Development of time domain vector generalized finite element method

Vector generalized finite element method (VGFEM) has been successfully applied for solving many electromagnetic (EM) problems in the frequency domain. VGFEM is a powerful technique as it permits flexibility in the choice of basis functions, use of mixed polynomial orders, use of mixed basis functions in EM simulations, and inclusion of physics in solution space. In this paper, we develop a time domain VGFEM (TD-VGFEM) technique in order to use all these appealing features of the method in the solution of transient EM problems. Detailed bilinear formulation of TD-VGFEM is given for different boundary conditions. Temporal convergence and spatial convergence of the method are shown.