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hP Finite Element Approximation for Full-Potential Electronic Structure Calculations

Chapter

Abstract

The (continuous) finite element approximations of different orders for the computation of the solution to electronic structures was proposed in some papers and the performance of these approaches is becoming appreciable and is now well understood. In this publication, the author proposes to extend this discretization for full-potential electronic structure calculations by combining the refinement of the finite element mesh, where the solution is most singular with the increase of the degree of the polynomial approximations in the regions where the solution is mostly regular. This combination of increase of approximation properties, done in an a priori or a posteriori manner, is well-known to generally produce an optimal exponential type convergence rate with respect to the number of degrees of freedom even when the solution is singular. The analysis performed here sustains this property in the case of Hartree-Fock and Kohn-Sham problems.

Keywords

Electronic structure calculation Density functional theory Hartree-Fock model Kohn-Sham model Nonlinear eigenvalue problem hP version Finite element method 

Mathematics Subject Classification

65N25 65N30 65T99 35P30 35Q40 81Q05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.UPMC University, Paris 06, UMR 7598 LJLLParisFrance
  2. 2.Institut Universitaire de France and Division of Applied MathematicsBrown UniversityProvidenceUSA

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