Fast Spectral-Galerkin Methods: Applications to Computational Fluid Dynamics
Abstract
We shall present in this talk some fast spectral-Galerkin algorithms with
quasi-optimal computational complexity for solving elliptic equations on
regular domains: More precisely, we shall present fast direct methods for
problems with constant coefficients, and iterative methods with optimal
preconditioners, including in particular a finite element multigrid
preconditioner on spectral-collocation points, for problems with variable
coefficients. These fast solvers can be used in particular as subspace
solvers in a domain decomposition framework.
The combination of fast elliptic solvers with an appropriate projection
scheme provides an extremely efficient algorithm for solving time
dependent Navier-Stokes equations. We shall present numerical
investigations of a number of canonical rotating flows in enclosed
cylinder(s).
