Moving meshes to solve the time-dependent neutron diffusion equation in hexagonal geometry
TLDR
A moving mesh scheme based on hp-finite element method is proposed for the time dependent neutron diffusion equation that uses spatial meshes that change with the movement of the control rods avoiding the necessity of using equivalent material cross sections for the partially inserted cells.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2016-01-01 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Finite element method & Polygon mesh.read more
Citations
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Journal ArticleDOI
A time and frequency domain analysis of the effect of vibrating fuel assemblies on the neutron noise
TL;DR: In this article, the effect in the neutron field of the oscillation of one single fuel assembly was analyzed and compared between a time-domain and a frequency-domain analysis of the phenomena to calculate the spatial response of the neutron noise.
Journal ArticleDOI
Control rod treatment for FEM based radiation transport methods
Sebastian Schunert,Yaqi Wang,Javier Ortensi,Vincent Laboure,Frederick N. Gleicher,Mark DeHart,Richard C. Martineau +6 more
TL;DR: It is demonstrated that the smoothly varying cross sections can be obtained by projecting the piecewise set of cross sections onto the set of Legendre polynomials up to a finite order and provided accurate results based on the C5G7-TD benchmark.
Journal ArticleDOI
Modal methods for the neutron diffusion equation using different spatial modes
TL;DR: In this article, the authors used a high order finite element method for the spatial discretization of the neutron diffusion equation and compared the performance of the different modal kinetic equations with two 3D transient benchmark problems.
Journal ArticleDOI
Mathematical Modeling and Computational Methods
TL;DR: This issue includes a collection of contributed papers that covers many relevant and modern aspects about the state of several aspects on the art of computational methods and mathematical modeling, giving a rather fair picture of the current research interests in this scientific field.
Journal ArticleDOI
Adaptive time-step control for modal methods to integrate the neutron diffusion equation
TL;DR: This work proposes the use of an adaptive control time-step that reduces automatically the time- step when the algorithm detects large errors and increases this value when it is not necessary to use small steps.
References
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Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Journal ArticleDOI
Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
TL;DR: Gmsh as mentioned in this paper is an open-source 3D finite element grid generator with a build-in CAD engine and post-processor that provides a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities.
Book
The Finite Element Method: Its Basis and Fundamentals
TL;DR: The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications.
Book ChapterDOI
Efficient management of parallelism in object-oriented numerical software libraries
TL;DR: The PETSc 2.0 package as discussed by the authors uses object-oriented programming to conceal the details of the message passing, without concealing the parallelism, in a high-quality set of numerical software libraries.
Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries.
TL;DR: The concepts discussed are appropriate for all scalable computing systems and provide many of the data structures and numerical kernels required for the scalable solution of PDEs, offering performance portability.
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