Application of two-grid interpolation to enhance average gradient method for solving partial differential equations

Abstract

Previously presented method of calculating local average gradients for solving partial differential equations (PDEs) is enhanced by using interpolating gridpoints and triangular grids. The interpolating mesh provides finer computational grid, which is then used for solving the PDE. The combined use of the finer interpolating grid together with the original sparser grid is a two-grid method. By comparing the previous application of rectilinear grid for diffusion from initial point concentration to the new triangular two grid method, it was found that the application of triangular two-grid method improves stability of the solution and it provides more rapid convergence to the correct analytical solution.