311 research outputs found
Discontinuous Galerkin approximation of the Maxwell eigenproblem
A theoretical framework for the analysis of discontinuous Galerkin
approximations of the Maxwell eigenproblem with discontinuous coefficients is
presented. Necessary and sufficient conditions for a spurious-free
approximation are established, and it is shown that, at least on conformal
meshes, basically all the discontinuous Galerkin methods in the literature
actually fit into this framework. Relations with the classical theory for
conforming approximations are also discussed
A locally divergence-free interior penalty method for two-dimensional curl-curl problems
An interior penalty method for certain two-dimensional curl-curl problems is investigated in this paper. This method computes the divergence-free part of the solution using locally divergence-free discontinuous P vector fields on graded meshes. It has optimal order convergence (up to an arbitrarily small e) for the source problem and the eigenproblem. Results of numerical experiments that corroborate the theoretical results are also presented. © 2008 Society for Industrial and Applied Mathematics.
Dielectric multilayer waveguides for TE and TM mode matching
We analyse theoretically for the first time to our knowledge the perfect
phase matching of guided TE and TM modes with a multilayer waveguide composed
of linear isotropic dielectric materials. Alongside strict investigation into
dispersion relations for multilayer systems, we give an explicit qualitative
explanation for the phenomenon of mode matching on the basis of the standard
one-dimensional homogenization technique, and discuss the minimum number of
layers and the refractive index profile for the proposed device scheme. Direct
applications of the scheme include polarization-insensitive, intermodal
dispersion-free planar propagation, efficient fibre-to-planar waveguide
coupling and, potentially, mode filtering. As a self-sufficient result, we
present compact analytical expressions for the mode dispersion in a finite,
N-period, three-layer dielectric superlattice.Comment: 13 pages with figure
Solution of the time-harmonic Maxwell equations using discontinuous Galerkin methods
We present numerical results concerning the solution of the time-harmonic
Maxwell's equations discretized by discontinuous Galerkin methods. In
particular, a numerical study of the convergence, which compares different
strategies proposed in the literature for the elliptic Maxwell equations, is
performed in the two-dimensional case.Comment: Preprint submitted for publication for the proceedings of ICCAM06
(11/04/2007
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