[Colloquium] A Computer Science Seminar

[Donna Brooms]

*REMINDER*

Wednesday, October 16, 2013
6:00 p.m.
Ryerson 251
 
Severin Thaler
University of Chicago, Comp.Sci.
www.cs.uchicago.edu/people/sthaler
 
Title:  “The criticality spectral problem in neutron transport”
 
Abstract:
This master thesis is about the criticality spectral problem in neutron transport. This is an eigenvalue problem used to determine whether a nuclear reactor is sub- or supercritifical. More precisely, there is a certain eigenpair which contains the criticality information. However, such an eigenpair does not necessarily exist, so that certain conditions have to be formulated under which the existence can be shown. In this respect, the Krein- Rutman Theorem for positive compact operators plays a central role. Once the existence is established, a variational formulation of the problem is introduced. This variational formulation turns out to be quite intricate, since it does not seem to _t into existing frameworks for variationally posed eigenvalue problems. Moreover, when it comes to the finite element discretization, the right choice for the discrete trial and test spaces is not obvious. In particular, one must decide whether or not to deal with a non-square matrix eigenvalue problem. After these problems have been roughly discussed, a hierarchy of model problems is considered. For the (1 + 1)-dimensional case, a concrete finite element discretization is formulated, which is then generalized to the (2 + 2)-dimensional case. In doing so, the efficient evaluation of the bilinear forms, especially the scattering bilinear form, is addressed. Then, a generalized finite element method is sketched, when the number of cells of the reactor is large. Finally, numerical examples for the standard finite element method are provided.
 
Host: Ridgway Scott
 
Refreshments will be served prior to the talk in Ry. 255 @ 5:45

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