Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system
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Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-Spline discretization of the Stokes system.pdf
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ArticleKAUST Department
Earth Science and Engineering ProgramNumerical Porous Media SRI Center (NumPor)
Physical Science and Engineering (PSE) Division
Date
2015-02-20Online Publication Date
2015-02-20Print Publication Date
2015-11Permanent link to this record
http://hdl.handle.net/10754/558296
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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 discretized Stokes equations, these spaces generate a symmetric and indefinite saddle-point linear system. Krylov subspace methods are usually the most efficient procedures to solve such systems. One of such methods, for symmetric systems, is the Minimum Residual Method (MINRES). However, the efficiency and robustness of Krylov subspace methods is closely tied to appropriate preconditioning strategies. For the discrete Stokes system, in particular, block-diagonal strategies provide efficient preconditioners. In this article, we compare the performance of block-diagonal preconditioners for several block choices. We verify how the eigenvalue clustering promoted by the preconditioning strategies affects MINRES convergence. We also compare the number of iterations and wall-clock timings. We conclude that among the building blocks we tested, the strategy with relaxed inner conjugate gradients preconditioned with incomplete Cholesky provided the best results.Citation
Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system 2015 Journal of Computational SciencePublisher
Elsevier BVJournal
Journal of Computational ScienceAdditional Links
http://linkinghub.elsevier.com/retrieve/pii/S1877750315000095ae974a485f413a2113503eed53cd6c53
10.1016/j.jocs.2015.01.005