Piecewise homotopy analysis method and convergence analysis for formally well-posed initial value problems |
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Authors: | Zhen Wang Li Zou Yupeng Qin |
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Affiliation: | 1.Institut de Mathématiques de Toulouse UMR5219,Université de Toulouse,Toulouse Cedex 9,France;2.Maison de la Simulation & Laboratoire Paul Painlevé, Université Lille Nord de France,Lille,France;3.Laboratoire J.A. Dieudonné,Université de Nice & Inria Sophia Antipolis,Nice,France |
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Abstract: | In this paper, we apply the Schwarz waveform relaxation (SWR) method to the one-dimensional Schrödinger equation with a general linear or a nonlinear potential. We propose a new algorithm for the Schrödinger equation with time-independent linear potential, which is robust and scalable up to 500 subdomains. It reduces significantly computation time compared with the classical algorithms. Concerning the case of time-dependent linear potential or the nonlinear potential, we use a preprocessed linear operator for the zero potential case as a preconditioner which leads to a preconditioned algorithm. This ensures high scalability. In addition, some newly constructed absorbing boundary conditions are used as the transmission conditions and compared numerically. |
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