(untitled) (Communications in Computational Physics, 2019)
A new approach for numerically solving 3-T diffusion equations on 2-D scattered point distributions is developed by the finite point method. In this paper, a new method for selecting neighboring points is designed, which is robust and well reflects variations of gradients of physical quantities. Based on this, a new discretization method is proposed for the diffusion operator, which results in a new scheme with the stencil of minimal size for numerically solving nonlinear diffusion equations. Distinguished from most of meshless methods often involving dozens of neighboring points, this method needs only five neighbors of the point under consideration. Numerical simulations show the good performance of the proposed methodology.