Analysis of the divide-and-conquer method for electronic structure calculations

Chen, Jingrun; Lu, Jianfeng

doi:10.1090/mcom/3066

Analysis of the divide-and-conquer method for electronic structure calculations
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by Jingrun Chen and Jianfeng Lu PDF

Math. Comp. 85 (2016), 2919-2938 Request permission

Abstract:

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.

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