标题： 新的针对一维薛定谔方程的一般势能的优化施瓦茨算法 显示英文标题

标题： New optimized Schwarz algorithms for one dimensional Schrödinger equation with general potential

摘要： 本文的目的是为带有线性或非线性势的一维薛定谔方程开发新的优化Schwarz算法。 在介绍了作为迭代过程的经典算法之后，我们为具有时间无关线性势的薛定谔方程提出了一种新算法。 通过两个主要因素（显式构建界面问题和使用直接方法求解界面问题），新算法变为一个直接过程。 因此，可以自由选择传输条件。 对于时间相关线性势或非线性势的情况，我们建议使用预处理线性算子作为预条件子，从而得到预条件算法。 数值上，收敛与传输条件无关。 此外，这两种新算法在并行集群上实现时具有鲁棒性，在多达256个子域（MPI进程）的情况下可扩展，并且比经典算法计算时间少得多，尤其是在非线性情况下。 显示英文摘要

摘要： The aim of this paper is to develop new optimized Schwarz algorithms for the one dimensional Schr{\"o}dinger equation with linear or nonlinear potential. After presenting the classical algorithm which is an iterative process, we propose a new algorithm for the Schr{\"o}dinger equation with time-independent linear potential. Thanks to two main ingredients (constructing explicitly the interface problem and using a direct method on the interface problem), the new algorithm turns to be a direct process. Thus, it is free to choose the transmission condition. Concerning the case of time-dependent linear potential or nonlinear potential, we propose to use a pre-processed linear operator as preconditioner which leads to a preconditioned algorithm. Numerically , the convergence is also independent of the transmission condition. In addition, both of these new algorithms implemented in parallel cluster are robust, scalable up to 256 sub domains (MPI process) and take much less computation time than the classical one, especially for the nonlinear case.