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Algebraic hybridization and static condensation with application to scalable \(H\)(div) preconditioning. (English) Zbl 1420.65029

Summary: We propose a unified algebraic approach for the practical application and preconditioning of static condensation and hybridization, two popular techniques in finite element discretizations. We demonstrate the use of this algebraic framework for the construction of scalable solvers for problems involving \(H\)(div)-spaces discretized by conforming (Raviart-Thomas) elements of arbitrary order. We illustrate through numerical experiments the relative performance of the two (in some sense dual) techniques in comparison with a state-of-the-art parallel solver, ADS [T. V. Kolev and P. S. Vassilevski, SIAM J. Sci. Comput. 34, No. 6, A3079–A3098 (2012; Zbl 1332.65042)], available at http://www.llnl.gov/casc/hypre and http://mfem.org. Based on these results, we recommend the use of the hybridization technique in practice, due to its clearly demonstrated superior performance with increased benefit for higher-order elements.

MSC:

65F10 Iterative numerical methods for linear systems
65N20 Numerical methods for ill-posed problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Citations:

Zbl 1332.65042

Software:

PCBDDC; BoomerAMG
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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