On the use of irregular grids in the zeroth-order vector finite element-time domain (VFE-TD) method

The vector finite element-time domain (VFE-TD) method has been proposed to solve Maxwell's equations adopting the leap-frog scheme. The finite differences have been applied to discretize the time domain and the vector finite elements have been used to approximate the curl operators of the electric and magnetic fields. The VFE-TD method seems to be more powerful and flexible of traditional point-matching techniques, because it permits to use irregular grids to discretize the space. This is an advantage in the solution of scattering problems when an accurate modeling of complex geometrical configurations is very significant. Good accuracy has been achieved in test problems using irregular grids only by means of first-order vector finite elements. The use of zeroth-order vector finite elements (or edge elements is investigated. The mathematical formulation of the zeroth-order VFE-TD method is examined to illustrate the solution of 2-D problems. The optimum choice of different irregular trapezoidal and triangular grids is also discussed.