Numerical convergence and physical fidelity analysis for Maxwell’s equations in metamaterials

Li, Jichun

doi:10.1016/j.cma.2009.05.018

Cited by 45 publications

(17 citation statements)

References 30 publications

(37 reference statements)

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“…Several proofs exist for the standard dispersive media models and the most classical time and space discretization schemes (see e.g. all the papers of J. Li and co-authors such as [JL06,Li07,LCE08,Li09]). Let us also mention the approach of [WXZ10] for the integro-differential version of the classical dispersive models.…”

mentioning

confidence: 99%

Analysis of a Generalized Dispersive Model Coupled to a DGTD Method with Application to Nanophotonics

Lanteri

Scheid²,

Viquerat

2017

SIAM J. Sci. Comput.

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Abstract. In this paper, we are concerned with the numerical modelling of the propagation of electromagnetic waves in dispersive materials for nanophotonics applications. We focus on a generalized model that allows for the description of a wide range of dispersive media. The underlying differential equations are recast into a generic form and we establish an existence and uniqueness result. We then turn to the numerical treatment and propose an appropriate Discontinuous Galerkin Time Domain framework. We obtain the semi-discrete convergence and prove the stability (and in a larger extent, convergence) of a Runge Kutta 4 fully discrete scheme via a technique relying on energy principles. Finally, we validate our approach through two significant nanophotonics test cases.

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confidence: 99%

Analysis of a Generalized Dispersive Model Coupled to a DGTD Method with Application to Nanophotonics

Lanteri

Scheid²,

Viquerat

2017

SIAM J. Sci. Comput.

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“…If it comes to electromagnetism, there are several "different" methods among scientists-for example see Bossavit (1988), Jiang (1998), Ciarlet Jr andZou (1999), Sadiku (2000), Hiptmair (2002), Bastos and Sadowski (2003), Monk (2003), (Demkowicz, 2006, Sect. 17), Gibson (2007), Li (2009), Gillette et al (2016), (Abali, 2016, Sect. 3)-and a consensus as to the "best" approach is yet missing. If one aims at solving electromagnetic fields E and B by satisfying Maxwell's equations, then FEM with standard elements cannot be used and there are various so-called mixed elements, see Arnold and Logg (2014), whose techniques are based on works of Raviart and Thomas (1977) and Nédélec (1980).…”

Section: Computational Approachmentioning

confidence: 99%

Theory and computation of electromagnetic fields and thermomechanical structure interaction for systems undergoing large deformations

Abali

Queiruga

2019

Journal of Computational Physics

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For an accurate description of electromagneto-thermomechanical systems, electromagnetic fields need to be described in a Eulerian frame, whereby the thermomechanics is solved in a Lagrangean frame. It is possible to map the Eulerian frame to the current placement of the matter and the Lagrangean frame to a reference placement. We present a rigorous and thermodynamically consistent derivation of governing equations for fully coupled electromagneto-thermomechanical systems properly handling finite deformations. A clear separation of the different frames is necessary. There are various attempts to formulate electromagnetism in the Lagrangean frame, or even to compute all fields in the current placement. Both formulations are challenging and heavily discussed in the literature. In this work, we propose another solution scheme that exploits the capabilities of advanced computational tools. Instead of amending the formulation, we can solve thermomechanics in the Lagrangean frame and electromagnetism in the Eulerian frame and manage the interaction between the fields. The approach is similar to its analog in fluid structure interaction, but more challenging because the field equations in electromagnetism must also be solved within the solid body while following their own different set of transformation rules. We additionally present a mesh-morphing algorithm necessary to accommodate finite deformations to solve the electromagnetic fields outside of the material body. We illustrate the use of the new formulation by developing an opensource implementation using the FEniCS package and applying this implementation to several engineering problems in electromagnetic structure interaction undergoing large deformations.

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“…The following lemma is useful for the error estimates of full-discrete scheme which can be found in [5,7,[9][10][11]22].…”

Section: The Fully-discrete Schemementioning

confidence: 99%

Nonconforming finite element approximation of time‐dependent Maxwell's equations in Debye medium

Shi

Yao

2014

Numerical Methods Partial

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In this article, a new nonconforming mixed finite element method (FEM) for approximating the Maxwell's equations with Debye medium in three-dimension are developed. By employing traditional variational formula, without adding "stability" or "penalty" terms, we show that the discrete scheme is robust. With the help of the element's typical properties, interpolation and derivative transfer skills, the convergence analysis is presented and error estimates for semidiscrete and leap-frog fully-discrete schemes are obtained, respectively. Numerical example shows the validity of the proposed method.

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Numerical convergence and physical fidelity analysis for Maxwell’s equations in metamaterials

Cited by 45 publications

References 30 publications

Analysis of a Generalized Dispersive Model Coupled to a DGTD Method with Application to Nanophotonics

Analysis of a Generalized Dispersive Model Coupled to a DGTD Method with Application to Nanophotonics

Theory and computation of electromagnetic fields and thermomechanical structure interaction for systems undergoing large deformations

Nonconforming finite element approximation of time‐dependent Maxwell's equations in Debye medium

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