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


Authors: Jingrun Chen and Jianfeng Lu
Journal: Math. Comp. 85 (2016), 2919-2938
MSC (2010): Primary 15A18, 35P99, 65N25
DOI: https://doi.org/10.1090/mcom/3066
Published electronically: January 28, 2016
MathSciNet review: 3522975
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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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Additional Information

Jingrun Chen
Affiliation: Mathematics Department, South Hall 6705, University of California, Santa Barbara, California 93106
Address at time of publication: Mathematical Center for Interdisciplinary Research and School of Mathematical Sciences, Soochow University, Zuzhou 215006, China
Email: jingrunchen@suda.edu.cn

Jianfeng Lu
Affiliation: Departments of Mathematics, Physics, and Chemistry, Duke University, Box 90320, Durham, North Carolina 27708
Email: jianfeng@math.duke.edu

DOI: https://doi.org/10.1090/mcom/3066
Keywords: Density functional theory, divide-and-conquer method, gap assumption, exponential decay
Received by editor(s): October 31, 2014
Received by editor(s) in revised form: November 7, 2014, March 15, 2015, and April 6, 2015
Published electronically: January 28, 2016
Article copyright: © Copyright 2016 American Mathematical Society