✦ LIBER ✦

MULTIGRID AND KRYLOV SUBSPACE METHODS FOR THE DISCRETE STOKES EQUATIONS

✍ Scribed by HOWARD C. ELMAN

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 845 KB
Volume: 22
Category: Article
ISSN: 0271-2091
DOI: 10.1002/(sici)1097-0363(19960430)22:8<755::aid-fld377>3.0.co;2-1

No coin nor oath required. For personal study only.

✦ Synopsis

Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizatiom a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the dkretization. In this paper we compare the performance of four such methods, namely variants of the Uzawa, preconditioned conjugate gradient, preconditioned conjugate residual and multigrid methods, for solving several two-dimensional model problems. The results indicate that multigrid with smoothing based on incomplete factorization is more efficient than the other methods, but typically by no more than a factor of two. The conjugate residual method has the advantage of being independent of iteration parameters.

📜 SIMILAR VOLUMES

On Newton–Krylov Multigrid Methods for t

On Newton–Krylov Multigrid Methods for the Incompressible Navier–Stokes Equations

✍ D.A. Knoll; V.A. Mousseau 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 46 KB

In this note we continue our investigation [1] of multigrid methods as preconditioners to a Jacobian-free Newton-Krylov method [2,3]. We consider two different options for the formation of the coarse grid operators required in the multigrid preconditioner. The first option (Method 1) involves restri

Spectral Multigrid Methods for the Refor

Spectral Multigrid Methods for the Reformulated Stokes Equations

✍ Wilhelm Heinrichs 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 547 KB

Direct methods and ADI-preconditioned Kr

Direct methods and ADI-preconditioned Krylov subspace methods for generalized Lyapunov equations

✍ T. Damm 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 225 KB

On preconditioned Krylov subspace method

On preconditioned Krylov subspace methods for discrete convection–diffusion problems

✍ Michael P. Chernesky 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 155 KB 👁 2 views

We study nonstationary iterative methods for solving preconditioned systems arising from discretizations of the convection-diffusion equation. The preconditioners arise from Gauss-Seidel methods applied to the original system. It is shown that the performance of the iterative solvers is affected by

Krylov subspace accelerated inexact Newt

Krylov subspace accelerated inexact Newton method for linear and nonlinear equations

✍ Robert J. Harrison 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 88 KB 👁 1 views

## Abstract A Krylov subspace accelerated inexact Newton (KAIN) method for solving linear and nonlinear equations is described, and its relationship to the popular direct inversion in the iterative subspace method [DIIS; Pulay, P., Chem Phys Lett 1980, 393, 73] is analyzed. The two methods are comp

Preconditioned Krylov subspace methods f

Preconditioned Krylov subspace methods for boundary element solution of the Helmholtz equation

✍ S. Amini; N. D. Maines 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 186 KB 👁 2 views

Discretization of boundary integral equations leads, in general, to fully populated complex valued non-Hermitian systems of equations. In this paper we consider the e cient solution of these boundary element systems by preconditioned iterative methods of Krylov subspace type. We devise preconditione