Modeling Material Interfaces and Boundary Conditions in High-Order Finite-Difference Methods

When solving the transmission-line equations using high-order finite-difference methods, it is extremely important to have appropriate procedures to enforce boundary conditions as well as the continuity of the fields at material interfaces where the material parameters are discontinuous. This paper presents general procedures to accomplish these two tasks on both uniform and nonuniform grids. The proposed procedures can be used to achieve high-order convergence on coarse grids even in the extreme case of analyzing a dispersive Lorentz material interfaced with vacuum and excited at the plasma frequency of the Lorentz material.