ADVANCED ITERATIVE SOLVERS FOR HIGH ORDER FINITE ELEMENTS

THIS PROJECT IS STUDYING A NEW CLASS OF VERY PROMISING, HIGHLY PARALLEL ITERATIVE METHODS FOR THE SOLUTION OF LARGE-SCALE SYSTEMS WHICH ARISE FROM HIGH-ORDER ELEMENTS (THE P-VERSION FINITE ELEMENT METHOD) IN THREE-DIMENSIONAL ELASTICITY FOR STRUCTURES WITH PLATES, SHELLS, AND JUNCTURES. THE SIZE OF PROBLEMS OF INTEREST NOW RULES OUT DIRECT SOLVERS, BUT HIGH ORDER ELEMENTS, PARTICULARLY THIN ELEMENTS, GIVE RISE TO VERY ILL-CONDITIONED SYSTEMS OF EQUATIONS, WHICH NECESSITATE NEW SPECIFIC PRECONDITIONERS. RESEARCHERS ARE INVESTIGATING NEW METHODS FOR PRECONDITIONING THIN, SOLID, HIGH-ORDER ELEMENTS AND STUDYING THEIR PERFORMANCE ON THREE-DIMENSIONAL PROBLEMS WITH UP TO OVER ONE MILLION DEGREES OF FREEDOM. THE DESIGN AND DEVELOPMENT IS GUIDED BY THEORETICAL ANALYSES AS WELL AS EXTENSIVE EXPERIMENTATION. RESEARCH WILL RESULT IN A COARSE GRAINED PARALLEL PROTOTYPE CODE RUNNING ON CRAY-YMP. THE PROJECT WILL FURTHER KNOWLEDGE IN THE AREAS OF MULTILEVEL AND DOMAIN DECOMPOSITION COMPUTATIONAL METHODS ON PARALLEL SUPERCOMPUTERS. THE AVAILABILITY OF THE METHODS WILL HAVE A SIGNIFICANT IMPACT ON MECHANICAL ENGINEERING PRACTICE.