Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning
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-i...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/872901 |
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| author | Luca Bergamaschi Angeles Martínez Giorgio Pini |
| author_facet | Luca Bergamaschi Angeles Martínez Giorgio Pini |
| author_sort | Luca Bergamaschi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c931e907048745e7823eb373649ac83c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c931e907048745e7823eb373649ac83c2025-02-03T01:10:51ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/872901872901Parallel Rayleigh Quotient Optimization with FSAI-Based PreconditioningLuca Bergamaschi0Angeles Martínez1Giorgio Pini2Department of Mathematical Methods and Models for Scientific Applications, University of Padova, Via Trieste 63, 35121 Padova, ItalyDepartment of Mathematical Methods and Models for Scientific Applications, University of Padova, Via Trieste 63, 35121 Padova, ItalyDepartment of Mathematical Methods and Models for Scientific Applications, University of Padova, Via Trieste 63, 35121 Padova, ItalyThe 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.http://dx.doi.org/10.1155/2012/872901 |
| spellingShingle | Luca Bergamaschi Angeles Martínez Giorgio Pini Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning Journal of Applied Mathematics |
| title | Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning |
| title_full | Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning |
| title_fullStr | Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning |
| title_full_unstemmed | Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning |
| title_short | Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning |
| title_sort | parallel rayleigh quotient optimization with fsai based preconditioning |
| url | http://dx.doi.org/10.1155/2012/872901 |
| work_keys_str_mv | AT lucabergamaschi parallelrayleighquotientoptimizationwithfsaibasedpreconditioning AT angelesmartinez parallelrayleighquotientoptimizationwithfsaibasedpreconditioning AT giorgiopini parallelrayleighquotientoptimizationwithfsaibasedpreconditioning |