MATRIX-FREE SOLUTION ALGORITHMS IN A FINITE ELEMENT CONTEXT

FINITE ELEMENT METHODS (FEM) APPLIED TO COMPUTATIONAL FLUID DYNAMICS OPEN UP THE POSSIBILITY OF NUMERICAL SIMULATION OF HIGHLY COMPLEX FLUID FLOWS OCCURRING IN INDUSTRIAL SITUATIONS. THE STATE-OF-THE-ART LIMITATION ON THE USE OF FEM IS COMPUTER RESOURCES: THE METHOD REQUIRES THE SOLUTION OF A VERY LARGE SYSTEM OF ALGEBRAIC EQUATIONS, CURRENTLY EFFECTED BY INVERTING THE JACOBIAN MATRIX, A PROCESS INVOLVING VERY HIGH COSTS IN COMPUTER TIME, IO AND PERIPHERAL STORAGE. THIS RESEARCH PROJECT AIMS TO INVESTIGATE AND IMPLEMENT A NEW MATRIX-FREE SOLUTION TECHNIQUE THAT OBVIATES THE COSTLY MATRIX INVERSION; THIS TECHNIQUE IS BASED ON A VARIANT OF THE CONJUGATE GRADIENT METHOD. RECENT RESEARCH AND TESTING ON SIMPLE PROBLEMS HAS INDICATED THE PROSPECT OF A DRAMATIC SAVING IN COSTS. SUCCESSFUL IMPLEMENTATION IN A FEM, FLUID DYNAMICS CONTEXT WILL VASTLY EXPAND THE RANGE OF FLOWS (TURBULENT, NON-NEWTONIAN, THREE-DIMENSIONAL) THAT CAN BE SIMULATED WITHCURRENTLY AVAILABLE HARDWARE.