Microlocal Diagonalization of Strictly Hyperbolic Pseudodifferential Systems and Application to the Design of Radiation Conditions in Electromagnetism. - Xavier Antoine; Helene Barucq (SIAM J. Appl. Math., 2001)

Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions. - Xavier Antoine; Christophe Besse; Vincent Mouysset (Math. Comput., 2004)

Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations. - Xavier Antoine; Christophe Besse; Stéphane Descombes (SIAM J. Numer. Anal., 2006)

An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations. - Xavier Antoine; Yassine Boubendir (Int. J. Comput. Math., 2008)

On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders. - Xavier Antoine; Chokri Chniti; Karim Ramdani (J. Comput. Phys., 2008)

Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps. - Jianhua Yuan; Ya Yan Lu; Xavier Antoine (J. Comput. Phys., 2008)

Far Field Modeling of Electromagnetic Time Reversal and Application to Selective Focusing on Small Scatterers. - Xavier Antoine; B. Pinçon; Karim Ramdani; Bertrand Thierry (SIAM J. Appl. Math., 2008)

A performance study of plane wave finite element methods with a Padé-type artificial boundary condition in acoustic scattering. - Riyad Kechroud; Azzeddine Soulaïmani; Xavier Antoine (Adv. Eng. Softw., 2009)

Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential. - Xavier Antoine; Christophe Besse; Pauline Klein (J. Comput. Phys., 2009)

Phase reduction models for improving the accuracy of the finite element solution of time-harmonic scattering problems I: General approach and low-order models. - Xavier Antoine; Christophe Geuzaine (J. Comput. Phys., 2009)

Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations. - Xavier Antoine; Christophe Besse; Pauline Klein (SIAM J. Sci. Comput., 2011)

A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation. - Yassine Boubendir; Xavier Antoine; Christophe Geuzaine (J. Comput. Phys., 2012)

Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations. - Xavier Antoine; Weizhu Bao; Christophe Besse (Comput. Phys. Commun., 2013)

Spectral and condition number estimates of the acoustic single-layer operator for low-frequency multiple scattering in dense media. - Bertrand Thierry; Xavier Antoine (J. Comput. Appl. Math., 2013)

Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. - Xavier Antoine; Christophe Besse; Pauline Klein (Numerische Mathematik, 2013)

A Non-overlapping Quasi-optimal Optimized Schwarz Domain Decomposition Algorithm for the Helmholtz Equation. - Yassine Boubendir; Xavier Antoine; Christophe Geuzaine (Domain Decomposition Methods in Science and Engineering XX, 2013)

GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations I: Computation of stationary solutions. - Xavier Antoine; Romain Duboscq (Comput. Phys. Commun., 2014)

Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates. - Xavier Antoine; Romain Duboscq (J. Comput. Phys., 2014)

Absorbing boundary conditions for relativistic quantum mechanics equations. - Xavier Antoine; Emmanuel Lorin; J. Sater; François Fillion-Gourdeau; André D. Bandrauk (J. Comput. Phys., 2014)

Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations. - Mohamed El Bouajaji; Xavier Antoine; Christophe Geuzaine (J. Comput. Phys., 2014)

GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: Dynamics and stochastic simulations. - Xavier Antoine; Romain Duboscq (Comput. Phys. Commun., 2015)

μ-diff: An open-source Matlab toolbox for computing multiple scattering problems by disks. - Bertrand Thierry; Xavier Antoine; Chokri Chniti; Hasan Alzubaidi (Comput. Phys. Commun., 2015)

A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations. - Mohamed El Bouajaji; Bertrand Thierry; Xavier Antoine; Christophe Geuzaine (J. Comput. Phys., 2015)

Domain Decomposition Method and High-Order Absorbing Boundary Conditions for the Numerical Simulation of the Time Dependent Schrödinger Equation with Ionization and Recombination by Intense Electric Field. - Xavier Antoine; Emmanuel Lorin; André D. Bandrauk (J. Sci. Comput., 2015)

