Title: Fast and Robust Multigrid methods for non-Newtonian fluids models
Speaker: Young Ju Lee,
leeyoung@math.rutgers.edu,
http://www.math.rutgers.edu/~leeyoung
Department of Mathematics, Rutgers, The State University of New Jersey
Abstract:
We present multigrid-based solution techniques to the time dependent
non-Newtonian equations. Non-Newtonian equations can be used to model abundant
daily examples such as toothpaste and paint. The presentation begins with
introducing discretization schemes that can deal with various non-Newtonian
model equations in a unified fashion, which are crucial in numerical modeling
of complex fluids. The discretization schemes are based on the finite element
methods in space and the semi-Lagrangian methods in time. We then demonstrate
how the resulting systems can be handled by fast solution techniques in a
robust manner in the sense that the solution speed can be shown to be
independent of all relevant physical parameters as well as time step and mesh
sizes. Our presentation shall include basic numerical examples to clarify the
underlying idea, some theoretical analysis that includes solution to some open
question, as well as real applications that arise in modeling problems if time
permits.