h−P Finite Element Approximation for Full-Potential Electronic Structure Calculations

Yvon Maday ()
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Yvon Maday: UPMC University, Paris 06, UMR 7598 LJLL

A chapter in Partial Differential Equations: Theory, Control and Approximation, 2014, pp 349-377 from Springer

Abstract: 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; h−P version; Finite element method; 65N25; 65N30; 65T99; 35P30; 35Q40; 81Q05 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-41401-5_14

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DOI: 10.1007/978-3-642-41401-5_14

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