Finite Difference Method Based on Node Set Vector for Numerical Computation of Poisson Equation

A novel finite difference method based on node set vectors for two-dimensional Poisson equation is proposed in this paper, the method, called as node set vector FDM (NSV-FDM), can be applied to structured or unstructured grids, and be used to deal with boundary conditions naturally as finite element method. Studies on basic discrete scheme of NSV-FDM, the second order discrete scheme of interior node and boundary node are investigated in detail in this paper, numerical computation of two samples with different distribution functions are also carried out, the results verify that NSV-FDM is effective for numerical computation of Poisson equation.