An implicit discontinuous Galerkin time‐domain method for two‐dimensional electromagnetic wave propagation

Abstract

PurposeThe purpose of this paper is to develop a time implicit discontinuous Galerkin method for the simulation of two‐dimensional time‐domain electromagnetic wave propagation on non‐uniform triangular meshes.Design/methodology/approachThe proposed method combines an arbitrary high‐order discontinuous Galerkin method for the discretization in space designed on triangular meshes, with a second‐order Cranck‐Nicolson scheme for time integration. At each time step, a multifrontal sparse LU method is used for solving the linear system resulting from the discretization of the TE Maxwell equations.FindingsDespite the computational overhead of the solution of a linear system at each time step, the resulting implicit discontinuous Galerkin time‐domain method allows for a noticeable reduction of the computing time as compared to its explicit counterpart based on a leap‐frog time integration scheme.Research limitations/implicationsThe proposed method is useful if the underlying mesh is non‐uniform or locally refined such as when dealing with complex geometric features or with heterogeneous propagation media.Practical implicationsThe paper is a first step towards the development of an efficient discontinuous Galerkin method for the simulation of three‐dimensional time‐domain electromagnetic wave propagation on non‐uniform tetrahedral meshes. It yields first insights of the capabilities of implicit time stepping through a detailed numerical assessment of accuracy properties and computational performances.Originality/valueIn the field of high‐frequency computational electromagnetism, the use of implicit time stepping has so far been limited to Cartesian meshes in conjunction with the finite difference time‐domain (FDTD) method (e.g. the alternating direction implicit FDTD method). The paper is the first attempt to combine implicit time stepping with a discontinuous Galerkin discretization method designed on simplex meshes.