Stability at Nonconforming Grid Interfaces for a High Order Discretization of the Schrödinger Equation
Stability at Nonconforming Grid Interfaces for a High Order Discretization of the Schrödinger Equation
复制标题
薛定谔方程高阶离散化的非相容网格界面的稳定性
DOI：
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发表时间：
2012
影响因子：
2.5
通讯作者：
M. Gerritsen
中科院分区：
文献类型：
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作者：
A. Nissen;G. Kreiss;M. Gerritsen
在本文中，我们使用分部求和-同时逼近项（SBP-SAT）方法扩展了我们早期关于Schrödinger方程稳定边界闭包的工作结果，以包括非一致性网格界面的稳定性和精度。用能量法表示网格界面处的稳定性，并将估计推广到多个维度。利用二阶和四阶形式内精度算子的正态模态分析研究了网格界面耦合的精度。我们证明了二阶和四阶算子保持了完全的精度。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，相对于靠近界面的低阶近似，精度提高了两个阶。
In this paper we extend the results from our earlier work on stable boundary closures for the Schrödinger 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.