A new explicit higher-order time-domain finite element method for solving maxwell’s equations

In this paper, an explicit, higher-order, TDFEM referred to as the element-level decomposition (ELD) method is introduced. The ELD method shares several similarities with the FDTD method. Both methods are explicit and they have comparable computational complexity. Both of them employ a leapfrog updating scheme and the stability conditions for the two methods are similar to each other. Since the ELD employs an unstructured FEM mesh, it thus has the extra flexibility in modeling complicated structures. Moreover, since its formulation is based on Galerkin´s procedure, higher-order basis functions developed in the FEM can be readily adopted in the ELD to construct higher-order schemes in a systematic manner.