Papers by christian daveau
In this paper, we propose a new method to approximate operators resulted from solving the scatter... more In this paper, we propose a new method to approximate operators resulted from solving the scattering Problem in electromagnetism by dielectrically coated conducting bodies, using integral equations and high order impedance boundary condition. We introduce the variational Problem and we prove that it is well-posed, we present the new theoretical approach and highlight its potential through numerical experiments.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 1, 2007
We consider for the time-dependent Maxwell's equations the inverse problem of identifying locatio... more We consider for the time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the tangential component of the magnetic field on the boundary ( or a part of the boundary) of a domain.
arXiv (Cornell University), Dec 6, 2009
This paper is devoted to the identification of the unknown smooth coefficient c entering the hype... more This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation c(x)∂ 2 t u -∆u = 0 in a bounded smooth domain in R d from partial (on part of the boundary) dynamic boundary measurements. In this paper we prove that the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subset Γ of the boundary determines explicitly the coefficient c provided that c is known outside a bounded domain. Then, through construction of appropriate test functions by a geometrical control method, we derive a formula for calculating the coefficient c from the knowledge of the difference between the local Dirichlet to Neumann maps.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 12, 2019
In this paper, we consider the transmission problem for the Stokes system in three dimensional ca... more In this paper, we consider the transmission problem for the Stokes system in three dimensional case. The aim of this work is to derive the development of high order terms in the asymptotic expansion of the solution caused by a small boundary perturbation for an inclusion. The derivation is rigorous and proved by layer potential techniques.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 1, 2022
In the framework solving electromagnetic scattering problems with a Leontovich impedance boundary... more In the framework solving electromagnetic scattering problems with a Leontovich impedance boundary condition (LIBC), the numerical resolution requires the evaluation of singular integrals appearing in the discretization of the variational formulation. Our main interest is to pricisely evaluate these integrals. Thus, we propose an analytic method to approximate it. The performance of this method will be evaluated by calculating the radar cross section (RCS). Then, we compare RCS to the Mie series solution for the unit sphere in various configurations.
arXiv (Cornell University), Jun 10, 2015
This work concerns with the discontinuous Galerkin (DG) method for the time-dependent linear elas... more This work concerns with the discontinuous Galerkin (DG) method for the time-dependent linear elasticity problem. We derive the a posteriori error bounds for semi-discrete and fully discrete problems, by making use of the stationary elasticity reconstruction technique which allows to estimate the error for time-dependent problem through the error estimation of the associated stationary elasticity problem. To this end, to derive the error bound for the stationary problem, we present two methods to obtain two different a posteriori error bounds, by L 2 duality technique and via energy norm. For fully discrete scheme, we make use of the backward-Euler scheme and an appropriate space-time reconstruction. The technique here can be applicable for a variety of DG methods as well.
HAL (Le Centre pour la Communication Scientifique Directe), 2012
We consider for the full time-dependent Maxwell's equations the inverse problem of identifying lo... more We consider for the full time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic boundary measurements on the boundary for a finite time interval.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 7, 2022
In this paper, we study boundary element method with high order impedance boundary conditions (HO... more In this paper, we study boundary element method with high order impedance boundary conditions (HOIBC) to solve Maxwell's equations. The unknowns are electric and magnetic currents J and M. We propose several formulations and study the existence and uniqueness of the solution. Then, we discretize these formulations with a finite element method based on Lagrange elements. We give numerical tests of the HOIBC solution.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 1, 2022
The present paper introduces a surface formulation to solve the scattering problem for coated obj... more The present paper introduces a surface formulation to solve the scattering problem for coated objects using the integral method and a high order impedance boundary condition (HOIBC). We study the existence and uniqueness of the solution, and we propose a discretization of this formulation trough Rao-Wilton-Glisson functions (RWG). Numerical results are obtained with a 3D MoM code running on MPI clusters. The experiments show how the HOIBC significantly improves the accuracy of the results compared to computations using the standard impedance boundary condition (SIBC).
