Stretched-coordinate PMLs for Maxwell’s equations in the discontinuous Galerkin time-domain method

König, Michael; Prohm, Christopher; Busch, Kurt; Niegemann, Jens

doi:10.1364/oe.19.004618

Cited by 9 publications

(8 citation statements)

References 17 publications

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“…Nevertheless, it is advantageous to use a Silver-Müller boundary condition in conjunction with PMLs, which helps to slightly reduce the reflection errors. More importantly, the error becomes less sensitive to the PML parameters [89]. Thus, we conclude that PMLs should always be terminated with a Silver-Müller boundary condition, which is easily (and efficiently) implemented via a modified numerical flux (see Sect.…”

Section: Laser and Photonics Reviewsmentioning

confidence: 84%

“…Alternatively, PMLs can be implemented in a stretchedcoordinate formulation [88,89]. In essence, in the PML region we map real-valued x; y; z onto the complex plane.…”

Section: A42 Stretched Coordinate Formulationmentioning

confidence: 99%

“…In particular, α 6 = 0 greatly improves the absorption of low-frequency waves. Compared to the UPML formulation, this can reduce numerical reflection errors by one order of magnitude [89]. Both formulations, however, lead to significantly more accurate results than a simple termination of the computational domain using a Silver-Müller boundary condition (see Sect.…”

Section: Laser and Photonics Reviewsmentioning

confidence: 99%

“…The remaining parameters must be carefully optimised to minimise the numerical errors. One such study was carried out in [89] for a three-dimensional reference system.…”

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confidence: 99%

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Discontinuous Galerkin methods in nanophotonics

Busch

König

Niegemann

2011

Laser & Photonics Reviews

148

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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.

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Section: Laser and Photonics Reviewsmentioning

confidence: 84%

“…Alternatively, PMLs can be implemented in a stretchedcoordinate formulation [88,89]. In essence, in the PML region we map real-valued x; y; z onto the complex plane.…”

Section: A42 Stretched Coordinate Formulationmentioning

confidence: 99%

Section: Laser and Photonics Reviewsmentioning

confidence: 99%

“…The remaining parameters must be carefully optimised to minimise the numerical errors. One such study was carried out in [89] for a three-dimensional reference system.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Discontinuous Galerkin methods in nanophotonics

Busch

König

Niegemann

2011

Laser & Photonics Reviews

148

View full text Add to dashboard Cite

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“…Lu et al introduced nonconforming UPML theory into DG calculations in the case of TM wave and compared the local relative error between PML and first-order SM-ABC [14]. König et al applied the stretched-coordinate PML technique to DGTD [15]. Gedney and Zhao proposed a kind of auxiliary differential equation (ADE) multilevel PML theory by complex frequency domain shift, which is used to cut off the boundary of DGTD region and take good absorption [16].…”

Section: Introductionmentioning

confidence: 99%

Implementation of an Approximate Conformal UPML in 2-D DGTD

Wei

Yang

et al. 2017

International Journal of Antennas and Propagation

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Using the numerical discrete technique with unstructured grids, conformal perfectly matched layer (PML) absorbing boundary in the discontinuous Galerkin time-domain (DGTD) can be set flexibly so as to save lots of computing resources. Based on the DGTD equations in an orthogonal curvilinear coordinate system, the processes of parameter transformation for 2-D UPML between the coordinate systems of elliptical and Cartesian are given; and the expressions of transition matrix are derived. The calculation scheme of conductivity distribution in elliptic cylinder absorbing layer is given, and the calculation coefficient of DGTD in elliptic UPML is calculated. Furthermore, the 2-D iterative formulas of DGTD and that of auxiliary equation in the elliptical cylinder UPML are derived; the conformal UPML calculation in DGTD is realized. Numerical results show that very good accuracy and computational efficiency are achieved by using the method in this paper. Compared to the rectangular computational region, both the memory and computation time of conformal UPML absorbing boundary are reduced by more than 20%.

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Simulation of three-dimensional nanoscale light interaction with spatially dispersive metals using a high order curvilinear DGTD method

Schmitt

Scheid

Viquerat

et al. 2018

Journal of Computational Physics

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In this work, we present and study a flexible and accurate numerical solver in the context of three-dimensional computational nanophotonics. More precisely, we focus on the propagation of electromagnetic waves through metallic media described by a non-local dispersive model. For this model, we propose a discretization based on a high-order Discontinuous Galerkin timedomain method, along with a low-storage Runge-Kutta time scheme of order four. The semidiscrete stability of the scheme is analyzed for classical numerical fluxes, i.e. centered and upwind. Furthermore, the numerical treatment is enriched with an enhanced approximation of the geometry based on isoparametric curvilinear meshes. We finally assess our approach on several test cases, from academic to more physical ones.

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Stretched-coordinate PMLs for Maxwell’s equations in the discontinuous Galerkin time-domain method

Cited by 9 publications

References 17 publications

Discontinuous Galerkin methods in nanophotonics

Discontinuous Galerkin methods in nanophotonics

Implementation of an Approximate Conformal UPML in 2-D DGTD

Simulation of three-dimensional nanoscale light interaction with spatially dispersive metals using a high order curvilinear DGTD method

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