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

Hassan Fahs (1)

1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media

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.

Mots clés: discontinuous Galerkin methods; Maxwell's equations; curved finite elements; stability; numerical integration; high-order accuracy

Domaines: Physique mathématique [math-ph]; Analyse numérique [math.NA]; Electromagnétisme

Hassan Fahs. Improving accuracy of high-order discontinuous Galerkin method for time-domain electromagnetics on curvilinear domains. International Journal of Computer Mathematics, 2011, 88 (10), pp.2124 - 2153. ⟨10.1080/00207160.2010.527960⟩. ⟨hal-00600465⟩