Schwarz波形松弛方法用于一维Schrödinger方程的一般势能
Schwarz waveform relaxation method for one dimensional Schr{ö}dinger equation with general potential
AI总结：
本文提出了一种适用于一维Schrödinger方程的Schwarz波形松弛方法，针对线性和非线性势能，设计了鲁棒且可扩展的算法，显著减少计算时间，并通过预处理线性算子和新构造的吸收边界条件提升可扩展性。
摘要：
本文将Schwarz波形松弛（SWR）方法应用于具有通用线性或非线性势能的一维Schrödinger方程。我们为时间不变的线性势能Schrödinger方程提出了一种新的算法，该算法在500个子域内具有鲁棒性和可扩展性。与经典算法相比，它显著减少了计算时间。对于时间依赖的线性势能或非线性势能情况，我们使用预处理线性算子（零势能情况）作为预条件子，从而得到预条件算法，确保了高可扩展性。此外，一些新构造的吸收边界条件被用作传输条件，并进行了数值比较。
英文摘要：
In this paper, we apply the Schwarz Waveform Relaxation (SWR) method to the one dimensional Schr{ö}dinger equation with a general linear or a nonlinear potential. We propose a new algorithm for the Schr{ö}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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