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| h ? P Finite Element Approximation for Full-PotentialElectronic Structure Calculations |
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Citation： |
Yvon MADAY.h ? P Finite Element Approximation for Full-PotentialElectronic Structure Calculations[J].Chinese Annals of Mathematics B,2014,35(1):1~24 |
| Page view： 1935
Net amount： 1570 |
Authors： |
Yvon MADAY; |
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| Abstract： |
The (continuous) finite element approximations of different orders for the computation
of the solution to electronic structures were 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 ? Pversion, Finite element method |
Classification： |
65N25, 65N30, 65T99, 35P30, 35Q40, 81Q05 |
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