American Journal of Computational and Applied Mathematics

American Journal of Computational and Applied Mathematics is a peer-reviewed international journal. This journal publishes significant research papers from all branches of applied mathematical and computational sciences. It publishes original papers of high scientific value in all areas of computational and applied mathematics.

Xavier Antoine

Editorial Board Member of American Journal of Computational and Applied Mathematics

Professor, Institut Elie Cartan Nancy, Universite H. Poincare, Vandoeuvre Les Nancy, France

Research Areas

Applied Mathematics, Computational Mathematics, Acoustic and Electromagnetic Waves, Simulation in Quantum

Education

1994-1997Ph.DUniversity de Pau, France

Experience

2005-presentFull Professor, Nancy Université, member of the INRIA CORIDA project team
2004-2005Visiting Associate Professor, Applied and Computational Mathematics, California Institute of Technology (CalTech), USA.
2004-2005Full time CNRS researcher, Applied and Computational Mathematics, California Institute of Technology (CalTech), USA.
2004Habilitation Thesis in Applied Mathematics, Toulouse Mathematics Institute, France
1998-2005Assistant Professor, Laboratoire de Mathématiques pour la Physique et l'Industrie, Toulouse, France

Publications: Journals

[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.
[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.
[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.
[4]  X. Antoine, H. Barucq and L. Vernhet, High-Frequency Asymptotic Analysis of a Dissipative Transmission Problem Resulting in Generalized Impedance Boundary Condition, Asymptotic Analysis 26 (3-4) (2001), pp. 257-283.
[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.
[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.
[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 181 (1) (2003), pp. 157-175.
[8]  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.
[9]  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.
[10]  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.
[11]  X. Antoine and M. Darbas, Alternative Integral Equations for the Iterative Solution of Acoustic Scattering Problems, Quarterly Journal of Mechanics and Applied Mathematics 58 (2005), pp. 107-128.
[12]  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.
[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.
[14]  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.
[15]  X. Antoine, C. Besse and S. Descombes, Artificial Boundary Conditions for Non-Linear Schrödinger Equations, SIAM Journal on Numerical Analysis 43 (6) (2006), pp. 2272-2293.
[16]  X. Antoine, M. Darbas and Y.Y. Lu, An Improved Surface Radiation Condition for High-Frequency Acoustic Scattering Problems, Computer Methods in Applied Mechanics and Engineering 195 (33-36) (2006), pp. 4060-4074.
[17]  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.
[18]  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.
[19]  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.
[20]  X. Antoine, A. Arnold, C. Besse, M. Ehrhardt, 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.
[21]  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.
[22]  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.
[23]  X. Antoine, Fractional Calculus and Non-Reflecting Boundary Conditions in Wave Propagation, Journal Européen des Systèmes Automatisés 42 (6-8) (2008), pp. 895-910.
[24]  X. Antoine, B. Pincon, K. Ramdani and B. Thierry, Far Field Modelling of Electromagnetic Time-Reversal and Application to Selective Focusing on Small Scatterers, SIAM Journal on Applied Mathematics 69 (3) (2008), pp. 830-844.
[25]  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.
[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.
[27]  X. Antoine and C. Geuzaine, Phase Reduction Models for Improving the Accuracy of the Finite Element Solution of Time-Harmonic Scattering Problems I: General Approach and Low-Order Models, Journal of Computational Physics 228 (8) (2009), pp. 3114-3136.
[28]  X. Antoine, C. Besse and J. Szeftel, Towards Accurate Artificial Boundary Conditions for Nonlinear PDEs, Cubo, A Mathematical Journal 11 (4) (2009), pp. 29-48.
[29]  X. Antoine, P. Dreyfuss and K. Ramdani, A Construction of Beam Propagation Methods for Optical Waveguides, Communications in Computational Physics 6 (3) (2009), pp. 565-576.
[30]  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.
[31]  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.
[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.
[33]  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.
[34]  Y. Boubendir, X. Antoine and C. Geuzaine, A Quasi-Optimal Non-Overlapping Domain Decomposition Methods for the Helmholtz Equation, to appear in Journal of Computational Physics (2011).
[35]  X. Antoine, K. Ramdani and B. Thierry, Wide frequency band numerical approaches for multiple scattering problems by disks, to appear in Journal of Algorithms & Computational Technologies 6 (2) (2012) (17 pages).

Publications: Books/Book Chapters

[1]  X. Antoine, Some Applications of the On-Surface Radiation Condition to the Integral Equations for Solving Electromagnetic Scattering Problems, in Industrial Mathematics and Statistics, Narosa Publishing House, J.C. Misra Editor, 2003, pp. 170-214 (ISBN: 8173194882).
[2]  X. Antoine, Advances in the On-Surface Radiation Condition Method: Theory, Numerics and Applications, in Computational Methods for Acoustics Problems, F. Magoulès Ed., Saxe-Coburg Editors, (2008), pp. 169-194 (ISBN: 978-1-874672-30-2).
[3]  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 and M. Darbas, Integral Equations and Iterative Schemes for Acoustic Scattering Problems, to appear (2011), 50 pages.