Time-harmonic Maxwell equations in biological cells. The differential form formalism to treat the thin layer
DURUFLÉ, Marc
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
PÉRON, Victor
Institut de Mathématiques de Bordeaux [IMB]
Advanced 3D Numerical Modeling in Geophysics [Magique 3D]
Institut de Mathématiques de Bordeaux [IMB]
Advanced 3D Numerical Modeling in Geophysics [Magique 3D]
DURUFLÉ, Marc
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
PÉRON, Victor
Institut de Mathématiques de Bordeaux [IMB]
Advanced 3D Numerical Modeling in Geophysics [Magique 3D]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Advanced 3D Numerical Modeling in Geophysics [Magique 3D]
Language
en
Article de revue
This item was published in
Confluentes Mathematici. 2011, vol. 3, n° 2, p. 325-357
Institut Camille Jordan et Unité de Mathématiques Pures et Appliquées
English Abstract
We study the behavior of the electromagnetic field in a biological cell modelled by a medium surrounded by a thin layer and embedded in an ambient medium. We derive approximate transmission conditions in order to replace ...Read more >
We study the behavior of the electromagnetic field in a biological cell modelled by a medium surrounded by a thin layer and embedded in an ambient medium. We derive approximate transmission conditions in order to replace the membrane by these conditions on the boundary of the interior domain. Our approach is essentially geometric and based on a suitable change of variables in the thin layer. Few notions of differential calculus are given in order to obtain the first order conditions in a simple way, and numerical simulations validate the theoretical results. Asymptotic transmission conditions at any order are given in the last section of the paper.Read less <
English Keywords
asymptotic expansion
time-harmonic Maxwell's equations
differential forms on manifolds
finite element method
edge elements
Origin
Hal imported