Copies of unpublished
papers are available upon request
Book Chapters
[6] X. Antoine and M.
Darbas, Integral Equations and Iterative Schemes for Acoustic
Scattering Problems, to appear (2010-2011).
[5] X. Antoine, C. Geuzaine
and K. Ramdani, Computational Methods for Multiple Scattering at High
Frequency with Applications to Periodic Structures Calculations, M.
Ehrhardt (Ed.), Wave Propagation in Periodic Media - Analysis,
Numerical Techniques and Practical Applications, Progress in
Computational Physics, Vol. 1, Bentham Science Publishers Ltd.,
2009.
[4] X. Antoine, C. Besse
and P. Klein, Open Boundary Conditions and Computational Schemes
for Schrödinger Equations with General Potentials and
Nonlinearities, in "Some Problems on Nonlinear Hyperbolic Equations and
Applications", The French-Chinese Summer Institute on Applied
Mathematics held at Fudan University, Shanghai, September 1-21, 2008.
Edited by Ta-Tsien Li, Yue-Jun Peng, Bopeng Peng. Series in
Contemporary Applied Mathematics, CAM15. Higher Education Press,
Beijing; World Scientific Publishing Co. Pte. Ltd., Singapore.
[3] X. Antoine, Advances in the On-Surface Radiation Condition Method:
Theory, Numerics and Applications, Book Chapter, Computational
Methods for Acoustics Problems, Editor F. Magoulès,
Saxe-Coburg Publications, 2008, pp. 169-194 (ISBN:
978-1-874672-30-2).
[2] X. Antoine and C. Besse, Artificial Boundary Conditions for
Schrödinger-type Equations and their Numerical Approximation, in
Advances in Scientific Computing and Applications, Y.Y. Lu, W.W. Sun
and T. Tang Ed., Science Press, Beijing/New York, 2004, pp. 8-21.
[1] X. Antoine, Some
Applications of the On-Surface Radiation Condition
to the Integral Equations for Solving Electromagnetic Scattering
Problems, Book Chapter, Industrial Mathematics and
Statistics,
Editor J.C. Misra, Narosa Publishing House, 2003, pp. 170-214 (ISBN:
8173194882).
Publications
[32] X. Antoine, C. Besse, M.
Ehrhardt and P. Klein, Modeling Boundary Conditions for the Stationary
Schrödinger Equation, submitted (2010).
[31] X. Antoine, K. Ramdani and B. Thierry, Wide Frequency Band
Numerical Approaches for Multiple Scattering Problems by Disk,
submitted (2010).
[30] X. Antoine, C. Besse and P. Klein, Absorbing Boundary Conditions for Schrödinger Equations, submitted (2010).
[29] X.
Antoine, Y. Huang and Y.Y. Lu, Computing
High-Frequency
Scattered Fields by Beam Propagation Methods: A Prospective Study, to
appear in Journal of Algorithms and Computational Technology, 2010.
[28] X. Antoine
and C.
Geuzaine, Phase Reduction Models for Improving the Accuracy of the
Finite Element Solution of Time-Harmonic Scattering Problems
I: General Theory and Low-Order
Models, Journal of Computational Physics 228 (8) (2009), pp. 3114-3136.
[27] X.
Antoine, P. Dreyfuss, K. Ramdani, A
Construction of Beam Propagation Methods for Optical
Waveguides, Communications in Computational Physics 6 (3) (2009), pp. 565-576. (submitted, 2008).
[26] R. Kerchroud, A. Soulaimani and X. Antoine, Performance Study of
Plane Wave Finite Element Methods with a Padé-Type
Artificial
Boundary Condition in Acoustic Scattering, Advances in Engineering Software 40 (2009), pp. 738-750.
[25] X. Antoine, C. Besse and J. Szeftel, Towards Accurate Artificial
Boundary Conditions for Nonlinear PDEs Through Examples, Cubo, A Mathematical Journal, 11 (4) (2009), pp. 29-48. (Open access online article.)
[24] X. Antoine, C. Besse and P. Klein, Absorbing Boundary Conditions
for the One-Dimensional Schrödinger Equation with an Exterior
Repulsive Potential, Journal of Computational Physics 228 (2) (2009), pp. 312-335.
[23] X. Antoine, B. Pinçon, K. Ramdani and B. Thierry, Far
Field
Modelling of Electromagnetic Time-Reversal and Applications to
Selective Focusing on Small Scatterers, SIAM Journal on Applied Mathematics 69 (3) (2008), pp. 830-844.
[22] X.
