Volume 29, Issue 5
A Mortar Spectral Element Method for Full-Potential Electronic Structure Calculations

Yichen Guo, Lueling Jia, Huajie Chen, Huiyuan Li & Zhimin Zhang

Commun. Comput. Phys., 29 (2021), pp. 1541-1569.

Published online: 2021-03

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  • Abstract

In this paper, we propose an efficient mortar spectral element approximation scheme for full-potential electronic structure calculations. As a subsequent work of [24], the paper adopts a similar domain decomposition that the computational domain is first decomposed into a number of cuboid subdomains satisfying each nucleus is located in the center of one cube, in which a small ball element centered at the site of the nucleus is attached, and the remainder of the cube is further partitioned into six curvilinear hexahedrons. Specially designed Sobolev-orthogonal basis is adopted in each ball. Classic conforming spectral element approximations using mapped Jacobi polynomials are implemented on the curvilinear hexahedrons and the cuboid elements without nuclei. A mortar technique is applied to patch the different discretizations. Numerical experiments are carried out to demonstrate the efficiency of our scheme, especially the spectral convergence rates of the ground state approximations. Essentially the algorithm can be extended to general eigenvalue problems with the Coulomb singularities.

  • Keywords

Kohn-Sham equation, full-potential calculations, mortar spectral element method, exponential order of convergence.

  • AMS Subject Headings

65N25, 35Q40, 35P30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-1541, author = {Guo , Yichen and Jia , Lueling and Chen , Huajie and Li , Huiyuan and Zhang , Zhimin}, title = {A Mortar Spectral Element Method for Full-Potential Electronic Structure Calculations}, journal = {Communications in Computational Physics}, year = {2021}, volume = {29}, number = {5}, pages = {1541--1569}, abstract = {

In this paper, we propose an efficient mortar spectral element approximation scheme for full-potential electronic structure calculations. As a subsequent work of [24], the paper adopts a similar domain decomposition that the computational domain is first decomposed into a number of cuboid subdomains satisfying each nucleus is located in the center of one cube, in which a small ball element centered at the site of the nucleus is attached, and the remainder of the cube is further partitioned into six curvilinear hexahedrons. Specially designed Sobolev-orthogonal basis is adopted in each ball. Classic conforming spectral element approximations using mapped Jacobi polynomials are implemented on the curvilinear hexahedrons and the cuboid elements without nuclei. A mortar technique is applied to patch the different discretizations. Numerical experiments are carried out to demonstrate the efficiency of our scheme, especially the spectral convergence rates of the ground state approximations. Essentially the algorithm can be extended to general eigenvalue problems with the Coulomb singularities.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0020}, url = {http://global-sci.org/intro/article_detail/cicp/18728.html} }
TY - JOUR T1 - A Mortar Spectral Element Method for Full-Potential Electronic Structure Calculations AU - Guo , Yichen AU - Jia , Lueling AU - Chen , Huajie AU - Li , Huiyuan AU - Zhang , Zhimin JO - Communications in Computational Physics VL - 5 SP - 1541 EP - 1569 PY - 2021 DA - 2021/03 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2020-0020 UR - https://global-sci.org/intro/article_detail/cicp/18728.html KW - Kohn-Sham equation, full-potential calculations, mortar spectral element method, exponential order of convergence. AB -

In this paper, we propose an efficient mortar spectral element approximation scheme for full-potential electronic structure calculations. As a subsequent work of [24], the paper adopts a similar domain decomposition that the computational domain is first decomposed into a number of cuboid subdomains satisfying each nucleus is located in the center of one cube, in which a small ball element centered at the site of the nucleus is attached, and the remainder of the cube is further partitioned into six curvilinear hexahedrons. Specially designed Sobolev-orthogonal basis is adopted in each ball. Classic conforming spectral element approximations using mapped Jacobi polynomials are implemented on the curvilinear hexahedrons and the cuboid elements without nuclei. A mortar technique is applied to patch the different discretizations. Numerical experiments are carried out to demonstrate the efficiency of our scheme, especially the spectral convergence rates of the ground state approximations. Essentially the algorithm can be extended to general eigenvalue problems with the Coulomb singularities.

Yichen Guo, Lueling Jia, Huajie Chen, Huiyuan Li & Zhimin Zhang. (2021). A Mortar Spectral Element Method for Full-Potential Electronic Structure Calculations. Communications in Computational Physics. 29 (5). 1541-1569. doi:10.4208/cicp.OA-2020-0020
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