A Vector Finite Element Time-Domain Method for Solving Maxwell's Equations on Unstructured Hexahedral Grids

In this paper the vector finite element time-domain (VFETD) method is derived, analyzed, and validated. The VFETD method uses edge vector finite elements as a basis for the electric field and face vector finite elements as a basis for the magnetic flux density. The Galerkin method is used to convert Maxwell's equations to a coupled system of ordinary differential equations. The leapfrog method is used to advance the fields in time. The method is shown to be stable and to conserve energy and charge for arbitrary hexahedral grids. A numerical dispersion analysis shows the method to be second order accurate on distorted hexahedral grids. Several computational experiments are performed to determine the accuracy and efficiency of the method.