Abstract
It is of interest to solve large scale sparse linear systems on distributed computers, using Krylov subspace methods along with domain decomposition methods. If accurate subdomain solutions are used, the restricted additive Schwarz preconditioner allows a reduction to the interface via the Schur complement, which leads to an unpreconditioned reduced operator for the interface unknowns. Our purpose is to form a preconditioner for this interface operator by approximating it as a low-rank correction of the identity matrix. To this end, we use a sequence of orthogonal vectors and their image under the interface operator, which are both available after some iterations of the generalized minimal residual method.
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Acknowledgement
This work has been supported by the French National Agency of Research, through the ANR-MONU12-0012 H2MNO4 project. The authors wish to express their thanks to Stéphane Aubert for some stimulating conversations and suggestions.
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Pacull, F., Tromeur-Dervout, D. (2016). Preconditioning of the Reduced System Associated with the Restricted Additive Schwarz Method. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_62
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DOI: https://doi.org/10.1007/978-3-319-18827-0_62
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18826-3
Online ISBN: 978-3-319-18827-0
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