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 matrice s with an irregular block structure. In this paper we discuss the vect orization of the matrix-vector multiply and of the Incomplete LU facto rization and backsolve for these types of matrices. The performance of the matrix-vector multiply is already optimal for a small number of g rid 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-pu rpose routines from the SLAP library shows a significant gain in compu tational time.