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

In this paper, the authors investigate an edge-based finite difference method based on the reduced dispersion finite difference method. In this method, an arbitrary stencil can be used to obtain a finite difference equation where optimal coefficients are derived for a plane wave propagating through a homogeneous region, in the presence of material discontinuities and also for an anisotropic absorber for use as a perfectly matched layer (PML). Numerical results obtained using the optimal finite difference method are compared to those obtained using the vector finite element method (VFEM) with H₀(curl) basis function to demonstrate the improved performance of the proposed method