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Mathematics & Computation
Division members promote the advancement of mathematical and computational methods for solving problems arising in all disciplines encompassed by the Society. They place particular emphasis on numerical techniques for efficient computer applications to aid in the dissemination, integration, and proper use of computer codes, including preparation of computational benchmark and development of standards for computing practices, and to encourage the development on new computer codes and broaden their use.
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2024 ANS Annual Conference
June 16–19, 2024
Las Vegas, NV|Mandalay Bay Resort and Casino
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The Standards Committee is responsible for the development and maintenance of voluntary consensus standards that address the design, analysis, and operation of components, systems, and facilities related to the application of nuclear science and technology. Find out What’s New, check out the Standards Store, or Get Involved today!
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Latest News
College students help develop waste-measuring device at Hanford
A partnership between Washington River Protection Solutions (WRPS) and Washington State University has resulted in the development of a device to measure radioactive and chemical tank waste at the Hanford Site. WRPS is the contractor at Hanford for the Department of Energy’s Office of Environmental Management.
Shaopeng Xia, Maosong Cheng, Zhimin Dai
Nuclear Science and Engineering | Volume 194 | Number 12 | December 2020 | Pages 1143-1161
Technical Paper | doi.org/10.1080/00295639.2020.1776057
Articles are hosted by Taylor and Francis Online.
Burnup calculations play a very important role in nuclear reactor design and analysis, and solving burnup equations is an essential topic in burnup calculations. In the last decade, several high-accuracy methods, mainly including the Chebyshev rational approximation method (CRAM), the quadrature-based rational approximation method, the Laguerre polynomial approximation method, and the mini-max polynomial approximation method, have been proposed to solve the burnup equations. Although these methods have been demonstrated to be quite successful in the burnup calculations, limitations still exist in some cases, one of which is that the accuracy becomes compromised when treating the time-dependent polynomial external feed rate. In this work, a new method called the Padé rational approximation method (PRAM) is proposed. Without directly approximating the matrix exponential, this new method is derived by using the Padé rational function to approximate the scalar exponential function in the formula of the inverse Laplace transform of burnup equations. Several test cases are carried out to verify the proposed new method. The high accuracy of the PRAM is validated by comparing the numerical results with the high-precision reference solutions. Against CRAM, PRAM is significantly superior in handling the burnup equations with time-dependent polynomial external feed rates and is much more efficient in improving the accuracy by using substeps, which demonstrates that PRAM is the attractive method for burnup calculations.