2022 Photonics & Electromagnetics Research Symposium (PIERS)
In this paper, we implement the high order boundary condition (HOIBC) in the integral equations t... more In this paper, we implement the high order boundary condition (HOIBC) in the integral equations to solve the scattering problem. We study the HOIBC operators that appear in the boundary integral equations and we propose a discretization of these operators in spaces H(div) and H(curl). Then, we give validations of the HOIBC by calculating the radar cross section (RCS), that show the improvement in accuracy over the standard impedance boundary condition (SIBC). The computation code implements the H-matrix approach with Adaptive Cross Approximation (ACA) and MPI parallelization.
ArXiv, 2021
In this paper, we propose some variational formulations with the use of high order impedance boun... more In this paper, we propose some variational formulations with the use of high order impedance boundary condition (HOIBC) to solve the scattering problem. We study the existence and uniqueness of the solution. Then, a discretization of these formulations is done. We give validations of the HOIBC obtained with a MoM code that show the improvement in accuracy over the standard impedance boundary condition (SIBC) computations.
arXiv: Mathematical Physics, 2017
We consider an inverse boundary value problem for the Maxwell's equations with a given data a... more We consider an inverse boundary value problem for the Maxwell's equations with a given data assumed to be known only in accessible part $\Gamma$ of the boundary. We aim to prove an uniqueness result using the Dirichlet to Neumann map with measurements limited to an open part of the boundary and we seek to reconstruct the complex refractive index $\emph{\textbf{n}}$ in the interior of a bounded domain Further, using the impedance map restricted to $\Gamma$, we may identify locations of small volume fraction perturbations of the refractive index.
arXiv: Mathematical Physics, 2017
We consider an inverse boundary value problem for the Maxwell equations with boundary data assume... more We consider an inverse boundary value problem for the Maxwell equations with boundary data assumed known only in accessible part $\Gamma$ of the boundary. We aim to prove a uniqueness result using the Dirichlet to Neumann data with measurements limited to an open part of the boundary and we seek to reconstruct the complex refractive index $n$ in the interior of a body. Further, using the impedance map restricted to $\Gamma$, we may identify locations of small volume fraction perturbations of the refractive index.
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2020
We present a new method for the explicit evaluation of single and double layers involved in a bou... more We present a new method for the explicit evaluation of single and double layers involved in a boundary element method to solve Maxwell's equations in the harmonic regime. This is an analytical method.
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2020
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Complex Variables and Elliptic Equations, 2019
In this paper, we consider the transmission problem for the Stokes system in three dimensional ca... more In this paper, we consider the transmission problem for the Stokes system in three dimensional case. The aim of this work is to derive the development of high-order terms in the asymptotic expansion of the solution caused by a small boundary perturbation for an inclusion. The derivation is rigorous and proved by layer potential techniques.
Mathematical Physics, Analysis and Geometry, 2017
We consider the Stokes eigenvalue problem in a bounded domain of R 3 with Dirichlet boundary cond... more We consider the Stokes eigenvalue problem in a bounded domain of R 3 with Dirichlet boundary conditions. The aim of this paper is to advance the development of high-order terms in the asymptotic expansions of the boundary perturbations of eigenvalues, eigenfunctions and eigenpressures for the Stokes operator caused by small perturbations of the boundary. Our derivation is rigorous and proved by layer potential techniques.
In this paper we determine a formula for calculating the refractive index ${\bf n}$ for the acous... more In this paper we determine a formula for calculating the refractive index ${\bf n}$ for the acoustic equation from the partial Dirichlet to Neumann map(DN) associated to ${\bf n}$. We apply these results to identify locations and values of small volume perturbations of this refractive index at fixed frequency $\omega$.
Methods and Applications of Analysis, 2010
We consider the inverse problem of reconstructing an unknown coefficient in a second order hyperb... more We consider the inverse problem of reconstructing an unknown coefficient in a second order hyperbolic equation from partial (on part of the boundary) dynamic boundary measurements. In this paper we prove that the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subset Γ of the boundary determines explicitly the coefficient c provided that c is known outside a bounded domain. Then, through construction of appropriate test functions by a geometrical control method, we derive a formula for calculating the coefficient c from the knowledge of the difference between the local Dirichlet to Neumann maps.
In this paper, a boundary integral method is used to solve an inverse linear heat conduction prob... more In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary measurements is considered. An algorithm is given by using the fundamental solution.
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Papers by christian daveau