Improving accuracy of high-order discontinuous Galerkin method for time-domain electromagnetics on curvilinear domains

Abstract

The paper discusses high-order geometrical mapping for handling curvilinear geometries in high-accuracy discontinuous Galerkin simulations for time-domain Maxwell problems. The proposed geometrical mapping is based on a quadratic representation of the curved boundary and on the adaptation of the nodal points inside each curved element. With high-order mapping, numerical fluxes along curved boundaries are computed much more accurately due to the accurate representation of the computational domain. Numerical experiments for two-dimensional and three-dimensional propagation problems demonstrate the applicability and benefits of the proposed high-order geometrical mapping for simulations involving curved domains.

Keywords:

• discontinuous Galerkin methods
• Maxwell's equations
• curved finite elements
• stability
• numerical integration
• high-order accuracy

2000 AMS Subject Classifications :

• 65M12
• 65M60
• 65D30
• 65D32
• 74S10
• 78A40

Acknowledgements

The author would like to thank the two anonymous referees for their constructive comments and suggestions that helped to improve the quality of this article. The author wish also to thank Mikolaj Szydlarski and Stéphane Lanteri for their help concerning the 3D part of the numerical experiments.