Algorithm 881: A Set of Flexible GMRES Routines for Real and Complex Arithmetics on High-Performance Computers In this article we describe our implementations of the FGMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared-memory, and distributed-memory computers. For the sake of portability, simplicity, flexibility, and efficiency, the FGMRES solvers have been implemented in Fortran 77 using the reverse communication mechanism for the matrix-vector product, the preconditioning, and the dot-product computations. For distributed-memory computation, several orthogonalization procedures have been implemented to reduce the cost of the dot-product calculation, which is a well-known bottleneck of efficiency for Krylov methods. Furthermore, either implicit or explicit calculation of the residual at restart is possible depending on the actual cost of the matrix-vector product. Finally, the implemented stopping criterion is based on a normwise backward error. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 17 articles )

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  1. Morikuni, Keiichi; Hayami, Ken: Inner-iteration Krylov subspace methods for least squares problems (2013)
  2. Bernsen, Erik; Dijkstra, Henk A.; Thies, Jonas; Wubs, Fred W.: The application of Jacobian-free Newton-Krylov methods to reduce the spin-up time of ocean general circulation models (2010)
  3. Giraud, L.; Haidar, A.; Pralet, S.: Using multiple levels of parallelism to enhance the performance of domain decomposition solvers (2010)
  4. Mercader, I.; Batiste, O.; Alonso, A.: An efficient spectral code for incompressible flows in cylindrical geometries (2010)
  5. Pernet, Sébastien: A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition (2010)
  6. Duff, Iain S.: The design and use of a sparse direct solver for skew symmetric matrices (2009)
  7. Giraud, L.; Haidar, A.: Parallel algebraic hybrid solvers for large 3D convection-diffusion problems (2009)
  8. Marques, F.; Mercader, I.; Batiste, O.; Lopez, J.M.: Centrifugal effects in rotating convection: Axisymmetric states and three-dimensional instabilities (2007)
  9. Frangi, A.; Spinola, G.; Vigna, B.: On the evaluation of damping in MEMS in the slip-flow regime (2006)
  10. Nadiga, Balasubramanya T.; Taylor, Mark; Lorenz, Jens: Ocean modelling for climate studies: Eliminating short time scales in long-term, high-resolution studies of ocean circulation (2006)
  11. Ni, Qin; Ling, Chen; Qi, Liqun; Teo, Kok Lay: A truncated projected Newton-type algorithm for large-scale semi-infinite programming (2006)
  12. Carpentieri, B.; Duff, I.S.; Giraud, L.; Sylvand, G.: Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations (2005)
  13. Frangi, A.: A fast multipole implementation of the qualocation mixed-velocity-traction approach for exterior Stokes flows (2005)
  14. Frangi, A.; Gioia, A.di.: Multipole BEM for the evaluation of damping forces on MEMS (2005)
  15. Frayssé, Valéire; Giraud, Luc; Gratton, Serge; Langou, Julien: Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers (2005)
  16. Strakoš, Zdeněk; Tichý, Petr: Error estimation in preconditioned conjugate gradients (2005)
  17. Carpentieri, Bruno; Duff, Iain S.; Giraud, Luc; Sylvand, Guillaume: An embedded iterative scheme in electromagnetism (2004)