X. Antoine - Academia.edu (original) (raw)
Papers by X. Antoine
Quelques applications de la diffraction multiple Retournement Temporel en milieu multi-diffusif... more Quelques applications de la diffraction multiple Retournement Temporel en milieu multi-diffusif Simulation de la propagation acoustique en milieu urbain (réduction de bruit) ... 4/28 ... 2 D, milieu homogène, non dissipatif, régime harmonique. ... On cherche l'onde diffractée u ...
Computer Physics Communications, 2016
We present an open finite element framework, called GetDDM, for testing optimized Schwarz domain ... more We present an open finite element framework, called GetDDM, for testing optimized Schwarz domain decomposition techniques for time-harmonic wave problems. After a review of Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver, along with ready-to-use examples for Helmholtz and Maxwell's equations, is freely available online for further testing.
This document presents the µ-diff Matlab toolbox that can be used for solving multiple scattering... more This document presents the µ-diff Matlab toolbox that can be used for solving multiple scattering problems by integral equations. The obstacles must be circular cylinders.
Journal of Computational Physics, 2015
This paper presents a new non-overlapping domain decomposition method for the time harmonic Maxwe... more This paper presents a new non-overlapping domain decomposition method for the time harmonic Maxwell's equations, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Magnetic-to-Electric operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented.
SIAM Journal on Applied Mathematics, 2008
A time harmonic far field model for closed electromagnetic time reversal mirrors is proposed. The... more A time harmonic far field model for closed electromagnetic time reversal mirrors is proposed. Then, a limit model corresponding to small perfectly conducting scatterers is derived. This asymptotic model is used to prove the selective focusing properties of the time reversal operator. In particular, a mathematical justification of the DORT method (Decomposition of the Time Reversal Operator method) is given for axially symmetric scatterers.
Computer Methods in Applied Mechanics and Engineering, 2013
The aim of this paper is to develop an analysis of the distribution of the eigenvalues of the aco... more The aim of this paper is to develop an analysis of the distribution of the eigenvalues of the acoustic single-layer potential for various low frequency two-dimensional multiple scattering problems. The obstacles are supposed to be distant (dilute media). In , it is shown that an approach based on the Gershgorin disks provides limited spectral information. We therefore introduce an alternative approach by applying the power iteration method to the limit matrix (associated with the zero order spatial modes) which results in satisfactory estimates. All these approximations are built for circular cylinders and formally extended to ellipses and rectangles for linear boundary element methods with non uniform meshes. This study is completed in by spectral estimates for the case of close obstacles.
Journal of Algorithms & Computational Technology, 2012
Efficient, robust and accurate algorithms are proposed for solving the multiple scattering proble... more Efficient, robust and accurate algorithms are proposed for solving the multiple scattering problem by M circular obstacles for the whole spectrum of frequency. The representation of the solution is based on an integral equation formulation next solved by using Fourier basis. Numerical examples are provided to show that the approaches are efficient.
Computer Physics Communications, 2015
Journal of Computational Acoustics, 2005
This study is devoted to some numerical issues in the boundary integral solution of the scatterin... more This study is devoted to some numerical issues in the boundary integral solution of the scattering of an acoustic wave by an open surface. More precisely, it deals with the construction of a cheap analytical preconditioner to enhance the iterative solving of this kind of equation. Detailed attention is paid to bring out the reasons that make this construction much more difficult than for closed surfaces. This preconditioner is carefully tested and compared to two more usual ones for twoand three-dimensional problems. It is shown that this preconditioner provides a cheap and efficient tool making reliable the iterative solving. The discussion also precisely brings out the issues where further studies are still needed to improve its efficiency.
Dans cet exposé, nous présenterons une nouvelle méthode de résolution du probl`eme de diffraction... more Dans cet exposé, nous présenterons une nouvelle méthode de résolution du probl`eme de diffraction mul-tiple par des cylindres circulaires, en particulier dans le cas o`u la longueur d'ondes est petite devant la taille caractéristique des cylindres. En effet, il est bien connu que ce ...
