A data parallel implementation of the multiplication of matrices of arbitrary shapes and sizes is presented. A systolic algorithm based on a rectangular processor layout is used by the implementation. All processors contain submatrices of the same size for a given operand. Matrix-vector multiplication is used as a primitive for local matrix-matrix multiplication in the Connection Machine system CM-2 implementation. The peak performance of the local matrix-matrix multiplication is in excess of 20 Gflops s-1. The overall algorithm including all required data motion has a peak performance of 5.8 Gflops s-1.

A data parallel formulation of the finite element method is described. The data structures and the algorithms for stiffness matrix generation and the solution of the equilibrium equations are presented briefly. The generation of the elemental stiffness matrices requires no communication, even though each finite element is distributed over several processors. The conjugate gradient method with a diagonal preconditioner has been used for the solution of the resulting sparse linear system. This formulation has been implemented on the Connection Machine® model CM-2. The simulations reported in this article investigate the influence of the mesh discretization and the interpolation order on the convergence behavior of the conjugate gradient method. A linear dependence of the convergence behavior on the mesh discretization parameter is observed. In addition, the convergence rate depends on the interpolation order p as Ο(p1.6). The peak floating point rate (single-precision) for the evaluation of the stiffness matrix is approximately 2.4 Gflops s-1. The iterative solver peaks at nearly 850 Mflops s-1.