On some features of the eigenvalue problem for the PN approximation of the neutron transport equation

2021 ◽  
Vol 163 ◽  
pp. 108477
Author(s):  
Nicolò Abrate ◽  
Sandra Dulla ◽  
Piero Ravetto ◽  
Paolo Saracco
Keyword(s):  
Eigenvalue Problem ◽  
Transport Equation ◽  
Neutron Transport ◽  
Neutron Transport Equation

scholarly journals COMPARISON OF CHEBYSHEV AND ANDERSON ACCELERATIONS FOR THE NEUTRON TRANSPORT EQUATION

2021 ◽  
Vol 247 ◽  
pp. 03001
Author(s):  
Ansar Calloo ◽  
Romain Le Tellier ◽  
David Couyras
Keyword(s):  
Eigenvalue Problem ◽  
Transport Equation ◽  
Fundamental Mode ◽  
Iteration Method ◽  
Neutron Transport ◽  
Neutron Transport Equation ◽  
Reactor Physics ◽  
Nonlinear Methods ◽  
Power Iteration ◽  
Acceleration Method

This work focuses on the k-eigenvalue problem of the neutron transport equation. The variables of interest are the largest eigenvalue (keff) and the corresponding eigenmode is called the fundamental mode. Mathematically, this problem is usually solved using the power iteration method. However, the convergence of this algorithm can be very slow, especially if the dominance ratio is high as is the case in some reactor physics applications. Thus, the power iteration method has to be accelerated in some ways to improve its convergence. One such acceleration is the Chebyshev acceleration method which has been widely applied to legacy codes. In recent years, nonlinear methods have been applied to solve the k-eigenvalue problem. Nevertheless, they are often compared to the unaccelerated power iteration. Hence, the goal of this paper is to apply the Anderson acceleration to the power iteration, and compare its performance to the Chebyshev acceleration.

High-Dimensional Model Representations for the Neutron Transport Equation

2014 ◽  
Vol 177 (3) ◽  
pp. 350-360 ◽  
Author(s):  
Zhengzheng Hu ◽  
Ralph C. Smith ◽  
Jeffrey Willert ◽  
C. T. Kelley
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
High Dimensional ◽  
Dimensional Model ◽  
Neutron Transport Equation

scholarly journals Note on the Solution of Transport Equation by Tau Method and Walsh Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Transport Equation ◽  
Legendre Polynomials ◽  
Neutron Transport ◽  
Three Dimensional ◽  
Walsh Function ◽  
Dimensional Case ◽  
Angular Variable ◽  
Tau Method ◽  
Algebraic Equations ◽  
Neutron Transport Equation

We consider the combined Walsh function for the three-dimensional case. A method for the solution of the neutron transport equation in three-dimensional case by using the Walsh function, Chebyshev polynomials, and the Legendre polynomials are considered. We also present Tau method, and it was proved that it is a good approximate to exact solutions. This method is based on expansion of the angular flux in a truncated series of Walsh function in the angular variable. The main characteristic of this technique is that it reduces the problems to those of solving a system of algebraic equations; thus, it is greatly simplifying the problem.

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