Edit Profile (opens in new tab) Antoine, Xavier Compute Distance To: Compute Author ID: antoine.xavier Published as: Antoine, Xavier; Antoine, X. External Links: MGP · ORCID Documents Indexed: 100 Publications since 1998 Reviewing Activity: 97 Reviews Co-Authors: 67 Co-Authors with 95 Joint Publications 1,187 Co-Co-Authors all top 5 Co-Authors 4 single-authored 19 Besse, Christophe 16 Lorin, Emmanuel 15 Geuzaine, Christophe A. 8 Darbas, Marion 7 Barucq, Hélène 7 Klein, Pauline 7 Thierry, Bertrand 6 Tang, Qinglin 5 Duboscq, Romain 4 Bendali, Abderrahmane 4 Lu, Ya Yan 4 Ramdani, Karim 3 Bériot, Hadrien 3 Chniti, Chokri 3 Ehrhardt, Matthias 3 El Bouajaji, Mohamed 3 Marchner, Philippe 3 Vernhet, Laurent 3 Zhang, Jiwei 3 Zhang, Yong 2 Alzubaidi, Hasan 2 Bandrauk, André D. 2 Boubendir, Yassine 2 Fillion-Gourdeau, François 2 Gasperini, David 2 Kechroud, Riyad 2 Khajah, Tahsin 2 Modave, Axel 2 Pang, Gang 2 Rispoli, Vittorio 2 Schröder, Udo 2 Soulaimani, Azzeddine 1 Amalberti, Julien 1 Arnold, Anton 1 Bao, Weizhu 1 Beise, Hans-Peter 1 Biese, Hans-Peter 1 Bordas, Stéphane Pierre Alain 1 Burnard, Pete 1 Caudron, B. 1 Colignon, D. 1 Descombes, Stéphane 1 Dreyfuss, Pierre 1 Dsouza, Shaima M. 1 Gabard, Gwénaël 1 Hou, Fengji 1 Huang, Yuexia 1 Ji, Songsong 1 Lemou, Mohammed 1 Levitt, Antoine 1 Li, Dongfang 1 Lieu, Alice 1 MacLean, Steve 1 Marsic, N. 1 Mouysset, Vincent 1 Natarajan, Sundararajan 1 Petrov, Pavel S. 1 Pinçon, Bruno 1 Sater, J. 1 Schädle, Achim 1 Szeftel, Jérémie 1 Tang, Shaoqiang 1 Tournier, Simon 1 Vion, Alexandre 1 Yang, Xu 1 Yang, Yibo 1 Yuan, Jianhua all top 5 Serials 24 Journal of Computational Physics 7 Computer Physics Communications 6 Communications in Computational Physics 5 Computer Methods in Applied Mechanics and Engineering 3 International Journal for Numerical Methods in Engineering 3 SIAM Journal on Applied Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Mathematics of Computation 2 Applied Mathematics and Computation 2 Journal of Computational and Applied Mathematics 2 Numerische Mathematik 2 Journal of Scientific Computing 2 International Journal of Computer Mathematics 2 SIAM Journal on Scientific Computing 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Algorithms & Computational Technology 1 IMA Journal of Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Quarterly Journal of Mechanics and Applied Mathematics 1 Wave Motion 1 SIAM Journal on Numerical Analysis 1 Applied Mathematics Letters 1 Asymptotic Analysis 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Numerical Algorithms 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Advances in Engineering Software 1 Numerical Linear Algebra with Applications 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Mathematical and Computer Modelling of Dynamical Systems 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Computational Acoustics 1 Cubo 1 Mathematical Geosciences all top 5 Fields 65 Numerical analysis (65-XX) 62 Partial differential equations (35-XX) 25 Optics, electromagnetic theory (78-XX) 17 Fluid mechanics (76-XX) 13 Quantum theory (81-XX) 9 Operator theory (47-XX) 5 Statistical mechanics, structure of matter (82-XX) 2 Real functions (26-XX) 2 Integral equations (45-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of deformable solids (74-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 80 Publications have been cited 1,165 times in 561 Documents Cited by ▼ Year ▼ Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations. Zbl 1344.35130Antoine, Xavier; Bao, Weizhu; Besse, Christophe 107 2013 A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations. Zbl 1364.65178Antoine, Xavier; Arnold, Anton; Besse, Christophe; Ehrhardt, Matthias; Schadle, Achim 107 2008 Bayliss-Turkel-like radiation conditions on surfaces of arbitrary shape. Zbl 0923.35179Antoine, X.; Barucq, H.; Bendali, A. 71 1999 A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation. Zbl 1243.65144Boubendir, Y.; Antoine, X.; Geuzaine, C. 55 2012 Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation. Zbl 1037.65097Antoine, X.; Besse, C. 53 2003 Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions. Zbl 1053.65072Antoine, Xavier; Besse, Christophe; Mouysset, Vincent 42 2004 Alternative integral equations for the iterative solution of acoustic scattering problems. Zbl 1064.76095Antoine, X.; Darbas, M. 40 2005 Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation. Zbl 1123.65117Antoine, Xavier; Darbas, Marion 36 2007 Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations. Zbl 1109.35102Antoine, Xavier; Besse, Christophe; Descombes, Stephane 33 2006 Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates. Zbl 1349.82027Antoine, Xavier; Duboscq, Romain 33 2014 An improved surface radiation condition for high-frequency acoustic scattering problems. Zbl 1120.76058Antoine, Xavier; Darbas, Marion; Lu, Ya Yan 31 2006 Absorbing boundary conditions for general nonlinear Schrödinger equations. Zbl 1231.35223Antoine, Xavier; Besse, Christophe; Klein, Pauline 26 2011 Fast approximate computation of a time-harmonic scattered field using the on-surface radiation condition method. Zbl 1001.78008Antoine, Xavier 25 2001 GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. I: Computation of stationary solutions. Zbl 1348.35003Antoine, Xavier; Duboscq, Romain 25 2014 Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods. Zbl 1380.81496Antoine, Xavier; Levitt, Antoine; Tang, Qinglin 24 2017 Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential. Zbl 1161.65074Antoine, Xavier; Besse, Christophe; Klein, Pauline 24 2009 Construction, structure and asymptotic approximations of a microdifferential transparent boundary condition for the linear Schrödinger equation. Zbl 1129.35324Antoine, Xavier; Besse, Christophe 22 2001 On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders. Zbl 1135.65403Antoine, Xavier; Chniti, Chokri; Ramdani, Karim 19 2008 Modeling and computation of Bose-Einstein condensates: stationary states, nucleation, dynamics, stochasticity. Zbl 1344.35114Antoine, Xavier; Duboscq, Romain 18 2015 A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell’s equations. Zbl 1349.78066El Bouajaji, M.; Thierry, B.; Antoine, X.; Geuzaine, C. 18 2015 On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions. Zbl 1380.65296Antoine, Xavier; Tang, Qinglin; Zhang, Yong 17 2016 Analytic preconditioners for the boundary integral solution of the scattering of acoustic waves by open surfaces. Zbl 1189.76356Antoine, Xavier; Bendali, Abderrahmane; Darbas, Marion 16 2005 Numerical accuracy of a Padé-type non-reflecting boundary condition for the finite element solution of acoustic scattering problems at high-frequency. Zbl 1113.76051Kechroud, R.; Antoine, X.; Soulaïmani, A. 16 2005 Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell’s equations. Zbl 1351.78010El Bouajaji, M.; Antoine, X.; Geuzaine, C. 16 2014 GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. II: Dynamics and stochastic simulations. Zbl 1344.82004Antoine, Xavier; Duboscq, Romain 15 2015 Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. I: Construction and a priori estimates. Zbl 1251.35096Antoine, Xavier; Besse, Christophe; Klein, Pauline 15 2012 Microlocal diagonalization of strictly hyperbolic pseudodifferential systems and application to the design of radiation conditions in electromagnetism. Zbl 0983.35138Antoine, Xavier 14 2001 Analytic preconditioners for the electric field integral equation. Zbl 1210.65193Antoine, X.; Bendali, A.; Darbas, M. 13 2004 Absorbing boundary conditions for relativistic quantum mechanics equations. Zbl 1349.81080Antoine, X.; Lorin, E.; Sater, J.; Fillion-Gourdeau, F.; Bandrauk, A. D. 13 2014 Computational performance of simple and efficient sequential and parallel Dirac equation solvers. Zbl 1411.35234Antoine, X.; Lorin, E. 12 2017 Corner treatments for high-order local absorbing boundary conditions in high-frequency acoustic scattering. Zbl 1453.65340Modave, A.; Geuzaine, C.; Antoine, X. 11 2020 An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations. Zbl 1168.78001Antoine, X.; Boubendir, Y. 10 2008 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. Zbl 1332.78026Antoine, X.; Lorin, E.; Bandrauk, A. D. 10 2015 Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. II: Discretization and numerical results. Zbl 1457.65093Antoine, Xavier; Besse, Christophe; Klein, Pauline 10 2013 High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations. Zbl 1422.65277Antoine, Xavier; Besse, Christophe; Rispoli, Vittorio 9 2016 GetDDM: an open framework for testing optimized Schwarz methods for time-harmonic wave problems. Zbl 1380.65477Thierry, B.; Vion, A.; Tournier, S.; El Bouajaji, M.; Colignon, D.; Marsic, N.; Antoine, X.; Geuzaine, C. 9 2016 Towards accurate artificial boundary conditions for nonlinear PDEs through examples. Zbl 1184.35014Antoine, Xavier; Besse, Christophe; Szeftel, Jérémie 9 2009 A non-overlapping