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 parallelhyprepackage, 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.
Highlights
The computation by iterative methods of the s partial eigenspectrum of the generalized eigenproblem: Au λBu, 1.1 where A, B ∈ Rn×n are large sparse symmetric positive definite SPD matrices, is an important and difficult task in many applications
The results presented in this paper show that the parallel DACG code accelerated by FSAI exhibits good scalability up to one thousand processors and displays comparable performance with respect to hypre, specially when a low number of eigenpairs is sought
We examine the performance of the parallel DACG preconditioned by both FSAI and BFSAI in the partial solution of four large-size sparse eigenproblems
Summary
The computation by iterative methods of the s partial eigenspectrum of the generalized eigenproblem: Au λBu, 1.1 where A, B ∈ Rn×n are large sparse symmetric positive definite SPD matrices, is an important and difficult task in many applications. The effectiveness of the FSAI preconditioner in the acceleration of DACG is compared to that of the Block FSAI-IC preconditioner, recently developed in , which combines the FSAI and the Block Jacobi-IC preconditioners obtaining good results on a small number of processors for the solution of SPD linear systems and for the solution of large eigenproblems. The results presented in this paper show that the parallel DACG code accelerated by FSAI exhibits good scalability up to one thousand processors and displays comparable performance with respect to hypre, specially when a low number of eigenpairs is sought.
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