FAST ADAPTIVE COMPOSITE GRID METHODS FOR HIGH PERFORMANCE COMPUTER SYSTEMS

THIS PROJECT WILL STUDY, IN THE CONTEXT OF HIGH PERFORMANCE COMPUTER SYSTEMS, THE NEWLY CONCEIVED FAST ADAPTIVE COMPOSITE GRID METHOD (FAC) FOR NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL BOUNDARY VALUE PROBLEMS. FAC IS A METHOD FOR ADAPTING LOCAL GRIDS TO RESOLVE LOCAL PHYSICAL PHENOMENA AND FOR VERY FAST SOLUTION OF THE RESULTING DISCRETE EQUATIONS; IT CAN IMPLEMENT THE CAREFULLY DEVELOPED DISCRETIZATION PRINCIPLES OF THE BEST MESH REFINEMENT STRATEGIES; IT CAN BE EASILY PATCHED TO EXISTING APPLICATIONS SOFTWARE; AND IT IS VERY SUITABLE FOR PARALLEL COMPUTATION SINCE IT PARTITIONS THE PROBLEM INTO SEVERAL INDEPENDENT, REGULAR TASKS AND PROVIDES A VERY EFFICIENT MEANS OF MULTI-TASK COMMUNICATION. THE OBJECTIVE OF THIS PHASE I PROJECT IS TO STUDY THE ATTRIBUTES OF FAC IN TERMS OF PARALLEL PROCESSING COMPUTER ARCHITECTURES. ONE GOAL IS TO DEVELOP A VERY EFFICIENT VERSION OF FAC IMPLEMENTED ON THE HEP AT LOS ALAMOS NATIONAL LABORATORY. THIS WILL INVOLVE DEVELOPING FAC PROCESSES TO ADAPT TO THE HEP, SOME OF WHICH MAY BE NEW IN ORDER TO TAKE FULL ADVANTAGE OF ITS ARCHITECTURE. THE UNDERLYING THEME HERE IS THE DEVELOPMENT OF AN UNDERSTANDING OF FAC FOR HIGH PERFORMANCE SYSTEMS IN GENERAL; THAT IS, IN THE PROCESS OF RECONSIDERING FAC SPECIFICALLY FOR ITS APPLICABILITY TO THE HEP, THE PROJECT WILL ALSO ATTEMPT TO DEVELOP INSIGHT INTO GENERAL FEATURES OF PARALLEL ARCHITECTURES THAT FACILITATE ADAPTIVE METHODS AND, CONVERSELY, TO STUDY THE PERFORMANCE CHARACTERISTICS OF THESE METHODS IN A GENERAL PARALLEL ENVIRONMENT.