A fully explicit Whitney element-time domain scheme with higher order vector finite elements for three-dimensional high frequency problems

In this paper we propose a new explicit Whitney Element-Time-Domain method for the solution of Maxwell's equations in three dimensions. This scheme could be considered a generalization of the well known Finite Difference Time Domain (FDTD) method for unstructured meshes. However, an entirely different methodology is introduced, based on the use of higher order tangential and normal vector finite elements. The exploitation of higher order approximations in an elaborate leapfrog scheme permits the use of the primary mesh only, thus avoiding the implementation of dual mesh. The new method is, finally, applied to a typical high frequency electromagnetic field formulation.