Publications

1999-today

 
 

Copies of unpublished papers are available upon request

My publications via google scholar or ISI. Join me on ResearchGate


Book Chapters


[7] X. Antoine and R. Duboscq, Modeling and Computation of Bose-Einstein Condensates: Stationary States, Nucleation, Dynamics, Stochasticity, Lecture Notes in Mathematics/Physics, to appear (88 pages).


[6] X. Antoine and M. Darbas, Integral Equations and Iterative Schemes for Acoustic Scattering Problems, to appear (50 pages) (2014).


[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, pp.73-108, Bentham Science Publishers Ltd.,  2010 (eISBN: 978-1-60805-150-2, 2010).


[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",  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, 2010, pages 3-34.


[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).


Journals


[44] X. Antoine and R. Duboscq, GPELab, a Matlab Toolbox to Solve Gross-Pitaevskii Equations I: Computation of Stationary Solutions, Computer Physics Communications, to appear, 2014.


[43] M. El Bouajaji, X. Antoine, C. Geuzaine, Approximate Local Magnetic-to-Electric Surface Operators for Time-Harmonic Maxwell's Equations, Journal of Computational Physics, revised version submitted, 2014.


[42] X. Antoine, E. Lorin, A.D. Bandrauk, Domain Decomposition Methods and High-Order Absorbing Boundary Conditions for the Numerical Simulation of the Time Dependent Schrödinger Equation with Ionization and Recombination by Intense Electric Field, Journal of Scientific Computing, to appear, 2014.


[41] X. Antoine, E. Lorin, J. Sater, F. Fillion-Gourdeau, A.D. Bandrauk, Absorbing Boundary Conditions for Relativistic Quantum Mechanics Equations, Journal of Computational Physics, to appear, 2014.


[40] X. Antoine and R. Duboscq, Robust and Efficient Preconditioned Krylov Spectral Solvers for Computing the Ground States of Fast Rotating and Strongly Interacting Bose-Einstein Condensates, Journal of Computational Physics, 258 (1) (2014), pp. 509-523.


[39] X. Antoine, W. Bao and C. Besse, Computational Methods for the Dynamics of the Nonlinear Schrödinger/Gross-Pitaevskii Equations, (A Feature Article) Computer Physics Communications 184 (12), (2013), pp.2621-2633.


[38] X. Antoine, C. Besse and P. Klein, Absorbing Boundary Conditions for the Two-Dimensional Schrödinger Equation with an Exterior Potential. Part II: Discretization and Numerical Results, Numerische Mathematik (2013), pp.1-33.


[37] X. Antoine and B. Thierry, Spectral and Condition Number Estimates of the Acoustic Single-Layer Operator for Low-Frequency Multiple Scattering in Dense Media, Journal of Computational and Applied Mathematics 239 (2013), pp. 380-395.


[36] X. Antoine and B. Thierry, Spectral and Condition Number Estimates of the Acoustic Single-Layer Operator for Low-Frequency Multiple Scattering in Dilute Media, Computer Methods in Applied Mechanics and Engineering 265 (2013), pp.242-256.


[35] X. Antoine, K. Ramdani and B. Thierry, Wide Frequency Band Numerical Approaches for Multiple Scattering Problems by Disks, Journal of Algorithms & Computational Technologies 6 (2) (2012), pp. 241-261.


[34] X. Antoine, C. Besse and P. Klein, Absorbing Boundary Conditions for the Two-Dimensional Schrödinger Equation with an Exterior Potential. Part I: Construction and a priori Estimates, M3AS 22 (10) (2012), Article number: 1250026, 38 pages.


[33] Y. Boubendir, X. Antoine and C. Geuzaine, A Quasi-Optimal Non-Overlapping Domain Decomposition Algorithm for the Helmholtz Equation, Journal of Computational Physics 231 (2), (2012), pp.262-280.


[32] X. Antoine, C. Besse and P. Klein, Numerical Solution of Time-Dependent Nonlinear Schrödinger Equations Using Domain Truncation Techniques Coupled With Relaxation Scheme, Laser Physics 21 (8) (2011), pp.1-12.


[31] P. Klein, X. Antoine, C. Besse, M. Ehrhardt, Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities, Communications in Computational Physics 10 (5) (2011), pp.1280-1304.


[30] X. Antoine, C. Besse and P. Klein, Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations, SIAM Journal on Scientific Computing 33 (2) (2011), pp. 1008-1033.


[29] X. Antoine, Y. Huang and Y.Y. Lu, Computing High-Frequency Scattered Fields by Beam Propagation Methods: A Prospective Study, Journal of Algorithms & Computational Technologies 4 (2)  (2010), pp.147-166.


[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.


[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


[13] C. Geuzaine, B. Thierry, N. Marsic, D. Colignon, A. Vion, S. Tournier, Y.  Boubendir, M. El Bouajaji, X. Antoine, An Open Source Domain Decomposition Solver for Time-Harmonic Electromagnetic Wave Problems, IEEE Explore, to appear.


[12] Y. Boubendir, X. Antoine and C. Geuzaine, A Non-overlapping Quasi-optimal Optimized Schwarz Domain Decomposition Algorithm for the Helmholtz Equation, Domain Decomposition Methods in Science and Engineering XX, Lecture Notes in Computational Science and Engineering Volume 91, 2013, pp. 519-526.


[11] P. Klein, X. Antoine, C. Besse, M. Ehrhardt, Absorbing Boundary Conditions for Solving Stationary Schrödinger Equations, Proceedings of the 16th European Conference on Mathematics for Industry, July 26-30, 2010, Wuppertal, Germany, Editors A. Bartel, M. Brunk, M. Günther, S. Schöps and M. Striebel, Springer Verlag, Berlin, Heidelberg, 2011 (6 pages).


[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 Sér. 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.


CIMPA Lecture Notes