[La méthode VPAW]
Dans les calculs de structure électronique de type Kohn–Sham, les fonctions d'ondes présentent des singularités aux positions des noyaux. Ces singularités empêchent une bonne approximation de la fonction par des ondes planes. La méthode PAW (projector augmented-wave) vise à contourner cette difficulté en remplaçant le problème aux valeurs propres d'origine par un autre ayant les mêmes valeurs propres, mais des vecteurs propres plus réguliers. Nous proposons et analysons une implémentation différente de cette méthode, baptisée VPAW (variational PAW). Elle permet d'obtenir une meilleure convergence en nombre d'ondes planes. Quelques résultats numériques sur un cas idéalisé confirment son efficacité.
In Kohn–Sham electronic structure computations, wave functions have singularities at nuclear positions. Because of these singularities, plane wave expansions give a poor approximation of the eigenfunctions. The PAW (projector augmented-wave) method circumvents this issue by replacing the original eigenvalue problem by a new one with the same eigenvalues, but smoother eigenvectors. Here a slightly different method, called VPAW (variational PAW), is proposed and analyzed. This new method allows for a better convergence with respect to the number of plane waves. Some numerical results on an idealized case corroborate this efficiency.
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@article{CRMATH_2017__355_6_665_0,
author = {Blanc, Xavier and Canc\`es, \'Eric and Dupuy, Mi-Song},
title = {Variational projector augmented-wave method},
journal = {Comptes Rendus. Math\'ematique},
pages = {665--670},
publisher = {Elsevier},
volume = {355},
number = {6},
year = {2017},
doi = {10.1016/j.crma.2017.05.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.05.004/}
}
TY - JOUR AU - Blanc, Xavier AU - Cancès, Éric AU - Dupuy, Mi-Song TI - Variational projector augmented-wave method JO - Comptes Rendus. Mathématique PY - 2017 SP - 665 EP - 670 VL - 355 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.05.004/ DO - 10.1016/j.crma.2017.05.004 LA - en ID - CRMATH_2017__355_6_665_0 ER -
%0 Journal Article %A Blanc, Xavier %A Cancès, Éric %A Dupuy, Mi-Song %T Variational projector augmented-wave method %J Comptes Rendus. Mathématique %D 2017 %P 665-670 %V 355 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.05.004/ %R 10.1016/j.crma.2017.05.004 %G en %F CRMATH_2017__355_6_665_0
Blanc, Xavier; Cancès, Éric; Dupuy, Mi-Song. Variational projector augmented-wave method. Comptes Rendus. Mathématique, Tome 355 (2017) no. 6, pp. 665-670. doi : 10.1016/j.crma.2017.05.004. http://www.numdam.org/articles/10.1016/j.crma.2017.05.004/
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