A Multilevel Stochastic Collocation Method for Schrodinger Equations with a Random Potential

Tobias Jahnke; Benny Stein

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A Multilevel Stochastic Collocation Method for Schrodinger Equations with a Random Potential

机译：一种随机势薛定谔方程的多级随机搭配方法

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We propose and analyze a numerical method for time-dependent linear Schrodinger equations with uncertain parameters in both the potential and the initial data. The random parameters are discretized by stochastic collocation on a sparse grid, and the sample solutions in the nodes are approximated with the Strang splitting method. The computational work is reduced by a multilevel strategy, i.e., by combining information obtained from sample solutions computed on different refinement levels of the discretization. We prove new error bounds for the time discretization which take the finite regularity in the stochastic variable into account, and which are crucial to obtain convergence of the multilevel approach. The predicted cost savings of the multilevel stochastic collocation method are verified by numerical examples.

机译：我们建议和分析的数值方法时间线性薛定谔方程在潜在的和不确定的参数初始数据。离散的随机搭配稀疏网格,在节点和示例解决方案近似的斯特朗分裂方法。计算工作是减少了一个多级策略,即通过结合获得的信息从样本计算在不同的解决方案改进的离散化水平。新的时间离散化误差范围把有限的规律随机变量考虑,获得收敛的多层次的关键的方法。多级随机搭配方法验证了数值例子。

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《SIAM/ASA Journal on Uncertainty Quantification》 |2022年第4期|1753-1780|共28页
作者
Tobias Jahnke; Benny Stein;
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作者单位

Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology KIT, Karlsruhe, Germany;

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正文语种英语
中图分类计量学;
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8. 量子力学系统控制中的薛定谔方程及其应用（Schrodinger Equation and Its Application in Quantum Mechanical System Control） [C] . Chinese Control Conference vol.2; 20040810-13; Wuxi(CN) . 2004

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A Multilevel Stochastic Collocation Method for Schrodinger Equations with a Random Potential

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