Element-free Galerkin modeling of neutron diffusion equation in X-Y geometry

The numerical treatment of partial differential equations with element-free discretization techniques has been attractive research area in the recent years. In this paper an Element-free Galerkin, EFG, method is applied to solve the neutron diffusion equation in X-Y geometry. The Moving Least Square (MLS), interpolation is used to construct the shape functions for the weak form of the equation. The constructed shape functions through using Gaussian and cubic weight functions, which are commonly used in Element-free Galerkin method, lack the Kronecker delta property; this causes additional numerical effort for satisfying the essential boundary conditions. In this study a new weight function which almost fulfills the essential boundary conditions with high accuracy is presented. Constructed shape functions along the new weight function provide much stable results for varying support domain size and distorted nodal arrangements. The efficiency and accuracy of the method was evaluated through a number of examples. Results are compared with the analytical and reference solutions. It is revealed that the applied EFG method provides highly accurate results and the method is attractive in some aspects such as nodes refinement and dealing with the curve boundaries. (C) 2012 Elsevier Ltd. All rights reserved.