Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1137/120882846 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
Brinkman problem,Stokes-Darcy coupling,saddle-point problems,block preconditioners,algebraic multigrid | Discretization,Mathematical optimization,Preconditioner,Mathematical analysis,Constant coefficients,Finite element method,Curl (mathematics),Multigrid method,Piecewise,Block matrix,Mathematics | Journal |
Volume | Issue | ISSN |
35 | 5 | 1064-8275 |
Citations | PageRank | References |
1 | 0.35 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Panayot S. Vassilevski | 1 | 101 | 13.75 |
| Umberto Villa | 2 | 30 | 6.64 |