High-order accurate thin layer approximations for time-domain electromagnetics, Part II: Transmission layers

Chun, Seok-Ju; Haddar, Houssem; Hesthaven, Jan S.

doi:10.1016/j.cam.2010.03.022

Cited by 13 publications

(23 citation statements)

References 4 publications

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“…The symbol [·] denotes the jump relative to the direction of n. Finally, the anisotropy inside the layer is assumed to be such that 8) where σ n m and σ τ m indicate respectively the transverse diffusion coefficient and tangential diffusion coefficient in the layer and τ represents the unit tangential vector. The important assumption we make in this paper (see (3.4) …”

Section: Geometrical Compartmentsmentioning

confidence: 99%

“…This ADTC couples volumetric diffusion equations with surface diffusion equations. We note that the natural expression of the second order transmission condition does not exhibit uniform time stability with respect to the layer thickness, but this well-known phenomenon for higher order asymptotic models can be corrected by the use of a Padé expansion, as in [8,14], and our ADTC is corrected in this way. Thus, in its final form, our ADTC has a mass-conservation property, which is important for dMRI modeling.…”

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confidence: 99%

“…To obtain asymptotic two-compartment models, we rely on a methodology based on classical scaled asymptotic expansions for thin structures (see [8,10,30]) and on an appropriate scaling of tangential and normal diffusion inside the myelin layer. This methodology has been extensively used to model thin coatings (see, e.g., [6,15] and references therein), rough boundaries (see, e.g., [1,19] and references therein) and imperfectly conducting obstacles (see, e.g., [16,17] and references therein).…”

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confidence: 99%

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New transmission condition accounting for diffusion anisotropy in thin layers applied to diffusion MRI

Caubet

Haddar

et al. 2017

ESAIM: M2AN

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Abstract. The Bloch−Torrey Partial Differential Equation (PDE) can be used to model the diffusion Magnetic Resonance Imaging (dMRI) signal in biological tissue. In this paper, we derive an Anisotropic Diffusion Transmission Condition (ADTC) for the Bloch−Torrey PDE that accounts for anisotropic diffusion inside thin layers. Such diffusion occurs, for example, in the myelin sheath surrounding the axons of neurons. This ADTC can be interpreted as an asymptotic model of order two with respect to the layer thickness and accounts for water diffusion in the normal direction that is low compared to the tangential direction. We prove uniform stability of the asymptotic model with respect to the layer thickness and a mass conservation property. We also prove the theoretical quadratic accuracy of the ADTC. Finally, numerical tests validate these results and show that our model gives a better approximation of the dMRI signal than a simple transmission condition that assumes isotropic diffusion in the layers.Mathematics Subject Classification. 35C20, 35Q92.

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Section: Geometrical Compartmentsmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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New transmission condition accounting for diffusion anisotropy in thin layers applied to diffusion MRI

Caubet

Haddar

et al. 2017

ESAIM: M2AN

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“…Chun et al have derived in [2] transmission conditions when the two boundaries Γ, Γ ε are not reduced to a single boundary. In this approach, the membrane is not meshed, and transmission conditions are set between Γ and Γ ε .…”

Section: Generalized Impedance Transmission Conditionsmentioning

confidence: 99%

“…• Chun model (using conditions (13) with α = 0.5) : this is the model obtained by Chun et al [2]. In this model, the membrane is not meshed, and the two boundaries Γ, Γ ε are distinct.…”

Section: Figure 2 Example Of Hexahedral Mesh Used For the Biologicalmentioning

confidence: 99%

Thin Layer Models for Electromagnetism

Duruflé

Péron

Poignard

2014

Commun. comput. phys.

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ABSTRACT. We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer. These models appear as first order approximations of the electromagnetic field. They are obtained thanks to a multiscale expansion of the exact solution with respect to the thickness of the thin layer, that makes possible to replace the thin layer by approximate conditions. We present the advantages and the drawbacks of several approximations together with numerical validations and simulations. The main motivation of this work concerns the computation of electromagnetic field in biological cells. The main difficulty to compute the local electric field lies in the thinness of the membrane and in the high contrast between the electrical conductivities of the cytoplasm and of the membrane, which provides a specific behavior of the electromagnetic field at low frequencies.

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Asymptotic expansion of steady-state potential in a high contrast medium with a thin resistive layer

Perrussel

Poignard

2013

Applied Mathematics and Computation

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High-order accurate thin layer approximations for time-domain electromagnetics, Part II: Transmission layers

Cited by 13 publications

References 4 publications

New transmission condition accounting for diffusion anisotropy in thin layers applied to diffusion MRI

New transmission condition accounting for diffusion anisotropy in thin layers applied to diffusion MRI

Thin Layer Models for Electromagnetism

Asymptotic expansion of steady-state potential in a high contrast medium with a thin resistive layer

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