Antoine,
Fractional Calculus and Non-Reflecting Boundary Conditions in
Wave Propagation, Journal Européen des Systèmes
Automatisés 42 (6-8) (2008), pp. 895-910.
[21] X. Antoine and Y. Boubendir,
An Integral Preconditioner for
Solving the Two-Dimensional Scattering Transmission Problem using
Integral Equations, International Journal of Computer Mathematics 85 (10) (2008), pp. 1473-1490.
[20] C. Geuzaine, J. Bedrossian and X. Antoine,
An Amplitude
Formulation to Reduce the Pollution Error in the Finite Element
Solution of Time-Harmonic Scattering Problems, IEEE
Transactions on Magnetics 44 (6) (2008), pp. 782-785.
[19] X. Antoine, A.
Arnold, C. Besse, M. Ehrhardt and A. Schädle,
A Review of Transparent and Artificial Boundary Conditions Techniques
for Linear and Nonlinear Schrödinger
Equations, Communications in Computational Physics 4 (4) (2008), pp. 729-796 (Open access online article). (More
informations can be found here where
a free Matlab GUI is provided for comparing the
different boundary conditions).
[18] J. Yuan, Y.Y. Lu and X.
Antoine,
Modeling Photonic Crystals by
Boundary Integral Equations and Dirichlet-to-Neumann Maps, Journal of Computational Physics 227 (9) (2008), pp. 4617-4629.
[17] X. Antoine, C. Chniti and K. Ramdani,
On the Numerical
Approximation of High-Frequency Acoustic Multiple Scattering Problems
by Circular Cylinders, Journal of Computational
Physics 227 (3)
(2008), pp. 1754-1771.
[16] X. Antoine and M. Darbas, Generalized
Combined Field Integral
Equations for the Iterative Solution of the Three-Dimensional Helmholtz
Equation, Mathematical Modelling and Numerical Analysis 41
(1) (2007), pp. 147-167.
[15] X. Antoine, C. Besse and S. Descombes, Artificial
Boundary
Conditions for One-Dimensional Cubic Nonlinear Schrödinger
Equations,
SIAM Journal on Numerical Analysis 43 (6) (2006), pp. 2272-2293.
[14] X. Antoine, M. Darbas, and Y.Y. Lu, An
Improved Surface Radiation
Condition for High-Frequency Acoustics Scattering
Problems, Computer Methods in Applied Mechanics and
Engineering
195 (33-36) (2006), pp. 4060-4074.
[13] R. Kerchroud, X. Antoine and A. Soulaimani, Numerical
Accuracy of
a Padé-Type Non-Reflecting Boundary Condition for the Finite
Element Solution of Acoustic Scattering Problems at High-Frequency,
International Journal for Numerical Methods in Engineering 64 (10)
(2005), pp. 1275-1302.
[12] X. Antoine, A. Bendali and M. Darbas, Analytic
Preconditioners for
the Boundary Integral Solution of the Scattering of Acoustic Waves by
Open Surfaces, Journal of Computational Acoustics,
13
(3), (2005), pp. 477-498.
[11] X. Antoine and H. Barucq, Approximation
by Generalized Impedance
Boundary Conditions of a Transmission Problem in Acoustic Scattering,
Mathematical Modelling and Numerical Analysis 39 (5) (2005), pp.
1041-1059.
[10] X. Antoine and M. Darbas, Alternative
Integral Equations for the
Iterative Solution of Acoustic Scattering Problems, Quarterly
Journal of
Mechanics and Applied Mathematics 58 (1) (2005), pp. 107-128.
[9] X. Antoine, A. Bendali and M. Darbas,
Analytic Preconditioners for
the
Electric Field Integral Equation, International Journal for
Numerical
Methods in Engineering 61 (2004), pp. 1310-1331.
[8] X. Antoine, C. Besse and V. Mouysset, Numerical
Schemes for the
Simulation of the Two-Dimensional Schrödinger Equation using
Non-Reflecting Boundary Conditions, Mathematics of
Computation 73
(2004), pp. 1779-1799.
[7] X. Antoine and C. Besse, Unconditionally
Stable Discretization
Schemes of Non-Reflecting Boundary Conditions for the One-Dimensional
Schrödinger Equation, Journal of Computational
Physics 188 (1) (2003),
pp. 157-175.
[6] X. Antoine, An
Algorithm Coupling the OSRC and FEM for the
Computation of an Approximate Scattered Acoustic Field by a Non-convex
Body, International Journal for Numerical Methods in
Engineering 54 (7)
(2002), pp. 1021-1041.
