A laguerre‐based time‐domain discontinuous Galerkin finite element‐boundary integral method

Abstract

ABSTRACTThis article develops a Laguerre‐based discontinuous Galerkin finite element‐boundary integral method for solving Maxwell's equations in the time domain. A set of hierarchical vector functions and weighted Laguerre polynomials as spatial and temporal basis functions are used to expand transient electromagnetic fields, respectively. The electromagnetic fields at truncated boundary are solved by the time‐domain boundary integral method and used in the partial penalized numerical flux in the discontinuous Galerkin time‐domain method, thus avoiding the use of absorbing boundary condition. With the use of the Galerkin temporal testing procedure, the Laguerre‐based algorithm eliminates the time variable, and hence the explicit time integration solution procedure is replaced by a recursive solution procedure in terms of the orders of temporal testing functions. The use of the partial penalized numerical flux with an optimized penalty factor can improve the accuracy of the proposed algorithm compared with the widely used central flux and upwind flux. Numerical results demonstrate that the proposed method becomes increasingly accurate with increase of the order of the spatial basis functions.© 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:2774–2780, 2016