domain decomposition method with high-order transmission conditions and cross-point treatment for Helmholtz problems. Zbl 07337986Modave, A.; Royer, A.; Antoine, X.; Geuzaine, C. 9 2020 High-frequency asymptotic analysis of a dissipative transmission problem resulting in generalized impedance boundary conditions. Zbl 0986.76080Antoine, X.; Barucq, H.; Vernhet, L. 7 2001 Wide frequency band numerical approaches for multiple scattering problems by disks. Zbl 1280.78002Antoine, Xavier; Ramdani, Karim; Thierry, Bertrand 7 2012 Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering. Zbl 1074.78004Antoine, Xavier; Barucq, Hélène 6 2005 Formulation and accuracy of on-surface radiation conditions for acoustic multiple scattering problems. Zbl 1410.78010Alzubaidi, Hasan; Antoine, Xavier; Chniti, Chokri 5 2016 \(\mu\)-diff: an open-source Matlab toolbox for computing multiple scattering problems by disks. Zbl 1380.65478Thierry, Bertrand; Antoine, Xavier; Chniti, Chokri; Alzubaidi, Hasan 5 2015 An analysis of Schwarz waveform relaxation domain decomposition methods for the imaginary-time linear Schrödinger and Gross-Pitaevskii equations. Zbl 1383.65122Antoine, X.; Lorin, E. 5 2017 On the construction of approximate boundary conditions for solving the interior problem of the acoustic scattering transmission problem. Zbl 1152.76466Antoine, X.; Barucq, H. 5 2005 Computing high-frequency scattered fields by beam propagation methods: a prospective study. Zbl 1210.78015Antoine, Xavier; Huang, Yuexia; Lu, Ya Yan 5 2010 Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps. Zbl 1143.78012Yuan, Jianhua; Lu, Ya Yan; Antoine, Xavier 5 2008 Frozen Gaussian approximation based domain decomposition methods for the linear Schrödinger equation beyond the semi-classical regime. Zbl 1349.65430Lorin, E.; Yang, X.; Antoine, X. 5 2016 Lagrange-Schwarz waveform relaxation domain decomposition methods for linear and nonlinear quantum wave problems. Zbl 1334.65152Antoine, X.; Lorin, E. 5 2016 Perfectly matched layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates. Zbl 1453.65353Antoine, Xavier; Geuzaine, Christophe; Tang, Qinglin 4 2020 Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves. Zbl 1407.65152Antoine, Xavier; Hou, Fengji; Lorin, Emmanuel 4 2018 An algorithm coupling the OSRC and FEM for the computation of an approximate scattered acoustic field by a non-convex body. Zbl 1098.76566Antoine, X. 4 2002 Wavelet approximations of a collision operator in kinetic theory. Zbl 1028.76059Antoine, Xavier; Lemou, M. 4 2003 Far field modeling of electromagnetic time reversal and application to selective focusing on small scatterers. Zbl 1287.35054Antoine, X.; Pinçon, B.; Ramdani, K.; Thierry, B. 4 2008 Towards perfectly matched layers for time-dependent space fractional PDEs. Zbl 1452.65266Antoine, Xavier; Lorin, Emmanuel 4 2019 Spectral and condition number estimates of the acoustic single-layer operator for low-frequency multiple scattering in dense media. Zbl 1258.65100Thierry, Bertrand; Antoine, Xavier 4 2013 Optimized Schwarz domain decomposition methods for scalar and vector Helmholtz equations. Zbl 1366.65110Antoine, X.; Geuzaine, C. 4 2017 Acceleration of the imaginary time method for spectrally computing the stationary states of Gross-Pitaevskii equations. Zbl 1411.81026Antoine, Xavier; Besse, Christophe; Duboscq, Romain; Rispoli, Vittorio 3 2017 An improved on-surface radiation condition for acoustic scattering problems in the high-frequency spectrum. Zbl 1073.76061Antoine, Xavier; Darbas, Marion; Lu, Ya Yan 3 2005 Phase reduction models for improving the accuracy of the finite element solution of time-harmonic scattering problems. I: General approach and low-order models. Zbl 1161.65082Antoine, Xavier; Geuzaine, Christophe 3 2009 Spectral and condition number estimates of the acoustic single-layer operator for low-frequency multiple scattering in dilute media. Zbl 1286.74054Antoine, Xavier; Thierry, Bertrand 3 2013 A preconditioned conjugated gradient method for computing ground states of rotating dipolar Bose-Einstein condensates via kernel truncation method for dipole-dipole interaction evaluation. Zbl 1475.65142Antoine, Xavier; Tang, Qinglin; Zhang, Yong 3 2018 Efficient numerical computation of time-fractional nonlinear Schrödinger equations in unbounded domain. Zbl 07416715Zhang, Jiwei; Li, Dongfang; Antoine, Xavier 3 2019 On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrödinger equation. Zbl 