High-performance sparse matrix-vector multiplication on GPUs for structured grid computations

In this paper, we address efficient sparse matrix-vector multiplication for matrices arising from structured grid problems with high degrees of freedom at each grid node. Sparse matrix-vector multiplication is a critical step in the iterative solution of sparse linear systems of equations arising in the solution of partial differential equations using uniform grids for discretization. With uniform grids, the resulting linear system Ax = b has a matrix A that is sparse with a very regular structure. The specific focus of this paper is on sparse matrices that have a block structure due to the large number of unknowns at each grid point. Sparse matrix storage formats such as Compressed Sparse Row (CSR) and Diagonal format (DIA) are not the most effective for such matrices.