Numerical Green’s function for a two-dimensional diffusion equation

Abstract

This paper presents a novel form to calculate Green's function by using a numerical method. In this paper, Green's function is calculated for the twodimensional diffusion equation. The numerical Green's function is defined as Green's matrix that represents the domain of the problem to be solved in terms of the physical properties and geometrical characteristic. Green's matrix is the basis of the numerical method called 'Explicit Green's Approach' (ExGA) that allows explicit time marching with a time step larger than the one required by other methods found in the literature, without losing precision. The method uses Green's matrix which is determined numerically by the Finite Element Method (FEM). The paper presents one application in heat conduction and another in groundwater flow, demonstrating that the results are quite accurate when compared to analytical solutions and to other numerical solutions.