Algebraic Hybridization and Static Condensation with Application to Scalable H(div) Preconditioning
This work provides an algebraic framework for two common finite element techniques, enabling more efficient scalable solvers for H(div) problems, which is important for computational mechanics and electromagnetics.
The paper proposes a unified algebraic approach for static condensation and hybridization in finite element discretizations, demonstrating that hybridization outperforms a state-of-the-art parallel solver (ADS) for H(div) problems, with increasing benefit for higher-order elements.
We propose an unified algebraic approach for static condensation and hybridization, two popular techniques in finite element discretizations. The algebraic approach is supported by 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, available in the software hypre and MFEM. The superior performance of the hybridization technique is clearly demonstrated with increased benefit for higher order elements.