1419.65049Antoine, X.; Lorin, E. 2 2019 Absorbing boundary conditions for solving \(N\)-dimensional stationary Schrödinger equations with unbounded potentials and nonlinearities. Zbl 1373.81202Klein, Pauline; Antoine, Xavier; Besse, Christophe; Ehrhardt, Matthias 2 2011 A performance study of plane wave finite element methods with a Padé-type artificial boundary condition in acoustic scattering. Zbl 1165.76025Kechroud, R.; Soulaimani, A.; Antoine, X. 2 2009 Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers. Zbl 1468.65159Antoine, Xavier; Lorin, Emmanuel; Zhang, Y. 2 2021 On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross-Pitaevskii equations. Zbl 07470677Antoine, Xavier; Tang, Qinglin; Zhang, Jiwei 2 2018 Generalized Brakhage-Werner integral formulations for the iterative solution of acoustics scattering problems. Zbl 1046.78005Antoine, Xavier; Darbas, Marion 1 2003 Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces. Zbl 1436.65127Antoine, Xavier; Fillion-Gourdeau, François; Lorin, Emmanuel; MacLean, Steve 1 2020 A numerical study of a scattering problem involving a generalized impedance boundary condition using the on-surface radiation condition method. Zbl 0943.78014Antoine, Xavier 1 1998 Approximate numerical solution of the acoustic scattering by a penetrable object using impedance boundary conditions. Zbl 0978.76081Antoine, X.; Barucq, H.; Vernhet, L. 1 2000 Open boundary conditions and computational schemes for Schrödinger equations with general potentials and nonlinearities. Zbl 1218.35221Antoine, Xavier; Klein, Pauline; Besse, Christophe 1 2010 A simple pseudospectral method for the computation of the time-dependent Dirac equation with perfectly matched layers. Zbl 1452.65267Antoine, Xavier; Lorin, Emmanuel 1 2019 Multilevel preconditioning technique for Schwarz waveform relaxation domain decomposition method for real- and imaginary-time nonlinear Schrödinger equation. Zbl 1427.65233Antoine, X.; Lorin, E. 1 2018 A construction of beam propagation methods for optical waveguides. Zbl 1364.78022Antoine, Xavier; Dreyfuss, Pierre; Ramdani, Karim 1 2009 A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics. Zbl 07413173Lieu, Alice; Marchner, Philippe; Gabard, Gwénaël; Bériot, Hadrien; Antoine, Xavier; Geuzaine, Christophe 1 2020 A frequency domain method for scattering problems with moving boundaries. Zbl 07425570Gasperini, D.; Beise, H. P.; Schroeder, U.; Antoine, X.; Geuzaine, C. 1 2021 ODE-based double-preconditioning for solving linear systems \(A^{\alpha}x=b\) and \(f(A)x=b\). Zbl 07478625Antoine, Xavier; Lorin, Emmanuel 1 2021 Stable perfectly matched layers with Lorentz transformation for the convected Helmholtz equation. Zbl 07501589Marchner, Philippe; Bériot, Hadrien; Antoine, Xavier; Geuzaine, Christophe 1 2021 Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers. Zbl 1468.65159Antoine, Xavier; Lorin, Emmanuel; Zhang, Y. 2 2021 A frequency domain method for scattering problems with moving boundaries. Zbl 07425570Gasperini, D.; Beise, H. P.; Schroeder, U.; Antoine, X.; Geuzaine, C. 1 2021 ODE-based double-preconditioning for solving linear systems \(A^{\alpha}x=b\) and \(f(A)x=b\). Zbl 07478625Antoine, Xavier; Lorin, Emmanuel 1 2021 Stable perfectly matched layers with Lorentz transformation for the convected Helmholtz equation. Zbl 07501589Marchner, Philippe; Bériot, Hadrien; Antoine, Xavier; Geuzaine, Christophe 1 2021 Corner treatments for high-order local absorbing boundary conditions in high-frequency acoustic scattering. Zbl 1453.65340Modave, A.; Geuzaine, C.; Antoine, X. 11 2020 A non-overlapping domain decomposition method with high-order transmission conditions and cross-point treatment for Helmholtz problems. Zbl 07337986Modave, A.; Royer, A.; Antoine, X.; Geuzaine, C. 9 2020 Perfectly matched layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates. Zbl 1453.65353Antoine, Xavier; Geuzaine, Christophe; Tang, Qinglin 4 2020 Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces. Zbl 1436.65127Antoine, Xavier; Fillion-Gourdeau, François; Lorin, Emmanuel; MacLean, Steve 1 2020 A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics. Zbl 07413173Lieu, Alice; Marchner, Philippe; Gabard, Gwénaël; Bériot, Hadrien; Antoine, Xavier; Geuzaine, Christophe 1 2020 Towards perfectly matched layers for time-dependent space fractional PDEs. Zbl 1452.65266Antoine, Xavier; Lorin, Emmanuel 4 2019 Efficient numerical computation of time-fractional nonlinear Schrödinger