Seminar Details
2010-10-12 (15.00) : Multigrid-based solvers for mixed partial differential equations
At Euler building
Organized by Mathematical Engineering
Speaker :
Samuel MELCHIOR (UCL)
Abstract :
Solving efficiently the incompressible NavierStokes equations is a major
challenge, especially in the three-dimensional case. One interesting
approach consists in applying a preconditioned GMRES method to the
linearized problem at each iteration of a nonlinear scheme. The
preconditioner can be built as an approximation of an ideal
block-preconditioner that guarantees convergence in 2 or 3 iterations. In
this talk, we investigate the numerical behavior for the three-dimensional
lid-driven cavity problem with wedge elements; the ultimate motivation of
this analysis is indeed the development of a preconditioned Krylov solver
for stratified oceanic flows which can be efficiently tackled using such
meshes. Numerical results for steady-state solutions of both the Stokes
and NavierStokes problem are presented. Theoretical bounds on the
spectrum and the rate of convergence appear to be in agreement with the
numerical experiments. Sensitivity analysis on different aspects of the
structure of the preconditioner and the block decomposition strategies are
also discussed. Particular emphasis is put on how to use the multigrid
scheme in this preconditioner. Extensions to the two-dimensional shallow
water equations are discussed.