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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 115, 2017 - Issue 15-16: Special Issue in honour of André D. Bandrauk
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ARTICLES

A friendly review of absorbing boundary conditions and perfectly matched layers for classical and relativistic quantum waves equations

X. AntoineInstitut Elie Cartan de Lorraine, Université de Lorraine, Vandoeuvre-lès-Nancy Cedex, FranceCorrespondence[email protected]
ORCID Iconhttp://orcid.org/0000-0002-6501-7757View further author information
ORCID Icon,
E. LorinCentre de Recherches Mathématiques, Université de Montréal, Montréal, Canada;School of Mathematics and Statistics, Carleton University, Ottawa, CanadaView further author information
&
Q. TangInstitut Elie Cartan de Lorraine, Université de Lorraine, Vandoeuvre-lès-Nancy Cedex, FranceView further author information
Pages 1861-1879 | Received 07 Oct 2016, Accepted 18 Jan 2017, Published online: 01 Mar 2017

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I. Nouira & M. Khenissi. (2022) Smoothing effect and exponential stability of discrete-time Schrödinger equation with fractional regularization term. International Journal of Computer Mathematics 99:6, pages 1201-1223.
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Xavier Antoine, Qinglin Tang & Jiwei Zhang. (2018) On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross–Pitaevskii equations. International Journal of Computer Mathematics 95:6-7, pages 1423-1443.
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Gang Pang, Songsong Ji & Xavier Antoine. (2022) Accurate absorbing boundary conditions for two-dimensional peridynamics. Journal of Computational Physics 466, pages 111351.
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Gang Pang, Songsong Ji & Xavier Antoine. (2022) A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis 56:5, pages 1687-1714.
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Jason Kaye, Alex Barnett & Leslie Greengard. (2020) A High‐Order Integral Equation‐Based Solver for the Time‐Dependent Schrödinger Equation. Communications on Pure and Applied Mathematics 75:8, pages 1657-1712.
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Karno Schwinn, Felipe Zapata, Antoine Levitt, Éric Cancès, Eleonora Luppi & Julien Toulouse. (2022) Photoionization and core resonances from range-separated density-functional theory: General formalism and example of the beryllium atom. The Journal of Chemical Physics 156:22.
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Feng Guo & Weizhong Dai. (2022) A new absorbing layer for simulation of wave propagation based on a KdV model on unbounded domain. Applied Numerical Mathematics 174, pages 46-70.
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Ying Ma & Jia Yin. (2021) Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime. Numerical Algorithms 89:4, pages 1415-1440.
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K.K. Sabirov, J.R. Yusupov, M. Ehrhardt & D.U. Matrasulov. (2022) Transparent boundary conditions for the sine-Gordon equation: Modeling the reflectionless propagation of kink solitons on a line. Physics Letters A 423, pages 127822.
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Xavier Antoine & Xiaofei Zhao. (2022) Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes. Journal of Computational Physics 448, pages 110728.
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Florent Pled & Christophe Desceliers. (2021) Review and Recent Developments on the Perfectly Matched Layer (PML) Method for the Numerical Modeling and Simulation of Elastic Wave Propagation in Unbounded Domains. Archives of Computational Methods in Engineering 29:1, pages 471-518.
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Songsong Ji, Gang Pang, Xavier Antoine & Jiwei Zhang. (2021) Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation. Journal of Computational Physics 444, pages 110575.
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Wim A. Mulder. (2021) A numerically exact nonreflecting boundary condition applied to the acoustic Helmholtz equation. GEOPHYSICS 86:4, pages T229-T238.
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X. Antoine, E. Lorin & Y. Zhang. (2020) Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers. Numerical Algorithms 87:1, pages 409-444.
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Emmanuel LORIN. (2021) Numerical analysis of the exact factorization of molecular time-dependent Schrödinger wavefunctions. Communications in Nonlinear Science and Numerical Simulation 95, pages 105627.
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Walter Pötz. (2021) Perfectly matched layers for the Dirac equation in general electromagnetic texture. Physical Review E 103:1.
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Walter Pötz. (2020) Perfectly matched layers for Schrödinger-type equations with nontrivial energy–momentum dispersion. Computer Physics Communications 257, pages 107503.
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W.A. Mulder. (2020) Research Note: A workaround for the corner problem in numerically exact non‐reflecting boundary conditions. Geophysical Prospecting 68:9, pages 2857-2866.
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Xavier Antoine, Christophe Geuzaine & Qinglin Tang. (2020) Perfectly matched layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates. Communications in Nonlinear Science and Numerical Simulation 90, pages 105406.
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Xavier Antoine, François Fillion-Gourdeau, Emmanuel Lorin & Steve MacLean. (2020) Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces. Journal of Computational Physics 411, pages 109412.
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P.S. Petrov & X. Antoine. (2020) Pseudodifferential adiabatic mode parabolic equations in curvilinear coordinates and their numerical solution. Journal of Computational Physics 410, pages 109392.
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Pengde Wang, Zhiguo Xu & Jia Yin. (2020) Simple high-order boundary conditions for computing rogue waves in the nonlinear Schrödinger equation. Computer Physics Communications 251, pages 107109.
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Wang Kong & Zhongyi Huang. (2020) Transparent boundary conditions and numerical computation for singularly perturbed telegraph equation on unbounded domain. Numerische Mathematik 145:2, pages 345-382.
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William Alexander Mulder. (2020) EXACT NON-REFLECTING BOUNDARY CONDITIONS WITH AN FDTD SCHEME FOR THE SCALAR WAVE EQUATION IN WAVEGUIDE PROBLEMS. Progress In Electromagnetics Research M 91, pages 39-48.
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Xavier Antoine & Emmanuel Lorin. (2019) A simple pseudospectral method for the computation of the time-dependent Dirac equation with Perfectly Matched Layers. Journal of Computational Physics 395, pages 583-601.
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Xavier Antoine & Emmanuel Lorin. (2019) Towards Perfectly Matched Layers for time-dependent space fractional PDEs. Journal of Computational Physics 391, pages 59-90.
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X. Antoine & E. Lorin. (2019) On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrödinger equation. Journal of Computational and Applied Mathematics 354, pages 15-30.
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Emmanuel Lorin. (2018) Domain decomposition method for the N-body time-independent and time-dependent Schrödinger equations. Numerical Algorithms 81:2, pages 655-694.
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Vishal Vaibhav. (2019) On the nonreflecting boundary operators for the general two dimensional Schrödinger equation. Journal of Mathematical Physics 60:1.
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Bo Wang & Dong Liang. (2018) The finite difference scheme for nonlinear Schrödinger equations on unbounded domain by artificial boundary conditions. Applied Numerical Mathematics 128, pages 183-204.
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Songsong Ji, Yibo Yang, Gang Pang & Xavier Antoine. (2018) Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains. Computer Physics Communications 222, pages 84-93.
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X. Antoine & E. Lorin. (2017) An analysis of Schwarz waveform relaxation domain decomposition methods for the imaginary-time linear Schrödinger and Gross-Pitaevskii equations. Numerische Mathematik 137:4, pages 923-958.
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X. Antoine & E. Lorin. (2017) Computational performance of simple and efficient sequential and parallel Dirac equation solvers. Computer Physics Communications 220, pages 150-172.
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