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

Adriano Mauricio Cortes, Lisandro Dalcin, Adel Sarmiento, N. Collier, Victor M. Calo

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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−supinf−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.
Original languageEnglish (US)
Pages (from-to)839-858
Number of pages20
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Oct 19 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This publication was made possible in part by a National Priorities Research Program grant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation), by the European Union’s Horizon 2020 Research and Innovation Program under the Marie Sklodowska-Curie grant agreement No 644602 and the Center for Numerical Porous Media at King Abdullah University of Science and Technology (KAUST). The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper.


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