equations in unbounded domain. Zbl 07416715Zhang, Jiwei; Li, Dongfang; Antoine, Xavier 3 2019 On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrödinger equation. Zbl 1419.65049Antoine, X.; Lorin, E. 2 2019 A simple pseudospectral method for the computation of the time-dependent Dirac equation with perfectly matched layers. Zbl 1452.65267Antoine, Xavier; Lorin, Emmanuel 1 2019 Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves. Zbl 1407.65152Antoine, Xavier; Hou, Fengji; Lorin, Emmanuel 4 2018 A preconditioned conjugated gradient method for computing ground states of rotating dipolar Bose-Einstein condensates via kernel truncation method for dipole-dipole interaction evaluation. Zbl 1475.65142Antoine, Xavier; Tang, Qinglin; Zhang, Yong 3 2018 On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross-Pitaevskii equations. Zbl 07470677Antoine, Xavier; Tang, Qinglin; Zhang, Jiwei 2 2018 Multilevel preconditioning technique for Schwarz waveform relaxation domain decomposition method for real- and imaginary-time nonlinear Schrödinger equation. Zbl 1427.65233Antoine, X.; Lorin, E. 1 2018 Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods. Zbl 1380.81496Antoine, Xavier; Levitt, Antoine; Tang, Qinglin 24 2017 Computational performance of simple and efficient sequential and parallel Dirac equation solvers. Zbl 1411.35234Antoine, X.; Lorin, E. 12 2017 An analysis of Schwarz waveform relaxation domain decomposition methods for the imaginary-time linear Schrödinger and Gross-Pitaevskii equations. Zbl 1383.65122Antoine, X.; Lorin, E. 5 2017 Optimized Schwarz domain decomposition methods for scalar and vector Helmholtz equations. Zbl 1366.65110Antoine, X.; Geuzaine, C. 4 2017 Acceleration of the imaginary time method for spectrally computing the stationary states of Gross-Pitaevskii equations. Zbl 1411.81026Antoine, Xavier; Besse, Christophe; Duboscq, Romain; Rispoli, Vittorio 3 2017 On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions. Zbl 1380.65296Antoine, Xavier; Tang, Qinglin; Zhang, Yong 17 2016 High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations. Zbl 1422.65277Antoine, Xavier; Besse, Christophe; Rispoli, Vittorio 9 2016 GetDDM: an open framework for testing optimized Schwarz methods for time-harmonic wave problems. Zbl 1380.65477Thierry, B.; Vion, A.; Tournier, S.; El Bouajaji, M.; Colignon, D.; Marsic, N.; Antoine, X.; Geuzaine, C. 9 2016 Formulation and accuracy of on-surface radiation conditions for acoustic multiple scattering problems. Zbl 1410.78010Alzubaidi, Hasan; Antoine, Xavier; Chniti, Chokri 5 2016 Frozen Gaussian approximation based domain decomposition methods for the linear Schrödinger equation beyond the semi-classical regime. Zbl 1349.65430Lorin, E.; Yang, X.; Antoine, X. 5 2016 Lagrange-Schwarz waveform relaxation domain decomposition methods for linear and nonlinear quantum wave problems. Zbl 1334.65152Antoine, X.; Lorin, E. 5 2016 Modeling and computation of Bose-Einstein condensates: stationary states, nucleation, dynamics, stochasticity. Zbl 1344.35114Antoine, Xavier; Duboscq, Romain 18 2015 A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell’s equations. Zbl 1349.78066El Bouajaji, M.; Thierry, B.; Antoine, X.; Geuzaine, C. 18 2015 GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. II: Dynamics and stochastic simulations. Zbl 1344.82004Antoine, Xavier; Duboscq, Romain 15 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. Zbl 1332.78026Antoine, X.; Lorin, E.; Bandrauk, A. D. 10 2015 \(\mu\)-diff: an open-source Matlab toolbox for computing multiple scattering problems by disks. Zbl 1380.65478Thierry, Bertrand; Antoine, Xavier; Chniti, Chokri; Alzubaidi, Hasan 5 2015 Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates. Zbl 1349.82027Antoine, Xavier; Duboscq, Romain 33 2014 GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. I: Computation of stationary solutions. Zbl 1348.35003Antoine, Xavier; Duboscq, Romain 25 2014 Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell’s equations. Zbl 1351.78010El Bouajaji, M.; Antoine, X.; Geuzaine, C. 16 2014 Absorbing boundary conditions for relativistic quantum mechanics equations. Zbl 1349.81080Antoine, X.; Lorin, E.; Sater, J.; Fillion-Gourdeau, F.; Bandrauk, A. D. 13 2014 Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations. Zbl 1344.35130Antoine, Xavier; Bao, Weizhu; Besse, Christophe 107 2013 Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. II: Discretization and numerical