An explicit finite-difference time-domain method using Whitney elements

The versatility of using the finite-element method (FEM) in modeling electromagnetic problems involving structures with irregular shape is well known. On the other hand, the simplicity and usefulness of the finite-difference time domain (FDTD) method are generally recognized. Therefore, there is a great need to develop a method that retains the simplicity of the FDTD and yet provides the modeling flexibility of the FEM. Finite-element time-domain methods have been reported by several researchers; all these methods require solving a system of linear algebraic equations for each time-step. While the matrix equation is very sparse and can be solved for using the preconditioned conjugate-gradient method, it is desirable to eliminate the memory storage and CPU required for the matrix solution entirely. Thus, the present authors give an explicit finite-difference time-domain method using Whitney 2-form elements. A simple 2D parallel-plate waveguide and a 3D rectangular waveguide are used as illustrative examples.