Development of generalized finite element method for vector electromagnetic problems

Time domain finite element methods (TDFEM) have seen a rise in popularity in the recent past. The principal advantages that this method enjoys over the other predominant differential equation based approach is the fact that one can use unstructured meshes, as well as a space of higher order basis functions. As is well known, the finite element approximation space is usually formulated in terms of polynomials both in space and time. It may be possible to obtain better approximation in space (and possibly in time) by using an approximation that comprises of functions other than polynomials. The generalized finite element method (GFEM) provides the framework for tailoring the function space to a specific problem. However, until recently this technique has been applied only to elliptic problems. We have recently developed a vector basis function that makes this technique applicable to vector electromagnetic problems. In this paper, an extension of the methodology to analyzing time domain phenomena is presented.