A high-order non-conforming discontinuous Galerkin method for time-domain electromagnetics

• Published in: Journal of computational and applied mathematics Vol. 234; no. 4; pp. 1088 - 1096
• Main Authors: Fahs, Hassan, Lanteri, Stéphane
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier B.V 15.06.2010; Elsevier
• Subjects: Approximations and expansions; Computational electromagnetism; Discontinuous Galerkin method; Electromagnetism; Engineering Sciences; Exact sciences and technology; Explicit time integration; Mathematical analysis; Mathematical Physics; Mathematics; Measure and integration; Non-conforming meshes; Numerical Analysis; Numerical analysis. Scientific computation; Numerical approximation; Sciences and techniques of general use; Time-domain Maxwell’s equations; Discontinuous Galerkin method; Computational electromagnetism; Time-domain Maxwell’s equations; Explicit time integration; Non-conforming meshes; Integration; Electromagnetism; Grid pattern; Numerical approximation; Interpolation; Time-domain Maxwell's equations; Numerical analysis; Applied mathematics; Maxwell equation; Numerical stability
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2009.05.015

In this paper, we discuss the formulation, stability and validation of a high-order non-dissipative discontinuous Galerkin (DG) method for solving Maxwell’s equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a second-order or a fourth-order leap-frog time integration scheme. Moreover, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary-level hanging nodes. The method is proved to be stable and conserves a discrete counterpart of the electromagnetic energy for metallic cavities. Numerical experiments with high-order elements show the potential of the method.