ALGEBRAIC HYBRIDIZATION AND STATIC CONDENSATION WITH APPLICATION TO SCALABLE H(div) PRECONDITIONING

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 (2012), pp. A3079-A3098], 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.