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My research deals with the development of numerical algorithms for solving partial differential equations and especially with strategies which are applicable to the design and analysis of nuclear reactors. In particular, I am interested in the radiation transport equation and associated diffusion equations. Radiation transport is governed by a Boltzmann equation, and its solutions are of interest in not only nuclear reactor design, but also medical imaging, planning of radiation cancer treatments, astrophysics, and numerous other fields.
The current primary focus of my research concerns the development of efficient solvers for eigenvalue problems occurring in the field of radiation transport. Such problems are commonly used to analyze nuclear reactors, and therefore the development of rapid solution strategies to such problems is of great importance in the design and analysis of new reactor designs as well as existing operating reactors. We are currently investigating the application of advanced eigenvalue solvers for the radiation transport equation. These solvers (such as the Implicitly Restarted Arnoldi Method and the Jacobi-Davidson method) have found much success in other areas of applied math and engineering, but to date little work has been conducted on applying them to reactor-type problems.
A secondary aspect of my research is on the development of non-negative discretizations of the transport equation. Nearly all commonly-used discretizations can potentially suffer from non-physical negative solutions. These negative solutions are highly undesirable, as they can introduce instabilities into coupled multiphysics solution strategies and acceleration techniques. Rather than follow one commonly-used path which involves resorting to a completely different and highly nonlinear discretization, we choose to work on making modifications to existing linear schemes. In this way, we arrive at systems which are ‘almost' linear, requiring less modification to existing code packages and allowing for simpler solution strategies.
S. Hamilton, M. Benzi, "Eigensolvers for radiation transport applications," proceedings of 11th Copper Mountain Conference on Iterative Methods (April 2010).
S. Hamilton, M. Benzi, E. Haber, "New Multigrid Smoothers for the Oseen Problem," Numerical Linear Algebra with Applications, accepted.
S. Hamilton, M. Benzi, E. Haber, "New Smoothers for the Oseen Problem," proceedings of 14th Copper Mountain Conference on Multigrid Methods (March 2009).
S. Hamilton, M. Benzi, J. Warsa, "Negative Flux Fixups in Discontinuous Finite Element SN Transport," proceedings of 2009 International Conference on Mathematics, Computational Methods and Reactor Physics (May 2009).
S. Hamilton, K. Clarno, C. de Oliveira, "Error Control in a Time-Dependent Slice-Balance Method," proceedings of the American Nuclear Society Winter Conference (November 2007).
W.M. Stacey et al., "Advances in the Sub-Critical, Gas-Cooled, Fast Transmutation Reactor Concept," "Nuclear Technology," July 2007.
S. Chiu, S. Hamilton, B. MacLaren, C. Sommer, and F. Willis, "Fuel Cycle Analysis of a Subcritical Fast, Gas-Cooled Transmutation Reactor," proceedings of ANS Winter Conference (November 2006).
K. Clarno, V. de Almeida, E. d'Azevedo, C. de Oliveira, S. Hamilton, "GNES-R: Global Nuclear Energy Simulator for Reactors, Task 1: High-Fidelity Neutron Transport," proceedings of PHYSOR-2006 Topical Meeting (Sept. 2006).
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