Journal of Mathematical Analysis and Applications, 1999
This paper addresses the extension of the Bayliss᎐Turkel second-order radiation condition to an a... more This paper addresses the extension of the Bayliss᎐Turkel second-order radiation condition to an arbitrarily shaped surface. The derivation is based mainly on the pseudo-differential calculus as well as on the introduction of a criterion providing a precise handling of the approximation process involved in the derivation of the radiation condition. The radiation condition then ranges among the most accurate of those of order two. As a by-product of the derivation, almost all known radiation conditions of order less than or equal to two are recovered and their respective accuracies are compared. ᮊ 1999 Academic Press
International Journal for Numerical Methods in Engineering, 2004
Since the advent of the fast multipole method, large-scale electromagnetic scattering problems ba... more Since the advent of the fast multipole method, large-scale electromagnetic scattering problems based on the electric field integral equation (EFIE) formulation are generally solved by a Krylov iterative solver. A well-known fact is that the dense complex non-hermitian linear system associated to the EFIE becomes ill-conditioned especially in the high-frequency regime. As a consequence, this slows down the convergence rate of Krylov subspace iterative solvers. In this work, a new analytic preconditioner based on the combination of a finite element method with a local absorbing boundary condition is proposed to improve the convergence of the iterative solver for an open boundary. Some numerical tests precise the behaviour of the new preconditioner. Moreover, comparisons are performed with the analytic preconditioner based on the Calderòn's relations for integral equations for several kinds of scatterers.
Lecture Notes in Computational Science and Engineering, 2005
The construction of accurate generalized impedance boundary conditions for the three-dimensional ... more The construction of accurate generalized impedance boundary conditions for the three-dimensional acoustic scattering problem by a homogeneous dissipative medium is analyzed. The technique relies on an explicit computation of the symbolic asymptotic expansion of the exact impedance operator in the interior domain. An efficient pseudolocalization of this operator based on Padé approximants is then proposed. The condition can be easily integrated in an iterative finite element solver without modifying its performances since the pseudolocal implementation preserves the sparse structure of the linear system. Numerical results are given to illustrate the method.
International Journal for Numerical Methods in Engineering, 2005
The present text deals with the numerical solution of two-dimensional high-frequency acoustic sca... more The present text deals with the numerical solution of two-dimensional high-frequency acoustic scattering problems using a new high-order and asymptotic Padé-type artificial boundary condition. The Padé-type condition is easy-to-implement in a Galerkin least-squares (iterative) finite element solver for arbitrarily convex-shaped boundaries. The method accuracy is investigated for different model problems and for the scattering problem by a submarine-shaped scatterer. As a result, relatively small computational domains, optimized according to the shape of the scatterer, can be considered while yielding accurate computations for high-frequencies.
Journal of Mathematical Analysis and Applications, 1999
This paper addresses the extension of the Bayliss᎐Turkel second-order radiation condition to an a... more This paper addresses the extension of the Bayliss᎐Turkel second-order radiation condition to an arbitrarily shaped surface. The derivation is based mainly on the pseudo-differential calculus as well as on the introduction of a criterion providing a precise handling of the approximation process involved in the derivation of the radiation condition. The radiation condition then ranges among the most accurate of those of order two. As a by-product of the derivation, almost all known radiation conditions of order less than or equal to two are recovered and their respective accuracies are compared. ᮊ 1999 Academic Press
SIAM Journal on Applied Mathematics, 2008
A time harmonic far field model for closed electromagnetic time reversal mirrors is proposed. The... more A time harmonic far field model for closed electromagnetic time reversal mirrors is proposed. Then, a limit model corresponding to small perfectly conducting scatterers is derived. This asymptotic model is used to prove the selective focusing properties of the time reversal operator. In particular, a mathematical justification of the DORT method (Decomposition of the Time Reversal Operator method) is given for axially symmetric scatterers.
International Journal for Numerical Methods in Engineering, 2002
This paper describes a new formulation to solve the acoustic scattering problem by a non-convex s... more This paper describes a new formulation to solve the acoustic scattering problem by a non-convex structure. The presented hybrid algorithms connect the on-surface radiation condition method to accel-erate the calculations with a two-dimensional finite element method to treat the ...
Computer Methods in Applied Mechanics and Engineering, 2006
In this paper, we consider the classical scattering problem of a time-harmonic acoustic or electr... more In this paper, we consider the classical scattering problem of a time-harmonic acoustic or electromagnetic wave by an obstacle. The problem can be formulated as a Helmholtz equation in an unbounded domain [13]. A number of different approaches have been developed to solve this ...
Journal of Computational Physics, 2014
This paper is devoted to the derivation of absorbing boundary conditions for the Klein-Gordon and... more This paper is devoted to the derivation of absorbing boundary conditions for the Klein-Gordon and Dirac equations modeling quantum and relativistic particles subject to classical electromagnetic fields. Microlocal analysis is the main ingredient in the derivation of these boundary conditions, which are obtained in the form of pseudodifferential equations. Basic numerical schemes are derived and analyzed to illustrate the accuracy of the derived boundary conditions.
Communications in Computational Physics, 2011
We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary S... more We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary Schrödinger equation with general (linear and nonlinear) potential. The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schrödinger equations. It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition. Finally, we give the extension of these ABCs to N-dimensional stationary Schrödinger equations.
