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The Mission of the Robotics and Remote Systems Division is to promote the development and application of immersive simulation, robotics, and remote systems for hazardous environments for the purpose of reducing hazardous exposure to individuals, reducing environmental hazards and reducing the cost of performing work.
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Utility Working Conference and Vendor Technology Expo (UWC 2024)
August 4–7, 2024
Marco Island, FL|JW Marriott Marco Island
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NRC engineers share their expertise at the University of Puerto Rico
Robert Roche-Rivera and Marcos Rolón-Acevedo are licensed professional engineers who work at the U.S. Nuclear Regulatory Commission. They are also alumni of the University of Puerto Rico–Mayagüez (UPRM) and have been sharing their knowledge and experience with students at their alma mater since last year, serving as adjunct professors in the university’s Department of Mechanical Engineering. During the 2023–2024 school year, they each taught two courses: Fundamentals of Nuclear Science and Engineering, and Nuclear Power Plant Engineering.
Anthony P. Barbu, Marvin L. Adams
Nuclear Science and Engineering | Volume 197 | Number 4 | April 2023 | Pages 517-533
Technical Paper | doi.org/10.1080/00295639.2022.2123205
Articles are hosted by Taylor and Francis Online.
Most methods that use low-order operators to accelerate the iterative solution of transport eigenvalue problems employ nonlinear functionals of the transport solution (such as Eddington tensors) in their low-order equations, which are themselves standard eigenvalue problems. Here, we discuss linear diffusion synthetic acceleration (DSA) for -eigenvalue problems, which belongs to a family of methods that has received less attention than its nonlinear counterparts. We review the history of these linear methods as far as we know it and describe theoretical questions that to our knowledge have remained unanswered. With these methods, a low-order problem is solved after each transport step for an updated eigenvalue and an additive correction to the eigenfunction. These low-order problems are not standard eigenvalue problems, for they contain residuals as fixed sources. The low-order problems admit infinitely many solutions (updated and additive correction to the eigenfunction), and the solution that is obtained depends on the initial guess and iterative method chosen for the low-order problems. Experience has shown that when the low-order problems are solved with a powerlike iteration method and certain initial guesses, they yield solutions that cause rapid convergence to the correct high-order solution. We study the convergence properties of this algorithm applied to two model problems: an infinite homogeneous medium and a one-cell problem. For the infinite homogeneous problem, we present a Fourier analysis of the linear DSA method, which demonstrates that when the low-order problems are solved using a powerlike iteration scheme, the linear DSA scheme provides immediate convergence of the -eigenvalue and rapid convergence of the eigenfunction (much like DSA applied to scattering iterations in fixed-source problems). For the one-cell problems, we find that the linear scheme for -eigenvalue problems performs approximately as well as DSA for fixed-source problems. The latter analysis reveals a quantitative bound on the consistency between low- and high-order operators that is necessary and sufficient for convergence of those problems. With some theoretical foundations for the linear methods now established, we turn to numerical testing. We find, as others have before us using different low-order operators, that the method works well in practice. We provide numerical results from reactor problems in which our linear DSA is approximately as effective as the more widely used nonlinear methods. Our theoretical and numerical results add to the body of evidence that the linear methodology offers a simple path to rapid convergence of -eigenvalue problems, especially for codes that already employ linear low-order operators to converge scattering iterations.