Chak, S. Lee
Parallel solver for H(div) problems using hybridization and AMG

Department of Mathematics
Mailstop 3368
Texas A&M University
College Station, TX 77843-3368
cslee@math.tamu.edu
Panayot S. Vassilevski

In this paper, a scalable parallel solver is proposed for ${\boldsymbol H}$ (div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied ${\boldsymbol H}$ (div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a $H^1$ -equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for $H^1$ problems. Weak and strong scaling of the method are examined through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [Kolev and Vassilevski, 2012], for ${\boldsymbol H}$ (div) problems. In fact, it outperforms ADS for higher order elements.