A Unified Form of Stabilized Finite Element Methods for Solving the First-order Neutron Transport Equation

2020 ◽  
Author(s):  
L. Cao ◽  
C. Fang ◽  
H. Wu
Keyword(s):  
Finite Element ◽  
Transport Equation ◽  
Finite Element Methods ◽  
Neutron Transport ◽  
Neutron Transport Equation ◽  
Stabilized Finite Element Methods ◽  
Stabilized Finite Element ◽  
First Order

Fast Sub-Grid Scale Finite Element Method for the First Order Neutron Transport Equation

2018 ◽  
Author(s):  
Chao Fang ◽  
Hongchun Wu ◽  
Liangzhi Cao ◽  
Yunzhao Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transport Equation ◽  
Neutron Transport ◽  
Coefficient Matrix ◽  
New Method ◽  
Element Formulation ◽  
Neutron Transport Equation ◽  
First Order ◽  
Element Method

This paper presents a fast sub-grid scale (SGS) finite element method for the first order neutron transport equation. The spherical harmonics method is adopted for the angular discretization. The sub-grid scale discretization embeds discontinuous component in each element to provide a stabilization term for the continuous finite element formulation. Traditional SGS method uses Riemann decomposition and vacuum boundary assumption to decouple the discontinuous component. Here we propose a new method to perform the decoupling based on the assumption that the convection term of the discontinuous component is proportional to the residual of angular flux in each element. The computing costs for the establishment of the coefficient matrix of discontinuous component are reduced to O(1) from O(n3). Further more, the computing costs for the inversion of the coefficient matrix are reduced to O(n) from O(n3) by applying mass lumping technique. Numerical results show that the new method is not only more efficient but also yields more accurate solution than traditional sub-grid scale method.

A least-squares finite-element Sn method for solving first-order neutron transport equation

2007 ◽  
Vol 237 (8) ◽  
pp. 823-829 ◽  
Author(s):  
Hai-Tao Ju ◽  
Hong-Chun Wu ◽  
Yong-Qiang Zhou ◽  
Liang-Zhi Cao ◽  
Dong Yao ◽  
...  
Keyword(s):  
Finite Element ◽  
Transport Equation ◽  
Least Squares ◽  
Neutron Transport ◽  
Neutron Transport Equation ◽  
First Order

Dispersion Analysis of Stabilized Finite Element Methods for Acoustic Fluid-Structure Interaction

2000 ◽  
Author(s):  
Lonny L. Thompson ◽  
Sridhar Sankar
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Finite Element Methods ◽  
Generalized Least Squares ◽  
Dispersion Analysis ◽  
Stabilized Finite Element Methods ◽  
Stabilized Finite Element ◽  
Stabilized Methods ◽  
Plate Elements ◽  
Acoustic Fluid

Abstract The application of stabilized finite element methods to model the vibration of elastic plates coupled with an acoustic fluid medium is considered. New stabilized methods based on the Hellinger-Reissner variational principle with a generalized least-squares modification are developed which yield improvement in accuracy over the Galerkin and Galerkin Generalized Least Squares (GGLS) finite element methods for both in vacuo and acoustic fluid-loaded Reissner-Mindlin plates. Through judicious selection of design parameters this formulation provides a consistent framework for enhancing the accuracy of mixed Reissner-Mindlin plate elements. Combined with stabilization methods for the acoustic fluid, the method presents a new framework for accurate modeling of acoustic fluid-loaded structures. The technique of complex wave-number dispersion analysis is used to examine the accuracy of the discretized system in the representation of free-waves for fluid-loaded plates. The influence of different finite element approximations for the fluid-loaded plate system are examined and clarified. Improved methods are designed such that the finite element dispersion relations closely match each branch of the complex wavenumber loci for fluid-loaded plates. Comparisons of finite element dispersion relations demonstrate the superiority of the hybrid least-squares (HLS) plate elements combined with stabilized methods for the fluid over standard Galerkin methods with mixed interpolation and shear projection (MITC4) and GGLS methods.

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