SPAR - A NEW ARCHITECTURE FOR LARGE FINITE-ELEMENT COMPUTATIONS

The finite element method is a general and powerful technique for solv ing partial differential equations. The computationally intensive step of this technique is the solution of a linear system of equations. Ve ry large and very sparse system matrices result from large finite-elem ent applications. The sparsity must be exploited for efficient use of memory and computational components in executing the solution step. In this paper we propose a scheme, called SPAR, for efficiently storing and performing computations on sparse matrices. SPAR consists of an al ternate method of representing sparse matrices and an architecture tha t efficiently executes computations on the proposed data structure. Th e SPAR architecture has not been built, but we have constructed a regi ster-transfer level simulator and executed the sparse matrix computati ons used with some large finite element applications. The simulation r esults demonstrate a 95% utilization of the floating-point units for s ome 3D applications. SPAR achieves high utilization of memory, memory bandwidth, and floating-point units when executing sparse matrix compu tations.