Software acceleration of CARP, an iterative linear solver and preconditioner

We present the results of software optimization of a row-wise preconditioner (Component Averaged Row Projections) for the method of conjugate gradients, which is used to solve the diagonally banded Helmholtz system representing frequency domain, isotropic acoustic seismic wave simulation. We demonstrate that in our application, a preconditioner bound to one processor core and accessing memory contiguously reduces execution time by 7% for matrices having on the order of 108 non-zeros. For reference we note that our C implementation is over 80 times faster than the corresponding code written for a high-level numerical analysis language.