Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Monday, November 2, 2009 - 04:00 to 05:00
GILK 113

Speaker Info

University of Nevada, Reno

In this talk I will briefly introduce our group, its motivation
and goals, some results that we obtained so far, and what we hope
to accomplish in the future.
In particular, I will explain why we believe that it makes sense
to design numerical methods that are independent of the partial
differential equations (PDE) solved. The current standard in my
field is to develop sophisticated error estimates and techniques
that only work (or work efficiently) for a narrow class of PDE.
In contrast to that, our methods work in the same way for any
PDE or multiphysics PDE system, and they can even be used in
other fields such as computer graphics or robotics. Examples
will be shown.
Main ideas of adaptive higher-order finite element methods
(hp-FEM) will be explained and their extremely fast, exponential
convergence will be demonstrated via live computations and
compared to the slow, algebraic convergence of traditional
low-order FEM.
I will mention the main ideas of our novel adaptive multimesh
hp-FEM that makes it possible to discretize a PDE system monolithically
(i.e., as if it was a single equation) while using individual
(optimal) meshes for all physical fields in the system. Numerical
comparisons to standard (single-mesh) hp-FEM will be presented.
We will show that even fluid flows can be handled as multiphysics
problems with velocity components and pressure approximated using
different meshes.
We will show that the multimesh hp-FEM makes it possible to design
simple and efficient adaptive algorithms for time-dependent PDE
problems based on dynamically-changing meshes. (Automatic adaptivity
for time-dependent problems is much more difficult than adaptivity
for statonary ones because of the necessity of mesh unrefinement).
I will explain the main idea and show several computational videos
related to various problems (flame propagation, thermally-conductive
flow, microwave heating, thermoelasticity, single and two-phase flow,
heat and moisture transfer in concrete, Gross-Pitaevski equation
of quantum physics, etc).
If some time is left, I will say a few words about our open source
project FEMhub whose objective is to create an open source distribution
of finite element codes with unified Python interface.