UN CO RR EC TE D PR O O F 1 Parallel Adaptive Deflated GMRES
نویسندگان
چکیده
Many scientific libraries are currently based on the GMRES method as a Krylov 7 subspace iterative method for solving large linear systems. The restarted formulation known as 8 GMRES(m) has been extensively studied and several approaches have been proposed to reduce 9 the negative effects due to the restarting procedure. A common effect in GMRES(m) is a slow 10 convergence rate or a stagnation in the iterative process. In this situation, it is less attractive 11 as a general solver in industrial applications. In this work, we propose an adaptive deflation 12 strategy which retains useful information at time of restart to avoid stagnation in GMRES(m) 13 and improve its convergence rate. We give a parallel implementation in the PETSc package. 14 The provided numerical results show that this approach can be effectively used in the hybrid 15 direct/iterative methods to solve large-scale systems. 16
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