Quelques applications de la diffraction multiple Retournement Temporel en milieu multi-diffusif... more Quelques applications de la diffraction multiple Retournement Temporel en milieu multi-diffusif Simulation de la propagation acoustique en milieu urbain (réduction de bruit) ... 4/28 ... 2 D, milieu homogène, non dissipatif, régime harmonique. ... On cherche l'onde diffractée u ...
Computer Physics Communications, 2016
We present an open finite element framework, called GetDDM, for testing optimized Schwarz domain ... more We present an open finite element framework, called GetDDM, for testing optimized Schwarz domain decomposition techniques for time-harmonic wave problems. After a review of Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver, along with ready-to-use examples for Helmholtz and Maxwell's equations, is freely available online for further testing.
This document presents the µ-diff Matlab toolbox that can be used for solving multiple scattering... more This document presents the µ-diff Matlab toolbox that can be used for solving multiple scattering problems by integral equations. The obstacles must be circular cylinders.
Journal of Computational Physics, 2015
This paper presents a new non-overlapping domain decomposition method for the time harmonic Maxwe... more This paper presents a new non-overlapping domain decomposition method for the time harmonic Maxwell's equations, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Magnetic-to-Electric operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented.
SIAM Journal on Applied Mathematics, 2008
A time harmonic far field model for closed electromagnetic time reversal mirrors is proposed. The... more A time harmonic far field model for closed electromagnetic time reversal mirrors is proposed. Then, a limit model corresponding to small perfectly conducting scatterers is derived. This asymptotic model is used to prove the selective focusing properties of the time reversal operator. In particular, a mathematical justification of the DORT method (Decomposition of the Time Reversal Operator method) is given for axially symmetric scatterers.
Computer Methods in Applied Mechanics and Engineering, 2013
The aim of this paper is to develop an analysis of the distribution of the eigenvalues of the aco... more The aim of this paper is to develop an analysis of the distribution of the eigenvalues of the acoustic single-layer potential for various low frequency two-dimensional multiple scattering problems. The obstacles are supposed to be distant (dilute media). In , it is shown that an approach based on the Gershgorin disks provides limited spectral information. We therefore introduce an alternative approach by applying the power iteration method to the limit matrix (associated with the zero order spatial modes) which results in satisfactory estimates. All these approximations are built for circular cylinders and formally extended to ellipses and rectangles for linear boundary element methods with non uniform meshes. This study is completed in by spectral estimates for the case of close obstacles.
Journal of Algorithms & Computational Technology, 2012
Efficient, robust and accurate algorithms are proposed for solving the multiple scattering proble... more Efficient, robust and accurate algorithms are proposed for solving the multiple scattering problem by M circular obstacles for the whole spectrum of frequency. The representation of the solution is based on an integral equation formulation next solved by using Fourier basis. Numerical examples are provided to show that the approaches are efficient.
Computer Physics Communications, 2015
Journal of Computational Acoustics, 2005
This study is devoted to some numerical issues in the boundary integral solution of the scatterin... more This study is devoted to some numerical issues in the boundary integral solution of the scattering of an acoustic wave by an open surface. More precisely, it deals with the construction of a cheap analytical preconditioner to enhance the iterative solving of this kind of equation. Detailed attention is paid to bring out the reasons that make this construction much more difficult than for closed surfaces. This preconditioner is carefully tested and compared to two more usual ones for twoand three-dimensional problems. It is shown that this preconditioner provides a cheap and efficient tool making reliable the iterative solving. The discussion also precisely brings out the issues where further studies are still needed to improve its efficiency.
Dans cet exposé, nous présenterons une nouvelle méthode de résolution du probl`eme de diffraction... more Dans cet exposé, nous présenterons une nouvelle méthode de résolution du probl`eme de diffraction mul-tiple par des cylindres circulaires, en particulier dans le cas o`u la longueur d'ondes est petite devant la taille caractéristique des cylindres. En effet, il est bien connu que ce ...
