Antoine, Xavier; Zhao, Xiaofei Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes. (English) Zbl 07516812 J. Comput. Phys. 448, Article ID 110728, 24 p. (2022). MSC: 35Qxx 65Mxx 65Nxx PDFBibTeX XMLCite \textit{X. Antoine} and \textit{X. Zhao}, J. Comput. Phys. 448, Article ID 110728, 24 p. (2022; Zbl 07516812) Full Text: DOI arXiv
Marchner, Philippe; Bériot, Hadrien; Antoine, Xavier; Geuzaine, Christophe Stable perfectly matched layers with Lorentz transformation for the convected Helmholtz equation. (English) Zbl 1515.65298 J. Comput. Phys. 433, Article ID 110180, 22 p. (2021). MSC: 65N30 35J05 PDFBibTeX XMLCite \textit{P. Marchner} et al., J. Comput. Phys. 433, Article ID 110180, 22 p. (2021; Zbl 1515.65298) Full Text: DOI HAL
Pang, Gang; Yang, Yibo; Antoine, Xavier; Tang, Shaoqiang Stability and convergence analysis of artificial boundary conditions for the Schrödinger equation on a rectangular domain. (English) Zbl 1473.35141 Math. Comput. 90, No. 332, 2731-2756 (2021). MSC: 35J10 PDFBibTeX XMLCite \textit{G. Pang} et al., Math. Comput. 90, No. 332, 2731--2756 (2021; Zbl 1473.35141) Full Text: DOI
Antoine, Xavier; Lorin, Emmanuel; Zhang, Y. Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers. (English) Zbl 1468.65159 Numer. Algorithms 87, No. 1, 409-444 (2021). MSC: 65M70 65M06 65N35 35R11 PDFBibTeX XMLCite \textit{X. Antoine} et al., Numer. Algorithms 87, No. 1, 409--444 (2021; Zbl 1468.65159) Full Text: DOI HAL
Modave, A.; Royer, A.; Antoine, X.; Geuzaine, C. A non-overlapping domain decomposition method with high-order transmission conditions and cross-point treatment for Helmholtz problems. (English) Zbl 1506.74420 Comput. Methods Appl. Mech. Eng. 368, Article ID 113162, 23 p. (2020). MSC: 74S05 65N30 65N55 74J20 PDFBibTeX XMLCite \textit{A. Modave} et al., Comput. Methods Appl. Mech. Eng. 368, Article ID 113162, 23 p. (2020; Zbl 1506.74420) Full Text: DOI HAL
Modave, A.; Geuzaine, C.; Antoine, X. Corner treatments for high-order local absorbing boundary conditions in high-frequency acoustic scattering. (English) Zbl 1453.65340 J. Comput. Phys. 401, Article ID 109029, 24 p. (2020). MSC: 65M60 35J05 PDFBibTeX XMLCite \textit{A. Modave} et al., J. Comput. Phys. 401, Article ID 109029, 24 p. (2020; Zbl 1453.65340) Full Text: DOI HAL
Antoine, Xavier; Geuzaine, Christophe; Tang, Qinglin Perfectly matched layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates. (English) Zbl 1453.65353 Commun. Nonlinear Sci. Numer. Simul. 90, Article ID 105406, 15 p. (2020). MSC: 65M70 35Q41 35Q55 82C10 PDFBibTeX XMLCite \textit{X. Antoine} et al., Commun. Nonlinear Sci. Numer. Simul. 90, Article ID 105406, 15 p. (2020; Zbl 1453.65353) Full Text: DOI HAL
Petrov, P. S.; Antoine, X. Pseudodifferential adiabatic mode parabolic equations in curvilinear coordinates and their numerical solution. (English) Zbl 1436.65221 J. Comput. Phys. 410, Article ID 109392, 9 p. (2020). MSC: 65Z05 86A05 35J05 PDFBibTeX XMLCite \textit{P. S. Petrov} and \textit{X. Antoine}, J. Comput. Phys. 410, Article ID 109392, 9 p. (2020; Zbl 1436.65221) Full Text: DOI HAL
Antoine, Xavier; Lorin, Emmanuel A simple pseudospectral method for the computation of the time-dependent Dirac equation with perfectly matched layers. (English) Zbl 1452.65267 J. Comput. Phys. 395, 583-601 (2019). MSC: 65M70 35Q41 81Q05 65Z05 PDFBibTeX XMLCite \textit{X. Antoine} and \textit{E. Lorin}, J. Comput. Phys. 395, 583--601 (2019; Zbl 1452.65267) Full Text: DOI HAL
Antoine, Xavier; Lorin, Emmanuel Towards perfectly matched layers for time-dependent space fractional PDEs. (English) Zbl 1452.65266 J. Comput. Phys. 391, 59-90 (2019). MSC: 65M70 35R11 35Q55 PDFBibTeX XMLCite \textit{X. Antoine} and \textit{E. Lorin}, J. Comput. Phys. 391, 59--90 (2019; Zbl 1452.65266) Full Text: DOI HAL
Antoine, X.; Geuzaine, C. Optimized Schwarz domain decomposition methods for scalar and vector Helmholtz equations. (English) Zbl 1366.65110 Lahaye, Domenico (ed.) et al., Modern solvers for Helmholtz problems. Basel: Birkhäuser/Springer (ISBN 978-3-319-28831-4/hbk; 978-3-319-28832-1/ebook). Geosystems Mathematics, 189-213 (2017). MSC: 65N55 65N30 35J05 65N12 PDFBibTeX XMLCite \textit{X. Antoine} and \textit{C. Geuzaine}, in: Modern solvers for Helmholtz problems. Basel: Birkhäuser/Springer. 189--213 (2017; Zbl 1366.65110) Full Text: DOI HAL
Thierry, B.; Vion, A.; Tournier, S.; El Bouajaji, M.; Colignon, D.; Marsic, N.; Antoine, X.; Geuzaine, C. GetDDM: an open framework for testing optimized Schwarz methods for time-harmonic wave problems. (English) Zbl 1380.65477 Comput. Phys. Commun. 203, 309-330 (2016). MSC: 65Y15 65N55 65N30 78A45 65-04 PDFBibTeX XMLCite \textit{B. Thierry} et al., Comput. Phys. Commun. 203, 309--330 (2016; Zbl 1380.65477) Full Text: DOI HAL
Boubendir, Y.; Antoine, X.; Geuzaine, C. A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation. (English) Zbl 1243.65144 J. Comput. Phys. 231, No. 2, 262-280 (2012). MSC: 65N55 65N30 35J05 65N12 PDFBibTeX XMLCite \textit{Y. Boubendir} et al., J. Comput. Phys. 231, No. 2, 262--280 (2012; Zbl 1243.65144) Full Text: DOI HAL
Antoine, Xavier; Chniti, Chokri; Ramdani, Karim On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders. (English) Zbl 1135.65403 J. Comput. Phys. 227, No. 3, 1754-1771 (2008). MSC: 65N35 PDFBibTeX XMLCite \textit{X. Antoine} et al., J. Comput. Phys. 227, No. 3, 1754--1771 (2008; Zbl 1135.65403) Full Text: DOI HAL
Antoine, X.; Besse, C. Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation. (English) Zbl 1037.65097 J. Comput. Phys. 188, No. 1, 157-175 (2003). Reviewer: Marek Brandner (Plzeň) MSC: 65M20 65M12 35Q40 65M60 81Q05 PDFBibTeX XMLCite \textit{X. Antoine} and \textit{C. Besse}, J. Comput. Phys. 188, No. 1, 157--175 (2003; Zbl 1037.65097) Full Text: DOI