A BLOCK-DIAGONAL ALGEBRAIC MULTIGRID PRECONDITIONER FOR THE BRINKMAN PROBLEM

作者：Vassilevski Panayot S^*; Villa Umberto

来源：SIAM Journal on Scientific Computing, 2013, 35(5): S3-S17.

DOI：10.1137/120882846

• Brinkman problem
• Stokes-Darcy coupling
• saddle-point problems
• block preconditioners
• algebraic multigrid

The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equations) and porous media (Darcy equations). In this work, we explore a novel mixed formulation of the Brinkman problem by introducing the flow's vorticity as an additional unknown. This formulation allows for a uniformly stable and conforming discretization by standard finite element (Nedelec, Raviart-Thomas, discontinuous piecewise polynomials). Based on the stability analysis of the problem in the H(curl) - H(div) - L-2 norms [P. S. Vassilevski and U. Villa, A mixed formulation for the Brinkman problem, SIAM J. Numer. Anal., submitted], we study a scalable block-diagonal preconditioner which is provably optimal in the constant coefficient case. Such a preconditioner takes advantage of the parallel auxiliary space AMG solvers for H(curl) and H(div) problems available in HYPRE [hypre: High Performance Preconditioners, http://www.llnl.gov/CASC/hypre/]. The theoretical results are illustrated by numerical experiments.

• 出版日期2013