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Dr. A.J. Wathen
| Speaker: |
Dr. A.J. Wathen (Oxford
University)
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| Date: |
Wednesday September 22,
2004 |
| Title: |
Preconditioning and fast
solvers for incompressible flow
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Abstract
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Iterative methods
have long been used for solving the large sets of equations, which arise
from discretisations of Incompressible Navier-Stokes and related problems.
In common with compressible problems, multigrid is a key component in attempts
to get “optimal
solvers” ie. solvers which compute the required solution with an ammount
of computational work proportional only to the dimension of the discrete
system. The range of Krylov Subspace methods now available give another set
of techniques of considerable and general utility especially (and usually
only if!) good preconditioners are used in conjunction.
In this talk we will describe and demonstrate a methodology for Stokes,
and Navier-Stokes problems which combines fast solvers for the simpler scalar
Laplace and Advection-Diffusion operators - these are typically simple multigrid
procedures - to give block preconditioners which not only are optimal in
terms of mesh size/problem size but also which are relatively insensitive
to Reynolds number.
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