Analysis of the divide-and-conquer method for electronic structure calculations
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- by Jingrun Chen and Jianfeng Lu PDF
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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.References
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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
- MR Author ID: 822782
- ORCID: 0000-0001-6255-5165
- Email: jianfeng@math.duke.edu
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Math. Comp. 85 (2016), 2919-2938
- MSC (2010): Primary 15A18, 35P99, 65N25
- DOI: https://doi.org/10.1090/mcom/3066
- MathSciNet review: 3522975