Algebraic Hybridization and Static Condensation with Application to Scalable H(div) Preconditioning

TL;DR

This paper introduces a unified algebraic framework for static condensation and hybridization in finite element methods, demonstrating improved scalability and performance for H(div) problems, especially with higher order elements.

Contribution

It develops a novel algebraic approach supporting scalable solvers for H(div)-space discretizations and compares the efficiency of hybridization versus static condensation.

Findings

Hybridization outperforms static condensation in scalability.

Higher order elements benefit more from hybridization.

The proposed methods outperform the state-of-the-art parallel solver ADS.

Abstract

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.