ANALYSIS OF THE DIVIDE-AND-CONQUER METHOD FOR ELECTRONIC STRUCTURE CALCULATIONS
ANALYSIS OF THE DIVIDE-AND-CONQUER METHOD FOR ELECTRONIC STRUCTURE CALCULATIONS
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DOI：
10.1090/mcom/3066
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发表时间：
2016-11-01
影响因子：
2
通讯作者：
Lu, Jianfeng
中科院分区：
文献类型：
--
作者：
Chen, Jingrun;Lu, Jianfeng
我们研究了电子结构计算的分而治之方法的精度。对该方法中的一个典型子域问题进行了分析。我们证明了在全局系统和子系统的间隙假设下，全局系统和子系统的电子密度之间的点态差作为离子系统边界的距离的函数呈指数衰减。数值算例表明，间隙假设对分而治之方法的精度是至关重要的。特别地，我们给出了当子系统的间隙假设无效时损失精度的例子。
We study the accuracy of the divide-and-conquer method for electronic structure calculations. The analysis is conducted for a prototypical subdomain problem in the method. We prove that the pointwise difference between electron densities of the global system and the subsystem decays exponentially as a function of the distance away from the boundary of the subsystem, under the gap assumption of both the global system and the subsystem. We show that the gap assumption is crucial for the accuracy of the divide-and-conquer method by numerical examples. In particular, we show examples with the loss of accuracy when the gap assumption of the subsystem is invalid.