Discontinuous Galerkin Inspired Framework for Vector Generalized Finite-Element Methods

Discontinuous Galerkin methods have been extensively used in simulations of various electromagnetic problems, in both time and frequency domains. In this paper, we exploit features of these methods to provide a framework that can be used to overcome a fundamental bottleneck in using as well as augmenting the capabilities of vector generalized finite element methods (VGFEM). This approach permits the use of VGFEM for analysis of piecewise inhomogeneous domains without defining additional constraints on basis functions and allows hybridization with other finite element formulations. Interior penalty discontinuous Galerkin method (IP-DGM) is used to enable communication among partitioned domains. We will present several results that demonstrate applications of these hybrid methods as well as their convergence characteristics.