Algorithm 881 - Archive ouverte HAL
Article Dans Une Revue ACM Transactions on Mathematical Software Année : 2008

Algorithm 881

Résumé

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.
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Dates et versions

hal-03707582 , version 1 (28-06-2022)

Identifiants

Citer

Valérie Frayssé, Luc Giraud, Serge Gratton. Algorithm 881. ACM Transactions on Mathematical Software, 2008, 35 (2), pp.1-12. ⟨10.1145/1377612.1377617⟩. ⟨hal-03707582⟩
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