time-domain solution of
Maxwell’s equations on locally
reﬁned grids with ﬁctitious
A. Bouquet and C. Dedeban
France Telecom R&D, La Turbie, France, and
Purpose – The use of the prominent ﬁnite difference time-domain (FDTD) method for the
time-domain solution of electromagnetic wave propagation past devices with small geometrical details
can require very ﬁne grids and can lead to unmanageable computational time and storage. The
purpose of this paper is to extend the analysis of a discontinuous Galerkin time-domain (DGTD)
method (able to handle possibly non-conforming locally reﬁned grids, based on portions of Cartesian
grids) and investigate the use of perfectly matched layer regions and the coupling with a ﬁctitious
domain approach. The use of a DGTD method with a locally reﬁned, non-conforming mesh can help
focusing on these small details. In this paper, the adaptation to the DGTD method of the ﬁctitious
domain approach initially developed for the FDTD is considered, in order to avoid the use of a volume
mesh ﬁtting the geometry near the details.
Design/methodology/approach – Based on a DGTD method, a ﬁctitious domain approach is
developed to deal with complex and small geometrical details.
Findings – The ﬁctitious domain approach is a very interesting complement to the FDTD method,
since it makes it possible to handle complex geometries. However, the ﬁctitious domain approach
requires small volume elements, thus making the use of the FDTD on wide, regular, ﬁne grids often
unmanageable. The DGTD method has the ability to handle easily locally reﬁned grids and the paper
shows it can be coupled to a ﬁctitious domain approach.
Research limitations/implications – Although the stability and dispersion analysis of the DGTD
method is complete, the theoretical analysis of the ﬁctitious domain approach in the DGTD context is not.
It is a subject of further investigation (which could provide important insights for potential improvements).
Originality/value – This is believed to be the ﬁrst time a DGTD method is coupled with a ﬁctitious
Keywords Galerkin method, Energy conservation, Fluxes
Paper type Research paper
The solution of the time-domain Maxwell equations on space grids is nowadays
commonly used for the modeling of systems involving electromagnetic waves.
The current issue and full text archive of this journal is available at
The authors thank P. Brachat and P. Ratajczak of France Telecom R&D for their constant help
and S. Lanteri of INRIA for fruitful discussions and kind hosting in his research team.
COMPEL: The International Journal
for Computation and Mathematics in
Electrical and Electronic Engineering
Vol. 29 No. 3, 2010
q Emerald Group Publishing Limited