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Variational projector augmented-wave method: theoretical analysis and preliminary numerical results

Abstract

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. In conjunction with the use of pseudo-potentials, the projector augmented-wave (PAW) 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 variational PAW, is proposed and analyzed. This new method allows for a better convergence with respect to the number of plane-waves. Some numerical tests on an idealized case corroborate this efficiency. This work has been recently announced in Blanc et al. (C R Math 355(6), 665–670, 2017. https://doi.org/10.1016/j.crma.2017.05.004).

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Correspondence to M.-S. Dupuy.

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Blanc, X., Cancès, E. & Dupuy, MS. Variational projector augmented-wave method: theoretical analysis and preliminary numerical results. Numer. Math. 144, 271–321 (2020). https://doi.org/10.1007/s00211-019-01082-2

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Mathematics Subject Classification

  • 65N15
  • 65G99
  • 35P15