Department of Mathematics,
Arizona State University
Tuesday,
May 5, 1997, 3:05 p.m. in GWC Room 604
Xiaohong Ding
Department of Mathematics
Theoretical and Numerical Evaluation of Convergence Acceleration
for the Stokes Problem (Dissertation Defense)
Abstract
This research utilized the finite element method for the numerical solution
of partial differential equation. The ultimate goal is to
apply the results obtained to the Navier-Stokes equation of fluid mechanics.
This research does not address the nonlinearity of this problem
and consequently considers
problems of Stokes type which we model by a mixed method for a linear elliptic
equation of second order. This results in a saddle-point problem for which
the efficient numerical solution by preconditioned conjugate gradient algorithms is
known to be much more difficult due to the indefiniteness of the system matrix.
This dissertation uses an Uzawa-type method to
iteratively approximate the discrete solution.
Based on the optimal determination of the spectral radius
for the iteration matrix at the elemental level an effective preconditioning
is proposed. The rate of convergence of the method is independent of the mesh
parameter and by an appropriate choice of parameters can be reduced substantially
over that for standard preconditioners, such as, by the diagonal of the system matrix.
The main results of this work are estimates of convergence factors for a
class of preconditioners and a verification of the obtained acceleration through
some numerical experiments for a Matlab implementation.
For further information please contact:
mittelmann@asu.edu