[5] X. Antoine and C. Besse,
Construction, Structure and Asymptotic
Approximations of a Microdifferential Transparent Boundary Condition
for the Linear Schrödinger Equation, Journal de
Mathématiques
Pures et Appliquées 80 (7) (2001), pp. 701-738.
[4] X. Antoine, H. Barucq and L. Vernhet,
High-frequency Asymptotic
Analysis of a Dissipative Acoustic Transmission Problem Resulting in
Generalized Impedance Boundary Conditions, Asymptotic
Analysis 26 (3-4)
(2001), pp. 257-283.
[3] X. Antoine and H. Barucq, Microlocal
Diagonalization of Strictly
Hyperbolic Pseudodifferential Systems and Application to the Design of
Radiation Conditions in Electromagnetism, SIAM Journal on
Applied
Mathematics 61 (2001), pp. 1877-1905.
[2] X. Antoine, Fast
Approximate Computation of a Time-Harmonic
Scattered Field using the On-Surface Radiation Condition Method,
IMA
Journal of Applied Mathematics 66 (2001), pp. 83-110.
[1] X. Antoine, H. Barucq and A. Bendali, Bayliss-Turkel-like
Radiation
Condition on Surfaces of Arbitrary Shape, Journal of
Mathematical
Analysis and Applications 229 (1999), pp. 184-211.
Notes
[10] X. Antoine, A. Arnold, C.
Besse, M. Ehrhardt, A. Schädle, A Review of Artificial Boundary
Conditions for the Schrödinger Equation, PAMM Vol. 7, Issue 1, pp
1023201-1023202, Special Issue: Sixth International Congress on
Industrial Applied Mathematics (ICIAM 2007) and GAMM Annual Meeting,
Zurich 2007.
[9] X. Antoine, M. Darbas and Y.Y. Lu, An Improved On-Surface Radiation
Condition for Acoustic Scattering in the High-Frequency Spectrum, C. R.
Acad. Sci. Paris Ser. I 340 (2005), pp. 769-774.
[8] X. Antoine and H. Barucq,
On the Construction of Approximate
Boundary Conditions for Solving the Interior Problem of the Acoustic
Scattering Transmission Problem, in Domain Decomposition
Methods in
Science and Engineering, Springer Series: Lecture Notes in
Computational Science and Engineering, Vol. 40, R. Kornhuber, R. Hoppe,
J. Periaux, O. Pironneau, O. Widlund, J. Xu (Eds), 2005, pp. 133-140.
[7] X. Antoine and M. Lemou,
Wavelet Approximations of a Collision
Operator in Kinetic Theory, C. R. Acad. Sci. Paris, t. 337,
Série
I, pp. 353-358, 2003.
[6] X. Antoine and M. Darbas,
Generalized Brakhage-Werner Integral Formulations for the Iterative
Solution of Acoustics Scattering Problems, Mathematical and Numerical
Aspects of Wave Propagation, Waves 2003, G. Cohen, E. Heikkola, P.
Joly, P. Neittaanmaki, Editors, pp. 268-273, Springer-Verlag, 2003.
[5] X. Antoine, A. Bendali and M. Darbas, Study and Improvement of the
Condition Number of the Electric Field Integral Equation, in
Proceedings of the European Symposium on Numerical Methods in
Electromagnetics, 2002, pp. 233-238.
[4] X. Antoine and C. Besse, Quasi-analytic Determination of the
Dirichlet-to-Neumann Operator Associated to a Linear Schrödinger-type
Equation, Mathematical and Numerical Aspects of Wave Propagation, Ed.
A. Bermudez, D. Gomez, C. Hazard, P. Joly and J.E. Roberts, pp.891-895,
SIAM Editors, Philadelphia, 2000.
[3] X. Antoine, H. Barucq and L. Vernhet, Approximate Numerical
Solution of the Acoustic Scattering by a Penetrable Object Using
Impedance Boundary Conditions, Mathematical and Numerical Aspects of
Wave Propagation, Ed. A. Bermudez, D. Gomez, C. Hazard, P. Joly and
J.E. Roberts, pp.709-713, SIAM Editors, Philadelphia, 2000.
[2] X. Antoine et C. Besse, Etude Microlocale d'une Condition
Transparente pour l'Equation de Schrödinger Linéaire, C. R. Acad. Sci.
Paris, t. 331, Série I, pp. 359-364, 2000.
[1] X. Antoine, A Numerical Study of a Scattering Problem Involving a
Generalized Impedance Boundary Condition using the On-Surface Radiation
Condition Method, Mathematical and Numerical Aspects of Wave
Propagation, Ed. by J. DoSanto, pp. 287-291, SIAM Editors,
Philadelphia, 1998.