SPAR: a new architecture for large finite element computations

Abstract

The finite element method is a general and powerful technique for solving partial differential equations. The computationally intensive step of this technique is the solution of a linear system of equations. Very large and very sparse system matrices result from large finite-element 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 alternate method of representing sparse matrices and an architecture that efficiently executes computations on the proposed data structure. The SPAR architecture has not been built, but we have constructed a register-transfer level simulator and executed the sparse matrix computations used with some large finite element applications. The simulation results demonstrate a 95% utilization of the floating-point units for some 3D applications. SPAR achieves high utilization of memory, memory bandwidth, and floating-point units when executing sparse matrix computations. >