results. Zbl 1457.65093Antoine, Xavier; Besse, Christophe; Klein, Pauline 10 2013 Spectral and condition number estimates of the acoustic single-layer operator for low-frequency multiple scattering in dense media. Zbl 1258.65100Thierry, Bertrand; Antoine, Xavier 4 2013 Spectral and condition number estimates of the acoustic single-layer operator for low-frequency multiple scattering in dilute media. Zbl 1286.74054Antoine, Xavier; Thierry, Bertrand 3 2013 A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation. Zbl 1243.65144Boubendir, Y.; Antoine, X.; Geuzaine, C. 55 2012 Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. I: Construction and a priori estimates. Zbl 1251.35096Antoine, Xavier; Besse, Christophe; Klein, Pauline 15 2012 Wide frequency band numerical approaches for multiple scattering problems by disks. Zbl 1280.78002Antoine, Xavier; Ramdani, Karim; Thierry, Bertrand 7 2012 Absorbing boundary conditions for general nonlinear Schrödinger equations. Zbl 1231.35223Antoine, Xavier; Besse, Christophe; Klein, Pauline 26 2011 Absorbing boundary conditions for solving \(N\)-dimensional stationary Schrödinger equations with unbounded potentials and nonlinearities. Zbl 1373.81202Klein, Pauline; Antoine, Xavier; Besse, Christophe; Ehrhardt, Matthias 2 2011 Computing high-frequency scattered fields by beam propagation methods: a prospective study. Zbl 1210.78015Antoine, Xavier; Huang, Yuexia; Lu, Ya Yan 5 2010 Open boundary conditions and computational schemes for Schrödinger equations with general potentials and nonlinearities. Zbl 1218.35221Antoine, Xavier; Klein, Pauline; Besse, Christophe 1 2010 Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential. Zbl 1161.65074Antoine, Xavier; Besse, Christophe; Klein, Pauline 24 2009 Towards accurate artificial boundary conditions for nonlinear PDEs through examples. Zbl 1184.35014Antoine, Xavier; Besse, Christophe; Szeftel, Jérémie 9 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. Zbl 1161.65082Antoine, Xavier; Geuzaine, Christophe 3 2009 A performance study of plane wave finite element methods with a Padé-type artificial boundary condition in acoustic scattering. Zbl 1165.76025Kechroud, R.; Soulaimani, A.; Antoine, X. 2 2009 A construction of beam propagation methods for optical waveguides. Zbl 1364.78022Antoine, Xavier; Dreyfuss, Pierre; Ramdani, Karim 1 2009 A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations. Zbl 1364.65178Antoine, Xavier; Arnold, Anton; Besse, Christophe; Ehrhardt, Matthias; Schadle, Achim 107 2008 On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders. Zbl 1135.65403Antoine, Xavier; Chniti, Chokri; Ramdani, Karim 19 2008 An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations. Zbl 1168.78001Antoine, X.; Boubendir, Y. 10 2008 Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps. Zbl 1143.78012Yuan, Jianhua; Lu, Ya Yan; Antoine, Xavier 5 2008 Far field modeling of electromagnetic time reversal and application to selective focusing on small scatterers. Zbl 1287.35054Antoine, X.; Pinçon, B.; Ramdani, K.; Thierry, B. 4 2008 Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation. Zbl 1123.65117Antoine, Xavier; Darbas, Marion 36 2007 Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations. Zbl 1109.35102Antoine, Xavier; Besse, Christophe; Descombes, Stephane 33 2006 An improved surface radiation condition for high-frequency acoustic scattering problems. Zbl 1120.76058Antoine, Xavier; Darbas, Marion; Lu, Ya Yan 31 2006 Alternative integral equations for the iterative solution of acoustic scattering problems. Zbl 1064.76095Antoine, X.; Darbas, M. 40 2005 Analytic preconditioners for the boundary integral solution of the scattering of acoustic waves by open surfaces. Zbl 1189.76356Antoine, Xavier; Bendali, Abderrahmane; Darbas, Marion 16 2005 Numerical accuracy of a Padé-type non-reflecting boundary condition for the finite element solution of acoustic scattering problems at high-frequency. Zbl 1113.76051Kechroud, R.; Antoine, X.; Soulaïmani, A. 16 2005 Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering. Zbl 1074.78004Antoine, Xavier; Barucq, Hélène 6 2005 On the construction of approximate boundary conditions for solving the interior problem of the acoustic scattering transmission problem. Zbl 1152.76466Antoine, X.; Barucq, H. 5 2005 An improved on-surface radiation condition for acoustic scattering problems in the high-frequency spectrum. Zbl 1073.76061Antoine, Xavier; Darbas, Marion; Lu, Ya