Print Email Facebook Twitter On POD-based Deflation Vectors for DPCG applied to porous media problems Title On POD-based Deflation Vectors for DPCG applied to porous media problems Author Diaz Cortes, G.B. (TU Delft Numerical Analysis) Vuik, Cornelis (TU Delft Numerical Analysis) Jansen, J.D. (TU Delft Civil Engineering & Geosciences; TU Delft Geoscience and Engineering) Faculty Civil Engineering & Geosciences Department Geoscience and Engineering Date 2018-03-01 Abstract We study fast and robust iterative solvers for large systems of linear equations resulting from simulation of flow trough strongly heterogeneous porous media. We propose the use of preconditioning and deflation techniques, based on information obtained frfrom the system, to reduce the time spent in the solution of the linear system.An important question when using deflation techniques is how to find good deflation vectors, which lead to a decrease in the number of iterations and a small increase in the required computing time per iteration. In this paper, we propose the use of deflation vectors based on a POD-reduced set of snapshots. We investigate convergence and the properties of the resulting methods. Finally, we illustrate these theoretical results with numerical experiments. We consider compressible and incompressible single-phase flow in a layered model with variations in the permeability layers up to 10 3 and the SPE 10 benchmark model with a contrast in permeability coefficients of 10 7. Using deflation for the incompressible problem, we reduce the number of iterations to 1 or 2 iterations. With deflation, for the compressible problem, we reduce up to ∼ 80% the number of iterations when compared with the only-preconditioned solver. Subject DeflationPODPCGSingle-phaseflowHeterogeneous porous media To reference this document use: http://resolver.tudelft.nl/uuid:e5a8f2ea-de2c-4cab-9c5c-be630e28202d DOI https://doi.org/10.1016/j.cam.2017.06.032 Embargo date 2018-02-15 ISSN 0377-0427 Source Journal of Computational and Applied Mathematics, 330, 193-213 Bibliographical note Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2018 G.B. Diaz Cortes, Cornelis Vuik, J.D. Jansen Files PDF 1_s2.0_S0377042717303400_main.pdf 2.84 MB Close viewer /islandora/object/uuid:e5a8f2ea-de2c-4cab-9c5c-be630e28202d/datastream/OBJ/view