Harlen, OG, Hwang, WR and Walkley, MA (2013) An efficient iterative scheme for the highly constrained augmented Stokes problem for the numerical simulation of flows in porous media. Korea-Australia Rheology Journal, 25 (1). 55 - 64. ISSN 1226-119X
Abstract
In this work, we present a new efficient iterative solution technique for large sparse matrix systems that are necessary in the mixed finite-element formulation for flow simulations of porous media with complex 3D architectures in a representative volume element. Augmented Stokes flow problems with the periodic boundary condition and the immersed solid body as constraints have been investigated, which form a class of highly constrained saddle point problems mathematically. By solving the generalized eigenvalue problem based on block reduction of the discrete systems, we investigate structures of the solution space and its subspaces and propose the exact form of the block preconditioner. The exact Schur complement using the fundamental solution has been proposed to implement the block-preconditioning problem with constraints. Additionally, the algebraic multigrid method and the diagonally scaled conjugate gradient method are applied to the preconditioning sub-block system and a Krylov subspace method (MINRES) is employed as an outer solver. We report the performance of the present solver through example problems in 2D and 3D, in comparison with the approximate Schur complement method. We show that the number of iterations to reach the convergence is independent of the problem size, which implies that the performance of the present iterative solver is close to O(N).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Verlag, 2013. This is an author produced version of a paper published in Korea-Australia Rheology Journal. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at link.springer.com |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Nov 2013 11:05 |
Last Modified: | 15 Sep 2014 01:33 |
Published Version: | http://dx.doi.org/10.1007/s13367-013-0006-9 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s13367-013-0006-9 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77020 |