Yan 3 2005 Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions. Zbl 1053.65072Antoine, Xavier; Besse, Christophe; Mouysset, Vincent 42 2004 Analytic preconditioners for the electric field integral equation. Zbl 1210.65193Antoine, X.; Bendali, A.; Darbas, M. 13 2004 Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation. Zbl 1037.65097Antoine, X.; Besse, C. 53 2003 Wavelet approximations of a collision operator in kinetic theory. Zbl 1028.76059Antoine, Xavier; Lemou, M. 4 2003 Generalized Brakhage-Werner integral formulations for the iterative solution of acoustics scattering problems. Zbl 1046.78005Antoine, Xavier; Darbas, Marion 1 2003 An algorithm coupling the OSRC and FEM for the computation of an approximate scattered acoustic field by a non-convex body. Zbl 1098.76566Antoine, X. 4 2002 Fast approximate computation of a time-harmonic scattered field using the on-surface radiation condition method. Zbl 1001.78008Antoine, Xavier 25 2001 Construction, structure and asymptotic approximations of a microdifferential transparent boundary condition for the linear Schrödinger equation. Zbl 1129.35324Antoine, Xavier; Besse, Christophe 22 2001 Microlocal diagonalization of strictly hyperbolic pseudodifferential systems and application to the design of radiation conditions in electromagnetism. Zbl 0983.35138Antoine, Xavier 14 2001 High-frequency asymptotic analysis of a dissipative transmission problem resulting in generalized impedance boundary conditions. Zbl 0986.76080Antoine, X.; Barucq, H.; Vernhet, L. 7 2001 Approximate numerical solution of the acoustic scattering by a penetrable object using impedance boundary conditions. Zbl 0978.76081Antoine, X.; Barucq, H.; Vernhet, L. 1 2000 Bayliss-Turkel-like radiation conditions on surfaces of arbitrary shape. Zbl 0923.35179Antoine, X.; Barucq, H.; Bendali, A. 71 1999 A numerical study of a scattering problem involving a generalized impedance boundary condition using the on-surface radiation condition method. Zbl 0943.78014Antoine, Xavier 1 1998 all cited Publications top 5 cited Publications all top 5 Cited by 778 Authors 62 Antoine, Xavier 21 Geuzaine, Christophe A. 21 Lorin, Emmanuel 17 Besse, Christophe 16 Barucq, Hélène 15 Bao, Weizhu 13 Zheng, Chunxiong 12 Cai, Yongyong 12 Djellouli, Rabia 12 Tang, Qinglin 12 Zhang, Jiwei 11 Darbas, Marion 8 Turc, Catalin 8 Wang, Tingchun 7 Boubendir, Yassine 7 Dehghan Takht Fooladi, Mehdi 7 Henning, Patrick 7 Tang, Shaoqiang 7 Thierry, Bertrand 7 Yin, Jia 7 Zlotnik, Alexander A. 6 Gander, Martin Jakob 6 Modave, Axel 6 Pang, Gang 6 Petrov, Pavel S. 6 Zhang, Yong 5 Acosta, Sebastian 5 Chaillat, Stéphanie 5 Čiegis, Raimondas 5 Claeys, Xavier 5 Duboscq, Romain 5 Han, Houde 5 Le Louër, Frédérique 5 Turkel, Eli L. 5 Wang, Pengde 5 Wu, Xiaonan 4 Abbaszadeh, Mostafa 4 Ashyralyev, Allaberen 4 Bandrauk, André D. 4 Bruno, Oscar P. 4 Chniti, Chokri 4 Collino, Francis 4 Diaz, Julien 4 Dolean, Victorita 4 Ehrhardt, Matthias 4 Farhat, Charbel H. 4 Huang, Chengming 4 Jiang, Chaolong 4 Joly, Patrick 4 Khajah, Tahsin 4 Levadoux, David P. 4 Li, Xianggui 4 Liang, Dong 4 Noble, Pascal 4 Pham, Ha Thanh 4 Sun, Zhizhong 4 Vaibhav, Vishal 4 Wang, Jilu 4 Zhang, Hui 4 Zhang, Rongpei 3 Abounouh, Mostafa 3 Al Moatassime, Hassan 3 Betcke, Timo 3 Birk, Carolin 3 Cassier, Maxence 3 Chabassier, Juliette 3 Coulombel, Jean-François 3 Cui, Jin 3 Duruflé, Marc 3 El Bouajaji, Mohamed 3 Guddati, Murthy N. 3 Guo, Boling 3 Harari, Isaac 3 He, Dongdong 3 Huang, Zhongyi 3 Jerez-Hanckes, Carlos 3 Jin, Jicheng 3 Ju, Lili 3 Klein, Pauline 3 Lakoba, Taras I. 3 Leng, Wei 3 Li, Buyang 3 Liang, Xiao 3 Liu, Wen-Jie 3 Luo, Songting 3 Ma, Ying 3 Mattesi, Vanessa 3 Medvinsky, Michael 3 Mei, Liquan 3 Pan, Kejia 3 Pérez-Arancibia, Carlos 3 Peterseim, Daniel 3 Pinaud, Olivier 3 Radziunas, Mindaugas 3 Ruan, Xinran 3 Saint-Guirons, A.