A Petrov-Galerkin finite element method for solving the neutron transport equation

Abstract

A finite element method using different trial and test spaces is introduced for solving the neutron transport equation in spherical geometry. It is shown that the widely used discrete ordinates method can also be thought of as such a finite element technique, in which integrals appearing in the difference equations are replaced by one-point Gauss quadrature formulas (midpoint rule). Comparison of accuracy between the new method and the discrete ordinates method is discussed, and numerical examples are given to illustrate the greater accuracy of the new technique.