Formulation and accuracy of On-Surface Radiation Conditions for acoustic multiple scattering problems. - Hasan Alzubaidi; Xavier Antoine; Chokri Chniti (Appl. Math. Comput., 2016)

Lagrange-Schwarz Waveform Relaxation domain decomposition methods for linear and nonlinear quantum wave problems. - Xavier Antoine; Emmanuel Lorin (Appl. Math. Lett., 2016)

Isogeometric finite element analysis of time-harmonic exterior acoustic scattering problems. - Tahsin Khajah; Xavier Antoine; Stéphane P. A. Bordas (CoRR, 2016)

GetDDM: An open framework for testing optimized Schwarz methods for time-harmonic wave problems. - Bertrand Thierry; Alexandre Vion; Simon Tournier; Mohamed El Bouajaji; David Colignon; Nicolas Marsic; Xavier Antoine; Christophe Geuzaine (Comput. Phys. Commun., 2016)

High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations. - Xavier Antoine; Christophe Besse; Vittorio Rispoli (J. Comput. Phys., 2016)

On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions. - Xavier Antoine; Qinglin Tang; Yong Zhang 005 (J. Comput. Phys., 2016)

Frozen Gaussian approximation based domain decomposition methods for the linear Schrödinger equation beyond the semi-classical regime. - Emmanuel Lorin; Xu Yang 018; Xavier Antoine (J. Comput. Phys., 2016)

Acceleration of the imaginary time method for spectrally computing the stationary states of Gross-Pitaevskii equations. - Xavier Antoine; Christophe Besse; Romain Duboscq; Vittorio Rispoli (Comput. Phys. Commun., 2017)

Computational performance of simple and efficient sequential and parallel Dirac equation solvers. - Xavier Antoine; Emmanuel Lorin (Comput. Phys. Commun., 2017)

Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods. - Xavier Antoine; Antoine Levitt; Qinglin Tang (J. Comput. Phys., 2017)

An analysis of Schwarz waveform relaxation domain decomposition methods for the imaginary-time linear Schrödinger and Gross-Pitaevskii equations. - Xavier Antoine; Emmanuel Lorin (Numerische Mathematik, 2017)

Multilevel preconditioning technique for Schwarz waveform relaxation domain decomposition method for real- and imaginary-time nonlinear Schrödinger equation. - Xavier Antoine; Emmanuel Lorin (Appl. Math. Comput., 2018)

Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains. - Songsong Ji; Yibo Yang; Gang Pang; Xavier Antoine (Comput. Phys. Commun., 2018)

On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross-Pitaevskii equations. - Xavier Antoine; Qinglin Tang; Jiwei Zhang 002 (Int. J. Comput. Math., 2018)

Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces. - Xavier Antoine; François Fillion-Gourdeau; Emmanuel Lorin; Steve McLean (CoRR, 2019)

On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrödinger equation. - Xavier Antoine; Emmanuel Lorin (J. Comput. Appl. Math., 2019)

Towards Perfectly Matched Layers for time-dependent space fractional PDEs. - Xavier Antoine; Emmanuel Lorin (J. Comput. Phys., 2019)

A simple pseudospectral method for the computation of the time-dependent Dirac equation with Perfectly Matched Layers. - Xavier Antoine; Emmanuel Lorin (J. Comput. Phys., 2019)

Perfectly matched layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates. - Xavier Antoine; Christophe Geuzaine; Qinglin Tang (Commun. Nonlinear Sci. Numer. Simul., 2020)

Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces. - Xavier Antoine; François Fillion-Gourdeau; Emmanuel Lorin; Steve MacLean (J. Comput. Phys., 2020)

Optimized weak coupling of boundary element and finite element methods for acoustic scattering. - Boris Caudron; Xavier Antoine; Christophe Geuzaine (J. Comput. Phys., 2020)

