Parallel GMRES with Adaptive preconditioner based on deflation. It enhances the convergence of the restarted GMRES by the deflation techniques. Eigencomponents that slow down the convergence of GMRES (usually the smallest eigenvalues of the coefficient matrix) are approximated along the restart cycles of GMRES and a preconditioner is built from that. This preconditioner is then associated with an additive Schwarz preconditioner to build a parallel iterative linear solver.

The code is included in PETSc since the 3.1 release.

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Parallel GMRES with adaptive augmented Newton basis. This version of GMRES uses the Newton polynomials to enhance the parallelism during the computation of the Krylov basis. Compared to the classical GMRES, it communicates less and produces less dependencies between the processes sharing the computation of the basis. The robustness is enhanced by allowing the searching subspace to be enriched by some well chosen eigenvectors to avoid stagnation in GMRES and accelerate the convergence of the method. This approach is implemented using the PETSc package via the KSP module. It benefits from the optimized linear algebra routines available and can be used with the numerous preconditioners implemented in the package.

The whole code is now included into the devel branch of PETSc.

Contributors : Roger B. Sidje, Guy Atenekeng

Related publications:

  • Désiré NUENTSA WAKAM and Jocelyne ERHEL, Parallelism and robustness in GMRES with the Newton basis and the deflated restarting, In revision for ETNA, Preprint.


GMRES Preconditioned by multiplicative Schwarz and Deflation. This solver implements a parallel multiplicative Schwarz preconditioner and a GMRES accelerator similar to that in AGMRES. The solver comprises a partitioning algorithm that permuts first the input matrix in block diagonal form. The parallelism are introduced at two levels in the solver. The first level is a pipeline parallelism between the subdomains. The second level is inside the submatrices induced by the preconditioner. This quite natural approach has been found useful to keep a small number of subdomains to guarantee the convergence while using more processors to speedup the solution phase.

The solver is built on top of PETSc. It will be shortly available with a public license. You can request a copy if you want to give a try.

Contributors: Guy Atenekeng, Laura Grigori, Denis Billon, Nadir Soualem

Related publications:

  • Désiré NUENTSA WAKAM and Guy-Antoine ATENEKENG, Parallel GMRES with a multiplicative Schwarz preconditioner, ARIMA Rev. Afr. Rech. Inform. Math. Appl., Vol 14, 2011.
  • Guy-Antoine ATENEKENG-KAHOU, Parallélisation de GMRES préconditionné par une itération de Schwarz multiplicatif, PhD thesis, University of Rennes I and University of Yaounde I, 2008.
  • Guy-Antoine ATENEKENG-KAHOU, Laura GRIGORI, Masha SOSONKINA, A partitioning algorithm for block-diagonal matrices with overlap, Parallel Computing, 34(6-8):332-344
  • G.-A. Atenekeng Kahou, E. Kamgnia, B. Philippe. An explicit formulation of the multiplicative Schwarz preconditioner, Applied Numerical Mathematics, 57:1197-1213, 2007


Simple Linear Solver Interface. This has been my first collection of routines to access in a uniform way several libraries for solving sparse linear systems on distributed-memory computers. The provided interface links to the interface routine provided in Hypre, pARMS, SuperLU_DIST, MUMPS and UMFPACK. The package is written in C and C++ and available on demand.

Contributors: Frederic Wang.

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