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Conference Spotlight
Nuclear Energy Conference & Expo (NECX)
September 8–11, 2025
Atlanta, GA|Atlanta Marriott Marquis
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Hash Hashemian: Visionary leadership
As Dr. Hashem M. “Hash” Hashemian prepares to step into his term as President of the American Nuclear Society, he is clear that he wants to make the most of this unique moment.
A groundswell in public approval of nuclear is finding a home in growing governmental support that is backed by a tailwind of technological innovation. “Now is a good time to be in nuclear,” Hashemian said, as he explained the criticality of this moment and what he hoped to accomplish as president.
Daniel F. Gill, Yousry Y. Azmy, James S. Warsa, Jeffery D. Densmore
Nuclear Science and Engineering | Volume 168 | Number 1 | May 2011 | Pages 37-58
Technical Paper | doi.org/10.13182/NSE10-01
Articles are hosted by Taylor and Francis Online.
Recently, Jacobian-Free Newton-Krylov (JFNK) methods have been used to solve the k-eigenvalue problem in diffusion and transport theories. We propose an improvement to Newton's method (NM) for solving the k-eigenvalue problem in transport theory that avoids costly within-group iterations or iterations over energy groups. We present a formulation of the k-eigenvalue problem where a nonlinear function, whose roots are solutions of the k-eigenvalue problem, is written in terms of a generic fixed-point iteration (FPI). In this way any FPI that solves the k-eigenvalue problem can be accelerated using the Newton approach, including our improved formulation. Calculations with a one-dimensional multigroup SN transport implementation in MATLAB provide a proof of principle and show that convergence to the fundamental mode is feasible. Results generated using a three-dimensional Fortran implementation of several formulations of NM for the well-known Takeda and C5G7-MOX benchmark problems confirm the efficiency of NM for realistic k-eigenvalue calculations and highlight numerous advantages over traditional FPI.