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Performance and Analysis of Saddle Point Preconditioners for the. Howard C. Elman. David J. Silvester. Andrew J. Wathen. July 2000.
We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier-Stokes equations. With a combination of analytic and empirical results, we study the effects of fundamental parameters on convergence. We demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. The structure of these distributions is independent of the discretization mesh size, but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller. These characteristics are directly correlated with the convergence properties of iterative solvers. (Also cross-refernced as UMIACS-TR-2000-54) University of Maryland Institute for Advanced Computer Studies, Department of Computer Science, University of Maryland,
Iterative Methods for Problems in Computational Fluid Dynamics. Howard C. Elman. David J. Silvester. Andrew J. Wathen. August 1996.
We discuss iterative methods for solving the algebraic systems of equations arising from linearization and discretization of primitive variable formulations of the incompressible Navier-Stokes equations. Implicit discretization in time leads to a coupled but linear system of partial differential equations at each time step, and discretization in space then produces a series of linear algebraic systems. We give an overview of commonly used time and space discretization techniques,and we discuss a variety of algorithmic strategies for solving the resulting systems of equations.The emphasis is on preconditioning techniques, which can be combined with Krylov subspace iterative methods.In many cases the solution of subsidiary problems such as the discrete convection-diffusion equation and the discrete Stokes equations plays a crucial role. We examine iterative techniques for these problems and show how they can be integrated into effective solution algorithms for the Navier-Stokes equations. (Also cross-referenced as UMIACS-TR-96-58) University of Maryland Institute for Advanced Computer Studies, Dept. of Computer Science, Univ. of Maryland, Dept. of Mathematics, University of Manchester Institute of Science, Oxford University Computing Laboratory,
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