Parallel Implementation of a Sparse Approximate Inverse Preconditioner

A parallel implementation of a sparse approximate inverse (spai) preconditioner for distributed memory parallel processors (dmpp) is presented. The fundamental spai algorithm is known to be a useful tool for improving the convergence of iterative solvers for ill-conditioned linear systems. The parallel implementation (parspai) exploits the inherent parallelism in the spai algorithm and the data locality on the dmpps, to solve structurally symmetric (but non-symmetric) matrices, which typically arise when solving partial diierential equations (pdes). Some initial performance results are presented which suggest the usefulness of parspai for tackling such large size systems on present day dmpps in a reasonable time. The parspai preconditioner is implemented using the Message Passing Interface (mpi) and is embedded in the parallel library for unstructured mesh problems (plump).