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= GPS Applied Mathematics Seminar =
= GPS Applied Mathematics Seminar =


The GPS (Graduate Participation Seminar) is a weekly seminar by and for graduate students.  If you're interested in presenting a topic or your own research, contact the organizers, [http://www.math.wisc.edu/~qinli/ Qin Li] and [http://www.math.wisc.edu/~matz/ Sarah Tumasz].
The GPS (Graduate Participation Seminar) is a weekly seminar by and for graduate students.  If you're interested in presenting a topic or your own research, contact the organizers, [http://www.math.wisc.edu/~matz/ Sarah Tumasz] and TBD.




All seminars are on Mondays from 2:25pm to 3:15pm in B211 Van Vleck.
All seminars are on TBD from TBD to TBD in TBD Van Vleck.


== Fall 2011 ==
== Spring 2012 ==


{| cellpadding="5"
{| cellpadding="5"
Line 14: Line 14:
!align="left" | title
!align="left" | title
|-
|-
|Sept 19
|date
|Qin Li
|speaker
|''AP scheme for multispecies Boltzmann equation''
|''title''
|-
|-
|Sept 26
|date
|Sarah Tumasz
|speaker
|''An Introduction to Topological Mixing''
|''title''
|-
|Oct 3
|Zhennan Zhou
|''Perturbation Theory and Molecular Dynamics''
|-
|Oct 10
|Li Wang
|''A class of well balanced scheme for hyperbolic system with source term''
|-
|Oct 17
|E. Alec Johnson
|''Boundary Integral Positivity Limiters''
|-
|Oct 24
|Bokai Yan
|''An introduction to elliptic flow''
|-
|Oct 31
|''No Talk this week''
|-
|Nov 7
|''No talk this week''
|-
|Nov 14
|
|
|-
|Nov 21
|Gerardo Hernandez-Duenas
|''A Hybrid Scheme for Flows in Porous Media''
|-
|Nov 28
|Jean-Luc Thiffeault
|''Modeling hagfish slime, perhaps the coolest substance in the world''
|-
|Dec 5
|''No talk this week''
|-
|Dec 12
|David Seal
|''A semi-Lagrangian discontinuous Galerkin method for solving the Vlasov-Poisson System''
|-
|Dec 19
|James Rossmanith
|''Residual Distribution Schemes for Hyperbolic Conservation Laws''
|}
|}


== Abstracts ==
== Abstracts ==


===Monday, Sept 19: Qin Li===
===Day, Date: Speaker===
''AP scheme for multispecies Boltzmann equation''
''title''
 
It is well-known that the Euler equation and the Navier–Stokes equation are 1st and 2nd order asymptotic limit of the Boltzmann equation when the Knudsen number goes to zero. Numerically the solution to the Boltzmann equation should converge to the Euler limit too. However, when the Knudsen number is small, one has to resolve the mesh to avoid instability, which causes tremendous computational cost. Asymptotic preserving scheme is a type of schemes that only uses coarse mesh but preserves the asymptotic limits of the Boltzmann equation in a discrete setting when Knudsen number vanishes. I'm going to present an AP scheme -- the BGK penalization method to solve the multispecies Boltzmann equation. New difficulties for this multispecies system come from: 1. the accurate definition of BGK term, 2. the different time scaling needed for different species to achieve the equilibrium.
 
===Monday, Sept 26: Sarah Tumasz===
''An Introduction to Topological Mixing''
 
What does topology have to do with mixing fluids?  I will give an introduction to topological mixing from the bottom up.  The talk will include a description of the basic theory, and demonstration of how to apply the techniques to a specific system.  No prior knowledge of topology is needed!
 
===Monday, Oct 3: Zhennan Zhou===
''Perturbation Theory and Molecular Dynamics''
 
I would like to give a brief introduction to quantum molecular dynamics  with the method
of adiabatic perturbation theory.In the framework of Quantum Mechanics, the dynamics of a
molecule is governed by the (time-dependent) Schr\"odinger equation, involving nuclei and
electrons coupled through electromagnetic interactions. In recent years, Born-Oppenheimer
approximation with many applications in mathematics, physics and chemistry, turns out to
be a very successful approximation scheme, which is a prototypical example of adiabatic
decoupling, and plays a fundamental role in the understanding of complex molecular
systems.
 
===Monday, Oct 10: Li Wang===
''A class of well balanced scheme for hyperbolic system with source term''
 
In many physical problems one encounters source terms that are balanced by internal
forces, and this kind of problem can be described by a hyperbolic system with source
term. In comparison with the homogeneous system, a significant difference is that this
system encounters non-constant stationary sloutions. So people want to preserve the steay
state solutions, or some discrete versions at least, with enough accuracy. This is the
so called well balanced scheme. I will give some basic idea of the scheme through a
typical example, the Saint-Venant system for shallow water flows with nonuniform bottom.
This talk is based on the paper [E.Audusse, etc SIAM J. Sci. Comput. 2004].
 
