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Volume 27, Issue 4
Explicit Computation of Robin Parameters in Optimized Schwarz Waveform Relaxation Methods for Schrödinger Equations Based on Pseudodifferential Operators

Xavier Antoine & Emmanuel Lorin

DOI: 10.4208/cicp.OA-2018-0259

Commun. Comput. Phys., 27 (2020), pp. 1032-1052.

Published online: 2020-02

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  • Abstract

The Optimized Schwarz Waveform Relaxation algorithm, a domain decomposition method based on Robin transmission condition, is becoming a popular computational method for solving evolution partial differential equations in parallel. Along with well-posedness, it offers a good balance between convergence rate, efficient computational complexity and simplicity of the implementation. The fundamental question is the selection of the Robin parameter to optimize the convergence of the algorithm. In this paper, we propose an approach to explicitly estimate the Robin parameter which is based on the approximation of the transmission operators at the subdomain interfaces, for the linear/nonlinear Schrödinger equation. Some illustrating numerical experiments are proposed for the one- and two-dimensional problems.

  • Keywords

Optimized Schwarz Waveform Relaxation, domain decomposition method, Schrödinger equation, dynamics, stationary states, Robin boundary condition, pseudodifferential operators, fast convergence.

  • AMS Subject Headings

65M55, 65M60, 65M06, 35S10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xavier.antoine@univ-lorraine.fr (Xavier Antoine)

elorin@math.carleton.ca (Emmanuel Lorin)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1032, author = {Antoine , Xavier and Lorin , Emmanuel}, title = {Explicit Computation of Robin Parameters in Optimized Schwarz Waveform Relaxation Methods for Schrödinger Equations Based on Pseudodifferential Operators}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {4}, pages = {1032--1052}, abstract = {

The Optimized Schwarz Waveform Relaxation algorithm, a domain decomposition method based on Robin transmission condition, is becoming a popular computational method for solving evolution partial differential equations in parallel. Along with well-posedness, it offers a good balance between convergence rate, efficient computational complexity and simplicity of the implementation. The fundamental question is the selection of the Robin parameter to optimize the convergence of the algorithm. In this paper, we propose an approach to explicitly estimate the Robin parameter which is based on the approximation of the transmission operators at the subdomain interfaces, for the linear/nonlinear Schrödinger equation. Some illustrating numerical experiments are proposed for the one- and two-dimensional problems.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0259}, url = {http://global-sci.org/intro/article_detail/cicp/14825.html} }
TY - JOUR T1 - Explicit Computation of Robin Parameters in Optimized Schwarz Waveform Relaxation Methods for Schrödinger Equations Based on Pseudodifferential Operators AU - Antoine , Xavier AU - Lorin , Emmanuel JO - Communications in Computational Physics VL - 4 SP - 1032 EP - 1052 PY - 2020 DA - 2020/02 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2018-0259 UR - https://global-sci.org/intro/article_detail/cicp/14825.html KW - Optimized Schwarz Waveform Relaxation, domain decomposition method, Schrödinger equation, dynamics, stationary states, Robin boundary condition, pseudodifferential operators, fast convergence. AB -

The Optimized Schwarz Waveform Relaxation algorithm, a domain decomposition method based on Robin transmission condition, is becoming a popular computational method for solving evolution partial differential equations in parallel. Along with well-posedness, it offers a good balance between convergence rate, efficient computational complexity and simplicity of the implementation. The fundamental question is the selection of the Robin parameter to optimize the convergence of the algorithm. In this paper, we propose an approach to explicitly estimate the Robin parameter which is based on the approximation of the transmission operators at the subdomain interfaces, for the linear/nonlinear Schrödinger equation. Some illustrating numerical experiments are proposed for the one- and two-dimensional problems.

Antoine , Xavier and Lorin , Emmanuel. (2020). Explicit Computation of Robin Parameters in Optimized Schwarz Waveform Relaxation Methods for Schrödinger Equations Based on Pseudodifferential Operators. Communications in Computational Physics. 27 (4). 1032-1052. doi:10.4208/cicp.OA-2018-0259
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