[grads] [Sem-coll] AM Dept. Colloquia & Seminars Nov. 16-20

Joe Millham jmillhamiit at gmail.com
Mon Nov 16 10:08:09 CST 2009


Please join the Applied Math department for the following Seminars and
colloquiua.  All are welcome to attend, and refreshments will be
served as some events.  For a complete listing of this semester's
events, please visit <http://www.iit.edu/csl/am/colloquia/>

Dept. Colloquium
Monday, Nov. 16  4:40 pm  E1 106
Zhiliang Xu, Notre Dame University
"Hierarchical Reconstruction for Discontinuous Galerkin (DG) Method
for Hyperbolic Conservation Laws and a New Formulation of DG Method"
See abstract below
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Dept. Colloquium
Wednesday, Nov. 18,   4:40 pm  E1 106
Mark Pinsky,  Northwestern University
"Browninan Motion on Riemannian Manifolds"
see abstract below
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Networks & Optimization Seminar
Monday, Nov. 16,   4:40 pm   E1  119
Hemanshu Kaul,  IIT Applied Math
"Finding Large Subgraphs"
See abstract below
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Dept. Colloquium
Monday, Nov. 16  4:40 pm  E1 106
Zhiliang Xu, Notre Dame University
"Hierarchical Reconstruction for Discontinuous Galerkin (DG) Method
for Hyperbolic Conservation Laws and a New Formulation of DG Method"
Abstract:
In this talk, I will present some recent developments of hierarchical
reconstruction (HR) [Liu etal., Central discontinuous Galerkin methods
on overlapping cells with a non-oscillatory hierarchical
reconstruction. SIAM J. Numer. Anal., 45:2442-2467, 2007 and Xu etal.

Hierarchical reconstruction for  discontinuous Galerkin methods on
unstructured grids with a WENO type linear reconstruction and partial
neighboring cells. J.C.P. 228:2194-2212, 2009] for limiting solutions
computed by Runge-Kutta (RK) DG methods for hyperbolic conservation
laws.  The idea of HR is to decompose the task of a high degree
polynomial reconstruction into a series of linear polynomial
reconstruction process. The main features of HR are order preserving
(for smooth solutions), compact, and without characteristic
decomposition.

We explore a WENO-type linear reconstruction on each hierarchical
level  for the reconstruction of these linear polynomials to preserve
the order of accuracy on unstructured meshes. We demonstrate that  the
hierarchical reconstruction can generate essentially non-oscillatory
solutions while keeping the resolution and desired order of accuracy
for smooth solutions.

In addition, I will discuss a new formulation of RKDG method based on
the conservation constraint. With this new formation, we can achieve a
larger CFL number for RKDG method of order >= 3.
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Dept. Colloquium
Wednesday, Nov. 18,   4:40 pm  E1 106
Mark Pinsky,  Northwestern University
"Browninan Motion on Riemannian Manifolds"
Abstract:
We begin with the Laplace operator on a complete Riemannian manifold.
The isotropic transport process is a Markov process on the tangent
bundle; in the limit of small mean free path, the process converges
weakly to a Markov process on the basic manifold. A number of analytic
problems can be discussed using the small ball power series of the
Laplace operator. These include the mean exit time, the distribution
of hitting place, and the principal eigenvalue of a small ball.
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Networks & Optimization Seminar
Monday, Nov. 16,   4:40 pm   E1  119
Hemanshu Kaul,  IIT Applied Math
"Finding Large Subgraphs"
Abstract:
The maximum subgraph problem for a fixed graph property P asks: Given
a graph, find a subgraph satisfying property P that has the maximum
number of edges. Similarly, we can talk about maximum induced subgraph
problem. This property can be planarity, acyclicity, bipartiteness,
etc.

We will discuss some old and new problems of this flavor with special
emphasis on properties defined in terms of forbidden minors. In
particular, we will describe some new results on the maximum K_4 -
minor-free subgraph problem (joint work with Calinescu and Fernandes).
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Joe Millham

Administrative Assistant
Department of Applied Mathematics
Illinois Institute of Technology
Engineering-1 Room 208
10 W. 32rd St.
Chicago IL 60616
312.567.8984 (Phone)
312.567.3135 (Fax)
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