Explicit Computation of Robin Parameters in Optimized Schwarz Waveform Relaxation Methods for Schrödinger Equations Based on Pseudodifferential Operators
Year: 2020
Author: Xavier Antoine, Emmanuel Lorin
Communications in Computational Physics, Vol. 27 (2020), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0259
Communications in Computational Physics, Vol. 27 (2020), Iss. 4 : pp. 1032–1052
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Optimized Schwarz Waveform Relaxation domain decomposition method Schrödinger equation dynamics stationary states Robin boundary condition pseudodifferential operators fast convergence.
Author Details
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A Jacobi spectral method for computing eigenvalue gaps and their distribution statistics of the fractional Schrödinger operator
Bao, Weizhu
Chen, Lizhen
Jiang, Xiaoyun
Ma, Ying
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https://doi.org/10.1016/j.jcp.2020.109733 [Citations: 4]