Parallel rapid operator for iterative finite element solvers on a shared memory machine

Abstract

The p-version of the finite element method, which uses high order hierarchic basis functions within an element, allows for ease of adaptive computation, and high accuracy with relatively few degrees of freedom. However, the solution time and storage requirements for large three-dimensional problems can be very high when a global matrix is assembled. The use of rapid operator application in iterative methods leads to minimal storage requirements, because neither elemental nor global matrices are formed. We show in this paper that this algorithm is amenable to parallel and vector computation, and is readily implemented on shared memory machines. Elements are assigned to processors as they become available, and the computations are completely dominated by matrix-matrix multiplications, which can be tuned for maximum speed. Results showing the high efficiency and scalability of such a scheme on an IBM 3090/600 with Vector Facility are given.