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

摘要

An alternate implementation of the Finite Difference Scheme is investigated. The optimal Finite Difference Coefficients are derived for simple canonical problems such as the Freespace, Perfect Electric Conductor (PEC), Perfect Magnetic Conductor (PMC) and the Dielectric Interface. Optimal coefficients are derived for an Anisotropic Perfectly Matched Layer (PML) to be used for boundary truncation. Numerical results obtained using the Optimal Finite Difference Scheme are compared to those obtained using the Vector Finite Element Method (VFEM).