The use of hybrid meshes to improve the efficiency of a discontinuous Galerkin method for the solution of Maxwell’s equations

This paper investigates the efficiency of a high-order nodal discontinuous Galerkin method for the numerical solution of Maxwell’s equations using hybrid meshes. An unstructured triangular or tetrahedral mesh is used near curved boundaries and a structured Cartesian mesh is used to fill the remainder of the domain. A quadrature-free implementation is employed for the regular quadrilateral and hexahedral elements which, together with the reduction in the number of internal faces, leads to a reduction in the cpu time requirements. Numerical examples in two and three dimensions are used to illustrate the benefits of using hybrid meshes.

► Hybrid meshes allow to combine geometric flexibility and computational efficiency.
► Saving in cpu time is highly dependent on the approximation order (p).
► In 3D hexahedra are between 7 and 15 times more efficient than tetrahedra.