Discontinuous Galerkin methods for dispersive and lossy Maxwell's equations and PML boundary conditions

Lu, Tiao; Zhang, Pingwen; Cai, Wei

doi:10.1016/j.jcp.2004.02.022

Cited by 199 publications

(127 citation statements)

References 20 publications

Supporting

Mentioning

126

Contrasting

Unclassified

Order By: Relevance

“…Quite naturally, most authors validate their implementation with some simple test particles, mostly squares, cylinders, and spheres [32,38,[59][60][61]. In this section, however, we have compiled some references which give a more application-oriented overview of what is possible with DG methods, especially in the time-domain.…”

Section: Applications To Nanophotonicsmentioning

confidence: 99%

See 1 more Smart Citation

Discontinuous Galerkin methods in nanophotonics

Busch

König

Niegemann

2011

Laser & Photonics Reviews

148

View full text Add to dashboard Cite

Nanophotonic systems facilitate a far-reaching control over the propagation of light and its interaction with matter. In view of the increasing sophistication of fabrication methods and characterisation tools, quantitative computational approaches are thus faced with a number of challenges. This includes dealing with the strong optical response of individual nanostructures and the multi-scattering processes associated with arrays of such elements. Both of these aspects may lead to significant modifications of light-matter interactions. This article reviews the state of the recently developed discontinuous Galerkin finite element method for the efficient numerical treatment of nanophotonic systems. This approach combines the accurate and flexible spatial discretisation of classical finite elements with efficient time stepping capabilities. The underlying principles of the discontinuous Galerkin technique and its application to the simulation of complex nanophotonic structures are described in detail. In addition, formulations for both time-and frequency-domain solvers are provided and specific advantages and limitations of the technique are discussed. The potential of the discontinuous Galerkin approach is illustrated by modelling and simulating several experimentally relevant systems.

show abstract

Section: Applications To Nanophotonicsmentioning

confidence: 99%

“…While the actual physical domain with arbitrary scatterers will benefit from conventional tetrahedral meshes, such boundary regions could be easily tessellated into hexahedral elements [61]. Here, nodes would be positioned in terms of a tensor product of one-dimensional node distributions.…”

Section: Improving the Spatial Discretisationmentioning

confidence: 99%

Discontinuous Galerkin methods in nanophotonics

Busch

König

Niegemann

2011

Laser & Photonics Reviews

148

View full text Add to dashboard Cite

show abstract

“…In practical applications [1][2][3][4], the dispersive media are often coupled with simple medium such as air. For example, a Debye slab is embedded between air, or a Debye medium is surrounded by air, see Fig.…”

Section: Extensions To Coupled Mediamentioning

confidence: 99%

“…In 2001, Jiao and Jin [3] initiated the application of time-domain finite element methods (TDFEM) for dispersive media. Then in 2004, Lu et al developed time-domain Discontinuous Galerkin methods for modeling dispersive media [4]. Though there are many excellent papers on FEM analysis for Maxwell's equations in the vacuum (e.g., [5][6][7][8][9][10][11][12] and references therein), to our knowledge, there exists little theoretical analysis of TDFEM for Maxwell's equations in dispersive media except our initial effort in this direction…”

Section: Introductionmentioning

confidence: 99%

Finite element study of time‐dependent Maxwell's equations in dispersive media

Chen

2008

Numerical Methods Partial

View full text Add to dashboard Cite

In this article, we consider the time-dependent Maxwell's equations in a bounded domain when dispersive media are involved. The Crank-Nicolson scheme is developed to approximate the electric field equation by Nedelec edge elements and is proved to be optimal convergent in energy norm. The analysis is carried out for Debye medium, but the same results hold true for other dispersive media such as plasma and Lorentz medium. Furthermore, our analysis extends straightforward to cases when a dispersive medium and a simple medium (such as air) are coupled. Mathematics Subject Classification (2000): 65N30, 35L15, 78-08.

show abstract

“…In order to accurately perform wideband electromagnetic simulations, we have to consider the effect of medium dispersion in the modeling equations. Applications of time-domain finite element method (TDFEM) for dispersive media have appeared only very recently [17,32]. However, there exists no theoretical error analysis except our initial efforts [20,21,22].…”

Section: Introductionmentioning

confidence: 99%

Superconvergence analysis for Maxwell's equations in dispersive media

Lin

2007

Math. Comp.

View full text Add to dashboard Cite

Abstract. In this paper, we consider the time dependent Maxwell's equations in dispersive media on a bounded three-dimensional domain. Global superconvergence is obtained for semi-discrete mixed finite element methods for three most popular dispersive media models: the isotropic cold plasma, the one-pole Debye medium, and the two-pole Lorentz medium. Global superconvergence for a standard finite element method is also presented. To our best knowledge, this is the first superconvergence analysis obtained for Maxwell's equations when dispersive media are involved.

show abstract

Discontinuous Galerkin methods for dispersive and lossy Maxwell's equations and PML boundary conditions

Cited by 199 publications

References 20 publications

Discontinuous Galerkin methods in nanophotonics

Discontinuous Galerkin methods in nanophotonics

Finite element study of time‐dependent Maxwell's equations in dispersive media

Superconvergence analysis for Maxwell's equations in dispersive media

Contact Info

Product

Resources

About