Software Implementation of the Finite Element Method for Neutron Diffusion Equation
The most of engineering codes, used in nuclear reactor calculations, are based on diffusion approximation of the neutron transport equation. The finite-difference method is widely used to solve the diffusion equation. Acceptable accuracy of the results reached only by using fine mesh or complementary approaches, such as nodal methods. We propose another approach based on finite-element method (FEM) and the use of modern methods of calculation based on free software. There are two ways to improve the accuracy: split up the grid and / or increase the order of finite element. There was created the neutronic code (software), which solves the stationary diffusion equation in 2D and 3D hexagonal geometry in the approximation of two energy groups, and has a GUI (interface). For the numerical solution it is used the finite element method implemented in the computer package FeniCS, a library for solving spectral problems SLEPc, and for the construction and mesh generation it is used the program Gmsh. For the testing of computational algorithm authors considered several numerical tests that produced good results. There was also conducted parallelization of code (in test mode).