Closed-form expressions for the numerical dispersion and reflection in FEMsimulations involving biaxial materials

Closed-form expressions for the numerical errors caused by finite-element d iscretization of problems involving materials of biaxial permittivity and p ermeability tensors are developed. In particular, we derive expressions for the numerical dispersion and reflection in both first-order node and edge basis function finite-element formulations in an equilateral triangular mes h. Results using these closed-form expressions are compared to practical nu merical simulations, The application of these expressions to the analysis o f the performance of the perfectly matched layer boundary is suggested.