Summary
Many scientific libraries are currently based on the GMRES method as a Krylov subspace iterative method for solving large linear systems. The restarted formulation known as GMRES(m) has been extensively studied and several approaches have been proposed to reduce the negative effects due to the restarting procedure. A common effect in GMRES(m) is a slow convergence rate or a stagnation in the iterative process. In this situation, it is less attractive as a general solver in industrial applications. In this work, we propose an adaptive deflation strategy which retains useful information at time of restart to avoid stagnation in GMRES(m) and improve its convergence rate. We give a parallel implementation in the PETSc package. The provided numerical results show that this approach can be effectively used in the hybrid direct/iterative methods to solve large-scale systems.
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Acknowledgements
This work is funded by the French National Agency of Research under the contract ANR-TLOG07-011-03 LIBRAERO. The work of the first author was done while visiting the NCSA at Urbana-Champaign in the context of the Joint laboratory INRIA-University of Illinois. Experiments in this paper have been carried out using the parapide cluster in the GRID’5000 experimental testbed (see https://www.grid5000.fr). We thank the referees for providing many instructive comments.
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Wakam, D.N., Erhel, J., Gropp, W.D. (2013). Parallel Adaptive Deflated GMRES. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_75
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DOI: https://doi.org/10.1007/978-3-642-35275-1_75
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