Factorized approximate inverse preconditioning of a parallel sparse eigensolver

n this paper we analyze the parallel efficiency of the approximate inverse preconditioners AINV and FSAI as DACG preconditioners for the solution of Finite Element and Finite Difference eigenproblems. DACG is an optimization method which sequentially computes the smallest eigenpairs of a symmetric, positive definite, generalized eigenproblem, by CG minimizations of the Rayleigh quotient over subspaces of decreasing size. Numerical tests on a Cray T3E Supercomputer were performed, showing the high degree of parallelism attainable by our code. We found that AINV and FSAI are both effective preconditioners for our parallel DACG algorithm.