Parallel Rayleigh Quotient Optimization with FSAI‐Based Preconditioning

Abstract

The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation‐Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized‐sparse‐approximate‐inverse‐ (FSAI‐) type preconditioners. We present an enhanced parallel implementation of the FSAI preconditioner and make use of the recently developed Block FSAI‐IC preconditioner, which combines the FSAI and the Block Jacobi‐IC preconditioners. Results onto matrices of large size arising from finite element discretization of geomechanical models reveal that DACG accelerated by these type of preconditioners is competitive with respect to the available public parallel hypre package, especially in the computation of a few of the leftmost eigenpairs. The parallel DACG code accelerated by FSAI is written in MPI‐Fortran 90 language and exhibits good scalability up to one thousand processors.