A new preconditioner for the Oseen equations
We describe a preconditioner for the linearised incompressible Navier-Stokes equations (the Oseen equations) which requires as components a preconditioner/solver for a discrete Laplacian and for a discrete advection-diffusion operator. With this preconditioner, convergence of an iterative method such as GMRES is independent of the mesh size and depends only mildly on the viscosity parameter (the inverse Reynolds number). Thus when the component preconditioner/solvers are effective on their respective subproblems (as one expects with an appropriate multigrid cycle for instance)a fast Oseen solver results.
KeywordsKrylov Subspace Picard Iteration Drive Cavity Conjugate Gradient Iteration Oseen Equation
Unable to display preview. Download preview PDF.
- Brezzi, F. (1987): New applications of mixed finite element methods. Proceedings of the International Congress of Mathematicians. Vol. 2. In: Gleason, A.M. (ed.): American Mathematical Society, Providence, RI, pp. 1335–1347Google Scholar
- Loghin, D., Wathen, A.J. (2001): Schur complement preconditioning for elliptic systems of partial differential equations. Numer. Linear Algebra Appl., submittedGoogle Scholar