An optimal edge based finite difference solution to the vector Helmholtz equation in two dimensions

In this paper, we investigate an edge-based finite difference method based on the reduced dispersion finite difference method. In this method, an arbi trary stencil can be used to obtain a finite difference equation where opti mal coefficients are derived for a plane wave propagating through a homogen eous region, in the presence of material discontinuities and also for an an isotropic absorber for use as a perfectly matched layer (PML). Numerical re sults obtained using the optimal finite difference method are compared to t hose obtained using the vector finite element method (VFEM) with H-0(curl) basis function to demonstrate the improved performance of the proposed meth od.