VECTORIZING MATRIX OPERATIONS ARISING FROM PDE DISCRETIZATION ON 9-POINT STENCILS

When solving a system of PDEs, discretized on 9-point stencils over a nonrectangular domain, the linear systems that arise will have matrices with an irregular block structure. In this paper we discuss the vectorization of the matrix-vector multiply and of the Incomplete LU factorization and backsolve for these types of matrices. The performance of the matrix-vector multiply is already optimal for a small number of grid points (one result per clock cycle). For the ILU factorization and backsolve the vector performance is not as satisfying, partly because the resulting vector length is generally small and partly because of the heavy use of indirect addressing. A comparison with the general-purpose routines from the SLAP library shows a significant gain in computational time.