COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

Purpose – The 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/approach – The 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.

Findings – Despite 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/implications – The 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 implications – The 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/value – In 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.