Wavefront computations of band-limited matrix operations on a torus data-driven array: FEM-TORUS

Let A be an N*n nonsingular matrix of bandwidth 2w+1 (n>>w) and b be an n*1 vector. The authors design of a torus array arrangement of data-driven processors of size (2w+2)*(2w+2), on which the diagonal data band of the extended matrix (Alb) is wrapped around in (n+w+1)/(2w+2) layers. They also present a matrix-data mapping onto the torus surface and wavefront-driven algorithms of three matrix operations essential in solution processes of a linear system Ax=b often arising in finite-element analysis: (1) triangulation by Givens plane rotations on the basis of the Sameh-Kuck annihilation scheme; (2) backward substitution for obtaining a Gaussian solution; and (3) matrix-vector multiplication that appears as a basic step in iterative improvement of the initial Gaussian solution. The system is named FEM-TORUS.<>