Vectorizing matrix operations arising from PDE discretization on 9-point stencils (Q1329109)

The authors discuss a vectorization of the matrix operations that are carried out when solving the system of linear equations that arises from the discretization of a system of partial differential equations on a 2D nonrectangular domain by a 9-point stencil. In particular, the authors consider an implementation of a matrix-vector multiplication and of the incomplete LU preconditioning by means of the block-diagonal storage and the indirect variant of the hyperplane method. Results of numerical experiments show a significant gain in computational time as compared with the general-purpose routines from the SLAP library.