Journal of Mathematical Analysis and Applications, 1999
This paper addresses the extension of the Bayliss᎐Turkel second-order radiation condition to an a... more This paper addresses the extension of the Bayliss᎐Turkel second-order radiation condition to an arbitrarily shaped surface. The derivation is based mainly on the pseudo-differential calculus as well as on the introduction of a criterion providing a precise handling of the approximation process involved in the derivation of the radiation condition. The radiation condition then ranges among the most accurate of those of order two. As a by-product of the derivation, almost all known radiation conditions of order less than or equal to two are recovered and their respective accuracies are compared. ᮊ 1999 Academic Press
International Journal for Numerical Methods in Engineering, 2004
Since the advent of the fast multipole method, large-scale electromagnetic scattering problems ba... more Since the advent of the fast multipole method, large-scale electromagnetic scattering problems based on the electric field integral equation (EFIE) formulation are generally solved by a Krylov iterative solver. A well-known fact is that the dense complex non-hermitian linear system associated to the EFIE becomes ill-conditioned especially in the high-frequency regime. As a consequence, this slows down the convergence rate of Krylov subspace iterative solvers. In this work, a new analytic preconditioner based on the combination of a finite element method with a local absorbing boundary condition is proposed to improve the convergence of the iterative solver for an open boundary. Some numerical tests precise the behaviour of the new preconditioner. Moreover, comparisons are performed with the analytic preconditioner based on the Calderòn's relations for integral equations for several kinds of scatterers.
Lecture Notes in Computational Science and Engineering, 2005
The construction of accurate generalized impedance boundary conditions for the three-dimensional ... more The construction of accurate generalized impedance boundary conditions for the three-dimensional acoustic scattering problem by a homogeneous dissipative medium is analyzed. The technique relies on an explicit computation of the symbolic asymptotic expansion of the exact impedance operator in the interior domain. An efficient pseudolocalization of this operator based on Padé approximants is then proposed. The condition can be easily integrated in an iterative finite element solver without modifying its performances since the pseudolocal implementation preserves the sparse structure of the linear system. Numerical results are given to illustrate the method.
International Journal for Numerical Methods in Engineering, 2005
The present text deals with the numerical solution of two-dimensional high-frequency acoustic sca... more The present text deals with the numerical solution of two-dimensional high-frequency acoustic scattering problems using a new high-order and asymptotic Padé-type artificial boundary condition. The Padé-type condition is easy-to-implement in a Galerkin least-squares (iterative) finite element solver for arbitrarily convex-shaped boundaries. The method accuracy is investigated for different model problems and for the scattering problem by a submarine-shaped scatterer. As a result, relatively small computational domains, optimized according to the shape of the scatterer, can be considered while yielding accurate computations for high-frequencies.
Journal of Mathematical Analysis and Applications, 1999
This paper addresses the extension of the Bayliss᎐Turkel second-order radiation condition to an a... more This paper addresses the extension of the Bayliss᎐Turkel second-order radiation condition to an arbitrarily shaped surface. The derivation is based mainly on the pseudo-differential calculus as well as on the introduction of a criterion providing a precise handling of the approximation process involved in the derivation of the radiation condition. The radiation condition then ranges among the most accurate of those of order two. As a by-product of the derivation, almost all known radiation conditions of order less than or equal to two are recovered and their respective accuracies are compared. ᮊ 1999 Academic Press
SIAM Journal on Applied Mathematics, 2008
A time harmonic far field model for closed electromagnetic time reversal mirrors is proposed. The... more A time harmonic far field model for closed electromagnetic time reversal mirrors is proposed. Then, a limit model corresponding to small perfectly conducting scatterers is derived. This asymptotic model is used to prove the selective focusing properties of the time reversal operator. In particular, a mathematical justification of the DORT method (Decomposition of the Time Reversal Operator method) is given for axially symmetric scatterers.
International Journal for Numerical Methods in Engineering, 2002
This paper describes a new formulation to solve the acoustic scattering problem by a non-convex s... more This paper describes a new formulation to solve the acoustic scattering problem by a non-convex structure. The presented hybrid algorithms connect the on-surface radiation condition method to accel-erate the calculations with a two-dimensional finite element method to treat the ...
Computer Methods in Applied Mechanics and Engineering, 2006
In this paper, we consider the classical scattering problem of a time-harmonic acoustic or electr... more In this paper, we consider the classical scattering problem of a time-harmonic acoustic or electromagnetic wave by an obstacle. The problem can be formulated as a Helmholtz equation in an unbounded domain [13]. A number of different approaches have been developed to solve this ...
Journal of Computational Physics, 2014
This paper is devoted to the derivation of absorbing boundary conditions for the Klein-Gordon and... more This paper is devoted to the derivation of absorbing boundary conditions for the Klein-Gordon and Dirac equations modeling quantum and relativistic particles subject to classical electromagnetic fields. Microlocal analysis is the main ingredient in the derivation of these boundary conditions, which are obtained in the form of pseudodifferential equations. Basic numerical schemes are derived and analyzed to illustrate the accuracy of the derived boundary conditions.
Communications in Computational Physics, 2011
We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary S... more We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary Schrödinger equation with general (linear and nonlinear) potential. The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schrödinger equations. It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition. Finally, we give the extension of these ABCs to N-dimensional stationary Schrödinger equations.