| Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
|---|---|---|
| Page(s) | 1657 - 1683 | |
| DOI | https://doi.org/10.1051/m2an/2025037 | |
| Published online | 18 June 2025 | |
Approximations of the Green’s function in multiple scattering theory for crystalline systems
1
Faculty of Arts and Sciences, Beijing Normal University, Zhuhai 519087, Guangdong, P.R. China
2
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P.R. China
* Corresponding author: chen.huajie@bnu.edu.cn
Received:
8
September
2024
Accepted:
9
May
2025
The multiple scattering theory (MST) is a Green’s function method that has been widely used in electronic structure calculations for crystalline disordered systems. The key object of the MST method is the scattering path matrix (SPM) that characterizes the Green’s function within a local solution representation. This paper studies various approximations of the SPM, under the condition that an appropriate reference is used. In particular, we justify the convergence of the SPM approximations with respect to the size of scattering region and the length of scattering path, which are the central numerical parameters to achieve a linear-scaling MST method. We present numerical experiments on several typical systems to support the theory.
Mathematics Subject Classification: 81V55 / 65N12 / 82D20
Key words: Multiple scattering theory / Green’s function / scattering path matrix / crystalline systems / convergence analysis
© The authors. Published by EDP Sciences, SMAI 2025
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