-G. 3 Sirma, Ali 3 Song, Chongmin 3 Szeftel, Jérémie 3 Tezaur, Radek ...and 678 more Authors all top 5 Cited in 105 Serials 99 Journal of Computational Physics 28 Applied Numerical Mathematics 28 Journal of Scientific Computing 27 Computers & Mathematics with Applications 24 Journal of Computational and Applied Mathematics 21 Computer Methods in Applied Mechanics and Engineering 18 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 15 SIAM Journal on Numerical Analysis 14 Wave Motion 14 Applied Mathematics and Computation 14 Numerische Mathematik 14 International Journal of Computer Mathematics 13 SIAM Journal on Scientific Computing 11 Numerical Algorithms 10 Communications in Computational Physics 9 Engineering Analysis with Boundary Elements 8 Journal of Mathematical Analysis and Applications 8 International Journal for Numerical Methods in Engineering 7 Computer Physics Communications 7 Mathematics of Computation 7 Numerical Methods for Partial Differential Equations 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 6 SIAM Journal on Applied Mathematics 5 Mathematics and Computers in Simulation 5 Applied Mathematics Letters 4 Advances in Computational Mathematics 4 Communications in Nonlinear Science and Numerical Simulation 4 Kinetic and Related Models 4 East Asian Journal on Applied Mathematics 3 Journal of Mathematical Physics 3 Mathematical Methods in the Applied Sciences 3 Physica D 3 Applied Mathematical Modelling 3 Mathematical Problems in Engineering 3 Mathematical Modelling and Analysis 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Advances in Difference Equations 3 Advances in Applied Mathematics and Mechanics 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 2 Applicable Analysis 2 Inverse Problems 2 Physics Letters. A 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 BIT 2 Computational Mechanics 2 Communications in Partial Differential Equations 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 SIAM Review 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Journal of Mathematical Sciences (New York) 2 Doklady Mathematics 2 Journal of Inequalities and Applications 2 Computational Methods in Applied Mathematics 2 Multiscale Modeling & Simulation 2 International Journal of Computational Methods 2 Journal of Computational Acoustics 2 Boundary Value Problems 2 Acta Mechanica Sinica 2 SIAM Journal on Imaging Sciences 2 Science China. Mathematics 2 SMAI Journal of Computational Mathematics 2 Communications on Applied Mathematics and Computation 2 SN Partial Differential Equations and Applications 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 Journal of Engineering Mathematics 1 Physica A 1 Chaos, Solitons and Fractals 1 Annales de l’Institut Fourier 1 Calcolo 1 Journal of Functional Analysis 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerical Functional Analysis and Optimization 1 Journal of Computational Mathematics 1 Mathematical and Computer Modelling 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Integral Equations and Applications 1 Journal of Elasticity 1 Advances in Engineering Software 1 Computational and Applied Mathematics 1 Filomat 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Journal of Difference Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 Mathematical and Computer Modelling of Dynamical Systems 1 Discrete Dynamics in Nature and Society 1 International Journal of Applied Mathematics and Computer Science 1 The ANZIAM Journal 1 Archives of Computational Methods in Engineering 1 Foundations of Computational Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Acta Numerica 1 Science in China. Series G 1 Frontiers of Mathematics in China 1 Discrete and Continuous Dynamical Systems. Series S 1 Analysis and Mathematical Physics 1 Journal of Applied Analysis and Computation 1 Journal of Computational Dynamics 1 EMS Surveys in Mathematical Sciences ...and 5 more Serials all top 5 Cited in 38 Fields 446 Numerical analysis (65-XX) 377 Partial differential equations (35-XX) 80 Optics, electromagnetic theory (78-XX) 79 Fluid mechanics (76-XX) 63 Quantum theory (81-XX) 45 Mechanics of deformable solids (74-XX) 42 Statistical mechanics, structure of matter (82-XX) 14 Integral equations (45-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 11 Dynamical systems and ergodic theory (37-XX) 10 Operator theory (47-XX) 8 Real functions (26-XX) 7 Approximations and expansions (41-XX) 7 Operations research, mathematical programming (90-XX) 6 Integral transforms, operational calculus (44-XX) 6 Functional analysis (46-XX) 5 Potential theory (31-XX) 5 Special functions (33-XX) 5 Ordinary differential equations (34-XX) 5 Computer science (68-XX) 4 Geophysics (86-XX) 4 Biology and other natural sciences (92-XX) 3 Difference and functional equations (39-XX) 3 Probability theory and stochastic processes (60-XX) 3 Astronomy and astrophysics (85-XX) 3 Systems theory; control (93-XX) 3 Information and communication theory, circuits (94-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Manifolds and cell complexes (57-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year