The Discontinuous Galerkin Finite Element Method for electromagnetics and elastodynamics

The propagation of electromagnetic waves can be studied by solving Maxwell’s equations. Similarly, a combination of Newton’s second law and Hooke’s law, leads to a system of partial differential equations (PDEs) that describe the propagation of elastodynamic waves. Both systems of PDEs can be solved by a broad range of numerical techniques. Well-known and applicable to both electromagnetics and elastodynamics are the Finite Volume Method (FVM) and the Finite Element Method (FEM). Other methods are the Finite Difference Time Domain (FDTD) method which is more targeted towards electromagnetic problems and the Elastodynamic Finite Integration Technique (EFIT) used in elastodynamics. A more recent technique that combines good properties of the previously mentioned methods (such as higher order accuracy, geometric flexibility and explicit timestepping), is the Discontinuous Galerkin Finite Element Method (DGFEM). It was first applied to an electromagnetic problem by Hesthaven and Warburton, but on a rather academic example [1, 2]. The details on how to extend this example towards more realistic problems are not explicitly stated. In this talk, we explain how we extended the Maxwell example from [2] towards applications involving more realistic situations. In addition, we illustrate the use of the DGFEM for solving linear and nonlinear elastodynamic wave propagation problems. A particularly interesting property of the DGFEM framework is that it allows a clear separation between problem-independent (kernel) code and code that is more tailored towards the problem (PDE) one is solving. References [1] J. S. Hesthaven and T. Warburton. Nodal high-order methods on unstructured grids. Journal of Computational Physics, 181:186–221, 2002. [2] Jan S. Hesthaven and Warburton Tim. Nodal Discontinuous Galerkin Methods - Algorithms, Analysis, and Applications. Springer, 2008.status: publishe