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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

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Abstract

This paper is devoted to the efficient computation of the time dependent Schrödinger equation for quantum particles subject to intense electromagnetic fields including ionization and recombination of electrons with their parent ion. The proposed approach is based on a domain decomposition technique, allowing a fine computation of the wavefunction in the vicinity of the nuclei located in a domain \(\Omega _1\) and a fast computation in a roughly meshed domain \(\Omega _2\) far from the nuclei where the electrons are assumed free. The key ingredients in the method are (i) well designed transmission boundary conditions on \(\partial \Omega _1\) (resp. \(\partial \Omega _2\)) in order to estimate the part of the wavefunction “leaving” Domain \(\Omega _1\) (resp. \(\Omega _2\)), (ii) a Schwarz waveform relaxation algorithm to accurately reconstruct the solution. The developed method makes it possible for electrons to travel from one domain to another without loosing accuracy, when the frontier or the overlapping region between two domains is crossed by the wavefunction.

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Acknowledgments

The first author thanks the support of the french ANR grants “Bond” (ANR-13-BS01-0009-01) and “BECASIM” (ANR-12-MONU-0007-02). The second and third authors would like to thank NSERC for the financial support.

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Authors and Affiliations

  1. Institut Elie Cartan de Lorraine, Université de Lorraine, 54506 , Vandoeuvre-lès-Nancy Cedex, France

    X. Antoine

  2. Inria Nancy Grand-Est/IECL - ALICE, Vandoeuvre-lès-Nancy Cedex, France

    X. Antoine

  3. Centre de Recherches Mathématiques, Université de Montréal, Montreal, H3T 1J4, Canada

    E. Lorin & A. D. Bandrauk

  4. School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6, Canada

    E. Lorin

  5. Laboratoire de Chimie Théorique, Université de Sherbrooke, Sherbrooke, J1K 2R1, Canada

    A. D. Bandrauk

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  1. X. Antoine
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Correspondence to E. Lorin.

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Antoine, X., Lorin, E. & Bandrauk, A.D. 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. J Sci Comput 64, 620–646 (2015). https://doi.org/10.1007/s10915-014-9902-5

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  • DOI: https://doi.org/10.1007/s10915-014-9902-5

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