Parallel preconditioning of a sparse eigensolver

We exploit an optimization method, called deflation-accelerated conjugate gradient (DACG), which sequentially computes the smallest eigenpairs of a symmetric, positive definite, generalized eigenproblem, by conjugate gradient (CG) minimizations of the Rayleigh quotient over deflated subspaces. We analyze the effectiveness of the AINV and FSAI approximate inverse preconditioners, to accelerate DACG for the solution of finite element and finite difference eigenproblems. Deflation is accomplished via CGS and MGS orthogonalization strategies whose accuracy and efficiency are tested. Numerical tests on a Cray T3E Supercomputer were performed, showing the high degree of parallelism attainable by the code. We found that for our DACG algorithm, AINV and FSAI are both effective preconditioners. They are more efficient than Block–Jacobi.