Corner treatments for high-order local absorbing boundary conditions in high-frequency acoustic scattering. - Axel Modave; Christophe Geuzaine; Xavier Antoine (J. Comput. Phys., 2020)

Pseudodifferential adiabatic mode parabolic equations in curvilinear coordinates and their numerical solution. - Pavel S. Petrov; Xavier Antoine (J. Comput. Phys., 2020)

BEC2HPC: A HPC spectral solver for nonlinear Schrödinger and rotating Gross-Pitaevskii equations. Stationary states computation. - Jérémie Gaidamour; Qinglin Tang; Xavier Antoine (Comput. Phys. Commun., 2021)

Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations. - Xavier Antoine; Jie Shen 001; Qinglin Tang (J. Comput. Phys., 2021)

Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation. - Songsong Ji; Gang Pang; Xavier Antoine; Jiwei Zhang 002 (J. Comput. Phys., 2021)

Stable Perfectly Matched Layers with Lorentz transformation for the convected Helmholtz equation. - Philippe Marchner; Hadrien Bériot; Xavier Antoine; Christophe Geuzaine (J. Comput. Phys., 2021)

Stability and convergence analysis of artificial boundary conditions for the Schrödinger equation on a rectangular domain. - Gang Pang; Yibo Yang; Xavier Antoine; Shaoqiang Tang (Math. Comput., 2021)

Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers. - Xavier Antoine; Emmanuel Lorin; Y. Zhang (Numer. Algorithms, 2021)

ODE-based double-preconditioning for solving linear systems A α x = b and f ( A ) x = b. - Xavier Antoine; Emmanuel Lorin (Numer. Linear Algebra Appl., 2021)

Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes. - Xavier Antoine; Xiaofei Zhao (J. Comput. Phys., 2022)

Accurate absorbing boundary conditions for two-dimensional peridynamics. - Gang Pang; Songsong Ji; Xavier Antoine (J. Comput. Phys., 2022)

Generalized Fractional Algebraic Linear System Solvers. - Xavier Antoine; Emmanuel Lorin (J. Sci. Comput., 2022)

Construction and Numerical Assessment of Local Absorbing Boundary Conditions for Heterogeneous Time-Harmonic Acoustic Problems. - Philippe Marchner; Xavier Antoine; Christophe Geuzaine; Hadrien Bériot (SIAM J. Appl. Math., 2022)

A Well-Conditioned Weak Coupling of Boundary Element and High-Order Finite Element Methods for Time-Harmonic Electromagnetic Scattering by Inhomogeneous Objects. - Ismaïl Badia; Boris Caudron; Xavier Antoine; Christophe Geuzaine (SIAM J. Sci. Comput., 2022)

A MultiHarmonic Finite Element Method for Scattering Problems with Small-Amplitude Boundary Deformations. - David Gasperini; Hans-Peter Biese; Udo Schröder; Xavier Antoine; Christophe Geuzaine (SIAM J. Sci. Comput., 2022)

Adaptation and assessement of projected Nesterov accelerated gradient flow to compute stationary states of nonlinear Schrödinger equations. - Xavier Antoine; Chorouq Bentayaa; Jérémie Gaidamour (Int. J. Comput. Math., 2024)

Normalized fractional gradient flow for nonlinear Schrödinger/Gross-Pitaevskii equations. - Xavier Antoine; Jérémie Gaidamour; Emmanuel Lorin (Commun. Nonlinear Sci. Numer. Simul., 2024)

Construction and analysis of discretization schemes for one-dimensional nonlocal Schrödinger equations with exact absorbing boundary conditions. - Gang Pang; Songsong Ji; Xavier Antoine (J. Comput. Appl. Math., 2024)

A Domain Decomposition Solver for Large Scale Time-Harmonic Flow Acoustics Problems. - Philippe Marchner; Hadrien Bériot; S. Le Bras; Xavier Antoine; Christophe Geuzaine (SIAM J. Sci. Comput., 2025)