			Home About us Contact

Saddle Point Problems (saddle + point_problem)

Distribution by Scientific Domains

Mathematics and Statistics	40%

Selected Abstracts

Two preconditioners for saddle point problems in fluid flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007
A. C. de Niet
Abstract In this paper two preconditioners for the saddle point problem are analysed: one based on the augmented Lagrangian approach and another involving artificial compressibility. Eigenvalue analysis shows that with these preconditioners small condition numbers can be achieved for the preconditioned saddle point matrix. The preconditioners are compared with commonly used preconditioners from literature for the Stokes and Oseen equation and an ocean flow problem. The numerical results confirm the analysis: the preconditioners are a good alternative to existing ones in fluid flow problems. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A comparative study of efficient iterative solvers for generalized Stokes equations

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2008
Maxim Larin
Abstract We consider a generalized Stokes equation with problem parameters ,,0 (size of the reaction term) and ,>0 (size of the diffusion term). We apply a standard finite element method for discretization. The main topic of the paper is a study of efficient iterative solvers for the resulting discrete saddle point problem. We investigate a coupled multigrid method with Braess,Sarazin and Vanka-type smoothers, a preconditioned MINRES method and an inexact Uzawa method. We present a comparative study of these methods. An important issue is the dependence of the rate of convergence of these methods on the mesh size parameter and on the problem parameters , and ,. We give an overview of the main theoretical convergence results known for these methods. For a three-dimensional problem, discretized by the Hood,Taylor ,,2,,,1 pair, we give results of numerical experiments. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Two preconditioners for saddle point problems in fluid flows

Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier,Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2002
Volker John
Abstract This paper presents a numerical study of the 3D flow around a cylinder which was defined as a benchmark problem for the steady state Navier,Stokes equations within the DFG high-priority research program flow simulation with high-performance computers by Schafer and Turek (Vol. 52, Vieweg: Braunschweig, 1996). The first part of the study is a comparison of several finite element discretizations with respect to the accuracy of the computed benchmark parameters. It turns out that boundary fitted higher order finite element methods are in general most accurate. Our numerical study improves the hitherto existing reference values for the benchmark parameters considerably. The second part of the study deals with efficient and robust solvers for the discrete saddle point problems. All considered solvers are based on coupled multigrid methods. The flexible GMRES method with a multiple discretization multigrid method proves to be the best solver. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A preconditioner for generalized saddle point problems: Application to 3D stationary Navier-Stokes equations

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2006
C. Calgaro
Abstract In this article we consider the stationary Navier-Stokes system discretized by finite element methods which do not satisfy the inf-sup condition. These discretizations typically take the form of a variational problem with stabilization terms. Such a problem may be transformed by iteration methods into a sequence of linear, Oseen-type variational problems. On the algebraic level, these problems belong to a certain class of linear systems with nonsymmetric system matrices ("generalized saddle point problems"). We show that if the underlying finite element spaces satisfy a generalized inf-sup condition, these problems have a unique solution. Moreover, we introduce a block triangular preconditioner and we show how the eigenvalue bounds of the preconditioned system matrix depend on the coercivity constant and continuity bounds of the bilinear forms arising in the variational problem. Finally we prove that the stabilized P1-P1 finite element method proposed by Rebollo is covered by our theory and we show that the condition number of the preconditioned system matrix is independent of the mesh size. Numerical tests with 3D stationary Navier-Stokes flows confirm our results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 [source]