A Block Version of the SPAI Preconditioner

We present a block version of the SPAI algorithm and test its performance on large nonsymmetric matrices in a parallel environment. The SPAI algorithm, initially proposed by Grote and Huckle 1], computes a SParse Approximate Inverse for use as a preconditioner for the iterative solution of a sparse linear system of equations. It has proved to be a robust and versatile preconditioner in numerous applications. Due to its inherent parallelism it does not suuer from the usual drawbacks of incomplete factorization methods when used in a parallel environment. Indeed, the parallel implementation of SPAI by Barnard 8] 9] demonstrated the high performance and excellent scaling behavior of the algorithm across various parallel architectures. The Block-SPAI algorithm is evaluated on standard test matrices which result from nite element discretizations of uid dynamics, which tend to be relatively dense and nonsymmetric. It greatly reduces the time required to compute the approximate inverse, while maintaining the robustness, full parallelism, and excellent scaling property of the original SPAI algorithm.