PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Fei Wang, Changhe Qiao, Stephanie Zerby, Shuonan Wu.

Title:Constraint Preconditioning for the Coupled Stokes-Darcy System
Seminar:CCMA PDEs and Numerical Methods Seminar Series
Speaker:Scott Ladenheim, Temple University
Abstract:
We propose the use of a constraint preconditioner for the iterative solution of the linear system arising from the finite element discretization of coupled Stokes-Darcy flow. The coupled Stokes-Darcy system is a set of partial differential equations modeling the coupling of free flow to porous media flow across an interface. The fully coupled system matrix is of saddle point form and therefore indefinite. The constraint preconditioner is also indefinite, mimicking the structure of the system matrix. We provide spectral bounds for the preconditioned system which are independent of the underlying mesh size. As a result of these bounds, the convergence of constraint preconditioned GMRES for this problem is fixed, independent of the mesh size. For large-scale, three dimensional flow problems, cheaper, inexact versions of the constraint preconditioner are needed and our bounds also extend to this case. We present a variety of numerical experiments implemented using the deal.II finite element library. We consider two- and three-dimensional coupled flow problems, using different types of finite element schemes (continuous and discontinuous Galerkin methods) as well as varying the viscosity of the fluid and permeability of the porous medium. The numerical experiments illustrate that the constraint preconditioner outperforms both standard block diagonal and block triangular preconditioners both with respect to iteration count and CPU times for the considered cases.

Room Reservation Information

Room Number:MB315
Date:02 / 27 / 2015
Time:01:00pm - 02:30pm