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arXiv · 1503.02564

Schwarz waveform relaxation method for one dimensional Schr{\"o}dinger equation with general potential

C Besse·F Xing
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Abstract

In this paper, we apply the Schwarz Waveform Relaxation (SWR) method to the one dimensional Schr{\"o}dinger equation with a general linear or a nonlinear potential. We propose a new algorithm for the Schr{\"o}dinger equation with time independent linear potential, which is robust and scalable up to 500 subdo-mains. It reduces significantly computation time compared with the classical algorithms. Concerning the case of time dependent linear potential or the non-linear potential, we use a preprocessed linear operator for the zero potential case as preconditioner which lead to a preconditioned algorithm. This ensures high scalability. Besides, some newly constructed absorbing boundary conditions are used as the transmission condition and compared numerically.

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C Besse, F Xing. 2015-03-09. Schwarz waveform relaxation method for one dimensional Schr{\"o}dinger equation with general potential. https://arxiv.org/abs/1503.02564

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