Matrix-Free Solution Algorithms in a Finite Element Context
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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 obviate 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 with                        currently available hardware.
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