A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

© 2016 Elsevier B.V.The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time. inf-sup stable and pointwise divergence-free. When applied to the discretized Stoke...

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Main Authors: Côrtes, A., Dalcin, L., Sarmiento, A., Collier, N., Calo, Victor
Format: Journal Article
Published: 2016
Online Access:http://hdl.handle.net/20.500.11937/51154
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author Côrtes, A.
Dalcin, L.
Sarmiento, A.
Collier, N.
Calo, Victor
author_facet Côrtes, A.
Dalcin, L.
Sarmiento, A.
Collier, N.
Calo, Victor
author_sort Côrtes, A.
building Curtin Institutional Repository
collection Online Access
description © 2016 Elsevier B.V.The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time. inf-sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show how the nesting of "black-box" solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.
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spelling curtin-20.500.11937-511542018-03-29T09:09:26Z A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem Côrtes, A. Dalcin, L. Sarmiento, A. Collier, N. Calo, Victor © 2016 Elsevier B.V.The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time. inf-sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show how the nesting of "black-box" solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section. 2016 Journal Article http://hdl.handle.net/20.500.11937/51154 10.1016/j.cma.2016.10.014 restricted
spellingShingle Côrtes, A.
Dalcin, L.
Sarmiento, A.
Collier, N.
Calo, Victor
A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem
title A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem
title_full A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem
title_fullStr A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem
title_full_unstemmed A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem
title_short A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem
title_sort scalable block-preconditioning strategy for divergence-conforming b-spline discretizations of the stokes problem
url http://hdl.handle.net/20.500.11937/51154