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An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
 
ID 2832508
Author(s) Neelov, A. I.; Goedecker, S.
Author(s) at UniBasel Goedecker, Stefan
Year 2006
Title An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis
Journal Journal of Computational Physics
Volume 217
Number 2
Pages / Article-Number 312-339
Keywords orthogonal wavelets; Schroedinger equation; numerical quadrature; electronic structure; Daubechies wavelets; multiresolution; adaptivity; real space methods; potential energy operator
Abstract An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our quadrature is also applicable in the case of adaptive spatial resolution. Our theoretical error estimates are confirmed by numerical test calculations of the ground state energy and wavefunction of the harmonic oscillator in one dimension with and without adaptive resolution. As a byproduct we derive a filter, which, upon application on the scaling function coefficients of a smooth function, renders the approximate grid values of this function. This also allows for a fast calculation of the charge density from the wavefunction.
Publisher Elsevier
ISSN/ISBN 0021-9991 ; 1090-2716
edoc-URL https://edoc.unibas.ch/76355/
Full Text on edoc No
Digital Object Identifier DOI 10.1016/j.jcp.2006.01.003
ISI-Number 000241415800003
Document type (ISI) Article
 
   

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