s∗-compressibility of the discrete Hartree-Fock equation

Heinz-Jürgen Flad; Reinhold Schneider

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 5, page 1055-1080
  • ISSN: 0764-583X

Abstract

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The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown that the s∗-compressibility is in accordance with convergence rates obtained from best N-term approximation for solutions of the Hartree-Fock equation. This is a necessary requirement in order to achieve numerical solutions for these equations with optimal complexity using the recently developed adaptive wavelet algorithms of Cohen, Dahmen and DeVore.

How to cite

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Flad, Heinz-Jürgen, and Schneider, Reinhold. "s∗-compressibility of the discrete Hartree-Fock equation." ESAIM: Mathematical Modelling and Numerical Analysis 46.5 (2012): 1055-1080. <http://eudml.org/doc/222110>.

@article{Flad2012,
abstract = {The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown that the s∗-compressibility is in accordance with convergence rates obtained from best N-term approximation for solutions of the Hartree-Fock equation. This is a necessary requirement in order to achieve numerical solutions for these equations with optimal complexity using the recently developed adaptive wavelet algorithms of Cohen, Dahmen and DeVore.},
author = {Flad, Heinz-Jürgen, Schneider, Reinhold},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Hartree-Fock equation; matrix compression; bestN-term approximation; wavelet bases; Galerkin matrices; Coulomb potentials; best -term approximation; numerical results},
language = {eng},
month = {2},
number = {5},
pages = {1055-1080},
publisher = {EDP Sciences},
title = {s∗-compressibility of the discrete Hartree-Fock equation},
url = {http://eudml.org/doc/222110},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Flad, Heinz-Jürgen
AU - Schneider, Reinhold
TI - s∗-compressibility of the discrete Hartree-Fock equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/2//
PB - EDP Sciences
VL - 46
IS - 5
SP - 1055
EP - 1080
AB - The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown that the s∗-compressibility is in accordance with convergence rates obtained from best N-term approximation for solutions of the Hartree-Fock equation. This is a necessary requirement in order to achieve numerical solutions for these equations with optimal complexity using the recently developed adaptive wavelet algorithms of Cohen, Dahmen and DeVore.
LA - eng
KW - Hartree-Fock equation; matrix compression; bestN-term approximation; wavelet bases; Galerkin matrices; Coulomb potentials; best -term approximation; numerical results
UR - http://eudml.org/doc/222110
ER -

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