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Aitken's acceleration of the Schwarz process using singular value decomposition for heterogeneous 3D groundwater flow problems

Abstract : This paper is devoted to the acceleration by Aitken's technique of the convergence of the Schwarz domain decomposition method applied to large scale 3D problems with non-separable linear operators. These operators come from the discretization of groundwater flow problems modeled by the linear Darcy equation, where the permeability field is highly heterogeneous and randomly generated. To be computationally efficient, a low-rank approximation of the Aitken's formula is computed from the singular value decomposition of successive iterated solutions on subdomains interfaces. Numerical results explore the efficiency of the solver with respect to the random distribution parameters, and specific implementations of the acceleration are compared for large scale 3D problems. These results confirm the numerical behavior of the methodology obtained on 2D Darcy problems (Tromeur-Dervout D. Meshfree adaptive Aitken-Schwarz domain decomposition with application to Darcy flow. Comput Sci Eng Technol 2009;21:217-50).
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https://hal.archives-ouvertes.fr/hal-00863497
Contributor : Damien Tromeur-Dervout Connect in order to contact the contributor
Submitted on : Thursday, September 19, 2013 - 9:35:15 AM
Last modification on : Monday, June 28, 2021 - 2:26:03 PM

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Laurent Berenguer, Thomas Dufaud, Damien Tromeur-Dervout. Aitken's acceleration of the Schwarz process using singular value decomposition for heterogeneous 3D groundwater flow problems. Computers and Fluids, Elsevier, 2013, 80, pp.320-326. ⟨10.1016/j.compfluid.2012.01.026⟩. ⟨hal-00863497⟩

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