Using Curved Elements in the Discontinuous Galerkin Time-Domain Approach

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

doi:10.1063/1.3506136

Cited by 4 publications

(5 citation statements)

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“…The five stage, fourth order accurate LSRK scheme by Carpenter and Kennedy [45] is most commonly used for the field evolution in DGTD [27]. Nevertheless, other choices [46,47] are possible and potentially advantageous. Hence, they are discussed in Sect.…”

Section: Time-stepping and The Runge-kutta Methodsmentioning

confidence: 99%

“…Here, the coefficients γ can be directly related to the coefficients A i and B i of the LSRK scheme [47]. In the absence of sources, the discretised physical system can be expressed as a matrix-vector product of a system matrix H and a number of unknowns, compare Eq.…”

Section: Eigenvalues Conditional Stability and Maximum Time Stepsmentioning

confidence: 99%

“…This is a reasonable measure because each stage requires one evaluation of the right-hand sidef (q i 1 ; t n +c i Δt). Hence, the normalised time step also represents a measure for time step per computational effort (CPU time [47]. With this approach, a fourth-order 14-stage scheme was generated, which outperforms the 5-stage scheme by Carpenter and Kennedy by around 40-50%.…”

Section: Optimised Runge-kutta Schemesmentioning

confidence: 99%

“…Such higher-order elements usually contain additional vertices, for example quadratic elements contain one additional vertex at the centre of every edge. For such a higher-order element, one can then explicitly generate a polynomial mapping [24,93].…”

Section: A5 Curvilinear Elementsmentioning

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: Time-stepping and The Runge-kutta Methodsmentioning

confidence: 99%

Section: Eigenvalues Conditional Stability and Maximum Time Stepsmentioning

confidence: 99%

Section: Optimised Runge-kutta Schemesmentioning

confidence: 99%

Section: A5 Curvilinear Elementsmentioning

confidence: 99%

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Discontinuous Galerkin methods in nanophotonics

Busch

König

Niegemann

2011

Laser & Photonics Reviews

148

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“…The most remarkable achievements in the nanophotonics domain since 2009 are due to Busch et al Busch [7]- [8]- [9] has been at the origin of seminal works on the development and application of the DGTD method in this domain. These works not only deal with the extension of the DGTD method with regards to the complex material models and source settings required by applications relevant to nanophotonics and plasmonics [10]- [11]- [2], but also to core contributions aiming at improving the accuracy and the e ciency of the proposed DGTD solvers [12]- [13]- [14]- [15].…”

Section: Dgtd Methods For Nanophotonics/plasmonicsmentioning

confidence: 99%

Simulation of near-field plasmonic interactions with a local approximation order discontinuous Galerkin time-domain method

Viquerat¹,

Lanteri²

2016

Photonics and Nanostructures - Fundamentals and Applications

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International audienceDuring the last ten years, the discontinuous Galerkin time-domain (DGTD) method has progressively emerged as a viable alternative to well established finite-difference time-domain (FDTD) and finite-element time-domain (FETD) methods for the numerical simulation of electromagnetic wave propagation problems in the time-domain. The method is now actively studied for various application contexts including those requiring to model light/matter interactions on the nanoscale. In this paper we further demonstrate the capabilities of the method for the simulation of near-field plasmonic interactions by considering more particularly the possibility of combining the use of a locally refined conforming tetrahedral mesh with a local adaptation of the approximation order

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