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首页> 外文期刊>Journal of Scientific Computing >Stability at Nonconforming Grid Interfaces for a High Order Discretization of the Schrodinger Equation
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Stability at Nonconforming Grid Interfaces for a High Order Discretization of the Schrodinger Equation

机译：Schrodinger方程的高阶离散化在非相容网格接口处的稳定性

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摘要

In this paper we extend the results from our earlier work on stable boundary closures for the Schrodinger equation using the summation-by-parts-simultaneous approximation term (SBP-SAT) method to include stability and accuracy at nonconforming grid interfaces. Stability at the grid interface is shown by the energy method, and the estimates are generalized to multiple dimensions. The accuracy of the grid interface coupling is investigated using normal mode analysis for operators of 2nd and 4th order formal interior accuracy. We show that full accuracy is retained for the 2nd and 4th order operators. The accuracy results are extended to 6th and 8th order operators by numerical simulations, in which case two orders of accuracy is gained with respect to the lower order approximation close to the interface.
机译：在本文中，我们使用分部加总同时逼近项（SBP-SAT）方法扩展了先前关于Schrodinger方程稳定边界闭合的工作结果，以包括不合格网格界面的稳定性和准确性。能量方法显示了网格界面的稳定性，并且将估计值推广到多个维度。使用二阶和四阶形式内部精度算子的正常模式分析来研究网格接口耦合的精度。我们证明了二阶和四阶算子的完全精度得以保留。通过数值模拟将精度结果扩展到6阶和8阶算子，在这种情况下，相对于靠近界面的较低阶近似，可以获得2阶精度。

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