Authors: JONG HO LEE

Title: DOMAIN DECOMPOSITION METHODS FOR REISSNER-MINDLIN PLATES DISCRETIZED WITH THE FALK-TU ELEMENTS

Abstract:
The Reissner-Mindlin plate theory models a thin plate with thickness t.
The condition number of finite element approximations of this model
deteriorates badly as the thickness t of the plate converges to 0.
In this thesis, we develop an overlapping domain decomposition method
for the Reissner-Mindlin plate model discretized by Falk-Tu elements
with a convergence rate which does not deteriorate when t converges to 0.
We use modern overlapping methods which use the Schur complements to
define coarse basis functions
and show that the condition number of this overlapping method is
bounded by C(1 + H/delta )^3*(1 + log(H/h))^2.
Here H is the maximum diameter of the subdomains, delta the size of
overlap between subdomains, and h the element size.
Numerical examples are provided to confirm the theory.
We also modify the overlapping method to develop a BDDC method for the
Reissner-Mindlin model.
We establish numerically an extension lemma to obtain a constant bound
and an edge lemma to obtain a C(1 + log(H/h))^2 bound.
Given such bounds, the condition number of this BDDC method is shown
to be bounded by C(1 + log(H/h))^2.