERY PROMISING MULTILEVEL METHODS DEVELOPED RECENTLY BY THE PROPOSERS. THESE METHODS EXHIBIT A VERY HIGH DEGREE OF PARALLELISM AND COMPUTATIONAL EFFICIENCY AND COUPLE WELL WITH AN EFFECTIVE LOAD BALANCER, WHICH WAS ALSO DEVELOPED BY THE PROPOSERS. THE PLAN IN PHASE I IS TO DEVELOP A SIMPLE PROTOTYPE OF THISMETHOD AND STUDY ITS PERFORMANCE ON POISSON'S EQUATION FIRST IN THE NSC SIMULATOR, THEN ON THE NSC ITSELF. PHASE II AND III WILL INVOLVE COUPLING THE ADAPTIVE SCHEME WITH THE LOAD BALANCER, EXTENDING THE CAPABILITIES TO INCLUDE MORE COMPLICATED GRID STRUCTURES AND EQUATION CHARACTERISTICS, MORE INTENSE EXPERIMENTATION, AND DEVELOPMENT OF SOFTWARE.