A Generalized Local Time-Step Scheme for Efficient FVTD Simulations in Strongly Inhomogeneous Meshes

Fumeaux, Christophe; Baumann, D.; Leuchtmann, P.; Vahldieck, R.

doi:10.1109/tmtt.2004.823595

Cited by 67 publications

(31 citation statements)

References 12 publications

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“…Appropriate interpolation schemes or interwoven time stepping schemes are required. While such schemes are available and employed, e. g., in finite volume calculations [73], they are usually restricted to lower orders. Higher-order schemes [74] (or schemes of mixed order) appear more suitable to accompany the higher-order spatial discretisation of DGTD.…”

Section: Time Steppingmentioning

confidence: 99%

Discontinuous Galerkin methods in nanophotonics

Busch

König

Niegemann

2011

Laser & Photonics Reviews

145

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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 Steppingmentioning

confidence: 99%

Discontinuous Galerkin methods in nanophotonics

Busch

König

Niegemann

2011

Laser & Photonics Reviews

145

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“…The rth order accurate reconstruction of the numerical flux in the ENO scheme is (14) where α r k,l are the reconstruction coefficients and k the stencil index selected among the r candidate stencils. The stencil S k can be written as…”

Section: Finite Volume Time-domain Methodsmentioning

confidence: 99%

“…Increased computational efficiency for the FVTD method has also been addressed through use of local time-stepping [14] and hybrid FVTD-integral Equation (15) approaches. In the proposed implementation, the surface current for a perfectly conducting scatterer is expressed locally using either only the incident field (as in a PO approximation) or as a combination of the incident field and a higher-order FVTD computed scattered field.…”

Section: Introductionmentioning

confidence: 99%

Efficient Implementation of Higher-Order Finite Volume Time-Domain Method for Electrically Large Scatterers

Chatterjee¹,

Myong²

2009

PIER B

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Abstract-The Finite Volume Time-Domain (FVTD) method finds limited application in the simulation of electromagnetic scattering from electrically large scatterers because of the fine discretization required in terms of points-per-wavelength. An efficient implementation of a higher-order FVTD method is proposed for electrically large, perfectly conducting scatterers. Higher-order and fine-grid accuracy are preserved, despite using only a first-order spatial accuracy and a coarse grid in substantial parts of the FVTD computational domain, by partially incorporating a time-domain Physical Optics (PO) approximation for the surface current. This can result in considerable savings in computational time while analyzing geometries containing electrically large, smooth sections using the FVTD method. The higher-order FVTD method in the present work is based on an Essentially Non-Oscillatory (ENO) reconstruction and results are presented for two-dimensional perfectly conducting scatterers subject to Transverse Magnetic (TM) or Transverse Electric (TE) illumination.

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“…The in-house implementation of the FVTD technique used in this study is based on a cell-centered scheme with upwind fluxes [16]. The efficiency of the solver is increased through a local time-stepping scheme [17] which combines the inhomogeneous spatial tetrahedral discretization with an inhomogeneous temporal discretization. Dispersive materials are handled as described in [18] and the computational domain can be truncated using spherical or conformal perfectlymatched absorbers [19].…”

Section: B Fvtdmentioning

confidence: 99%

Time-domain simulations of a 31-antenna array for breast cancer imaging

Klemm

Baumann

Craddock

2011

2011 IEEE International Symposium on Antennas and Propagation (APSURSI)

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Abstract-In this paper we discuss challenges related with timedomain simulations of a complete microwave radar imaging system for breast cancer detection. Two different numerical methods are considered to address this demanding electromagnetic problem featuring 31 ultra-wideband antennas. The first method is the Finite Integration Technique (FIT) applied in a regular grid and implemented in a commercial solver, whereas the second method is an in-house developed FiniteVolume Time-Domain (FVTD) code applied in a tetrahedral mesh. Our work focuses on the fundamental differences between the two approaches for the comprehensive full-wave modeling of the considered problem. The emphasis of the comparison is placed on the computational cost, which reveals the strengths and limitations of both methods for the problem considered.

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A Generalized Local Time-Step Scheme for Efficient FVTD Simulations in Strongly Inhomogeneous Meshes

Cited by 67 publications

References 12 publications

Discontinuous Galerkin methods in nanophotonics

Discontinuous Galerkin methods in nanophotonics

Efficient Implementation of Higher-Order Finite Volume Time-Domain Method for Electrically Large Scatterers

Time-domain simulations of a 31-antenna array for breast cancer imaging

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