Computation of electromagnetic scattering with a non‐conforming discontinuous spectral element method

In this paper we solve electromagnetic scattering problems by approximating Maxwell's equations in the time‐domain with a high‐order quadrilateral discontinuous spectral element method (DSEM). The method is a collocation form of the discontinuous Galerkin method for hyperbolic systems where the solution is approximated by a tensor product Legendre expansion and inner products are replaced with Gauss–Legendre quadratures. To increase flexibility of the method, we use a mortar element method to couple element faces. Mortars provide a means for coupling element faces along which the polynomial orders differ, which allows the flexibility to choose the approximation order within an element by considering only local resolution requirements. Mortars also permit local subdivision of a mesh by connecting element faces that do not share a full side. We present evidence showing that the convergence of the non‐conforming approximations is spectral along with examples of their use.