School: Texas A&M University

Began Rickover Fellowship: September 2006

Lab Assignment: BETTIS - Summer 2007, KAPL - Summer 2008

Lab Mentor: Bob Grove

Degree(s):
B.S Nuclear Engineering, Texas A&M University

Expected Graduation Date: August 2010

University Advisor: Dr. Marvin Adams

Field of Study: Nuclear Engineering

Email Address: joshjarrell@gmail.com

Summary of Research:

For my PhD Dissertation, I plan to work on adaptive angular discretizations for particle-transport problems.  Dr. Marvin Adams and his student Joseph Stone have developed promising strategies and methods, and I plan to work with Dr. Adams to build upon this foundation.  Stone and Adams have implemented their ideas in two-dimensional Cartesian geometry.  [J. C. Stone and M. L. Adams, “Adaptive Discrete-Ordinates Algorithms and Strategies,” Proc. Conf. Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications, Avignon, France, September 11-15 (2005).  CD-ROM.]  In my research, I plan to work with Dr. Adams extend this work to two-dimensional axi-symmetric problems as well as three-dimensional problems. 

This is not a trivial extension, for two reasons.  First, in curvilinear coordinates the particle-transport equations contains an “angular derivative” term that is not present in Cartesian coordinates.  The adaptive discretization will therefore need to control error in both the integral and the derivative of the discretized function, which is something that adaptive methods have not considered before.  Second, in two-dimensional axi-symmetric problems there is considerable lack of smoothness in the solution in the polar direction variable.  This is not the case in two-dimensional Cartesian problems, and it raises issues not previously addressed by Stone and Adams. 

Publications:

1. Comparison of Advanced Quadrature Sets using PARTISN
   CRS-11 / RPSD-2008, Callaway Gardens, GA April 2008

2. Quadrature Application in Three-Dimensional Model Shielding Problems
   2008 ANS Student Conference, College Station, TX April 2008
   Won “Outstanding Graduate Presentation in Mathematics and Computation”