A novel node collocation technique in radial basis function collocation method applied to neutron diffusion equations

A novel node collocation approach for the application of radial basis function meshless methods in neutron diffusion equations is presented in this paper. By introducing ghost nodes, the number and position of external nodes can be flexibly controlled to investigate their impact on the ill-conditioning of the coefficient matrix and the solution accuracy. The steady-state single-group neutron diffusion equation is solved using the improved method, and the discretization method and solution process are provided. The boundary scale factor, which measures the distance of external nodes from the computational domain, shows a negative correlation with the error once it stabilizes. An optimal boundary scale factor exists regarding its influence on the matrix condition number; as the shape factor of the radial basis function increases, the optimal value also increases. An increase in the number of layers of external nodes slightly enhances solution accuracy but significantly raises the condition number of the matrix. For a shape factor of 0.01, the computational error decreases by 4.01 % when the number of layers is increased from 1 to 4. When the outer number factor is small, fluctuations in the solution error are observed, with stability achieved once it exceeds 0.5. Although increasing the outer number factor raises the matrix condition number, its impact is less pronounced than that of increasing the number of layers.