===Monday, Oct 17: E. Alec Johnson===
''Boundary Integral Positivity Limiting''
 
We consider positivity-preserving discontinuous Galerkin (DG)
schemes for hyperbolic PDEs. For simplicity we focus on scalar
PDEs with flux functions that may be spatially varying. We assume
that physical solutions maintain positivity of the solution.
 
The DG method evolves a piecewise polynomial representation.
Specifically, the representation is typically discontinuous at
mesh cell interfaces and when restricted to a mesh cell is a
polynomial. The coefficients of the representation are evolved
using an ODE solver, which for simplicity we take to be the
explicit Euler method.
 
Positivity limiters maintain positivity of the cell average by
after each time step damping the deviation from the cell average
just enough so that a cell positivity condition is satisfied.
 
The question we consider is how the cell positivity condition
ought to be defined. The positivity condition should at least
require positivity at the boundary nodes (where Riemann problems
must be solved) and should at most require positivity everywhere
in the cell (lest order of accuracy be violated).
 
Testing whether a higher-order polynomial with extremum
arbitrarily close to zero is everywhere positive is NP-hard. We
therefore seek a less stringent positivity indicator which is
inexpensive to compute.
 
The time until an Euler step violates positivity of the cell
average is the ratio of the amount of stuff in the cell to the
rate at which it is flowing out of the boundary. This immediately
suggests a simple positivity indicator which we call the boundary
integral positivity indicator. Enforcing positivity of the
boundary integral positivity indicator is computationally no
more expensive than enforcing positivity at a single point
and guarantees the same positivity-preserving time step as if
positivity were enforced everywhere in the mesh cell.
 
This is joint work with James Rossmanith.
 
===Monday, Oct 24: Bokai Yan===
''An Introduction to Elliptic Flow''
 
===Monday, Nov 21: Gerardo Hernandez-Duenas===
''A Hybrid Scheme for Flows in Porous Media''
 
The Baer-Nunziato two-phase flow model describes flame propagation in gas-permeable reactive granular material. This is an averaged flow model, expressing conservation of mass, and momentum and energy balance of the gas and solid phases. They form a hyperbolic system with nonconservative products. The presence of nonconservative product implies both theoretical and numerical complications. We are interested in the Riemann problem, where the porosity has discontinuities in the so-called compaction wave. The compaction wave is characterized by six quantities that remain constant across it and are known as Riemann invariants. Conservative formulations are essential near  shock waves, but they perform poorly near the compaction wave, as it is unable to recognize the Riemann invariants. We propose a hybrid algorithm, where we use the conservative formulation near shock waves, and a nonconservative formulation that respects the Riemann invariants near the interface. In this talk, we will show the hybrid technique, and numerical results that show the merits of the scheme.
 
===Monday, Nov 28: Jean-Luc Thiffeault===
''Modeling hagfish slime, perhaps the coolest substance in the world''
 
I will discuss the hagfish -- an eel that fills a predator's mouth with slime when bit down upon.  Such a rapid gelling is impressive, and it is a challenge to understand how it occurs.  The hagfish slime fluid actually contains tiny little "balls of twine," which unspool under the effect of hydrodynamic flow.  This talk will be about the early steps involved in modelling this fluid.  It is very much work in progress.
 
===Monday, Dec 12: David Seal===
''A semi-Lagrangian discontinuous Galerkin method for solving the Vlasov-Poisson System''


===Monday, Dec 19: James Rossmanith===
abstract
''Residual Distribution Schemes for Hyperbolic Conservation Laws''


I will describe the basic concepts behind a class of numerical methods for hyperbolic conservation laws called residual distribution schemes. These schemes are naturally formulated on unstructured grids, which allows them to be used for problems with complex geometries. I will first explain how these methods can be used for solving steady-state problems, and then explain how this can be generalized to unsteady problems. Finally, I will briefly show some preliminary results from work in progress on applying these methods to astrophysical flows.
== Archived semesters ==
*[[Applied/GPS/Fall2011|Fall 2011]]

Revision as of 21:02, 23 January 2012

GPS Applied Mathematics Seminar

The GPS (Graduate Participation Seminar) is a weekly seminar by and for graduate students. If you're interested in presenting a topic or your own research, contact the organizers, Sarah Tumasz and TBD.


All seminars are on TBD from TBD to TBD in TBD Van Vleck.

Spring 2012

date speaker title
date speaker title
date speaker title

Abstracts

Day, Date: Speaker

title

abstract

Archived semesters

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