Volume 5, Issue 5
Numerical Methods for Solving the Hartree-Fock Equations of Diatomic Molecules I

John C. Morrison, Scott Boyd, Luis Marsano, Bernard Bialecki, Thomas Ericsson & Jose Paulo Santos

DOI:

Commun. Comput. Phys., 5 (2009), pp. 959-985.

Published online: 2009-05

Preview Full PDF 217 1090
Export citation
  • Abstract

The theory of domain decomposition is described and used to divide the variable domain of a diatomic molecule into separate regions which are solved independently. This approach makes it possible to use fast Krylov methods in the broad interior of the region while using explicit methods such as Gaussian elimination on the boundaries. As is demonstrated by solving a number of model problems, these methods enable one to obtain solutions of the relevant partial differential equations and eigenvalue equations accurate to six significant figures with a small amount of computational time. Since the numerical approach described in this article decomposes the variable space into separate regions where the equations are solved independently, our approach is very well-suited to parallel computing and offers the long term possibility of studying complex molecules by dividing them into smaller fragments that are calculated separately. 

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-5-959, author = {}, title = {Numerical Methods for Solving the Hartree-Fock Equations of Diatomic Molecules I}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {5}, pages = {959--985}, abstract = {

The theory of domain decomposition is described and used to divide the variable domain of a diatomic molecule into separate regions which are solved independently. This approach makes it possible to use fast Krylov methods in the broad interior of the region while using explicit methods such as Gaussian elimination on the boundaries. As is demonstrated by solving a number of model problems, these methods enable one to obtain solutions of the relevant partial differential equations and eigenvalue equations accurate to six significant figures with a small amount of computational time. Since the numerical approach described in this article decomposes the variable space into separate regions where the equations are solved independently, our approach is very well-suited to parallel computing and offers the long term possibility of studying complex molecules by dividing them into smaller fragments that are calculated separately. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7773.html} }
TY - JOUR T1 - Numerical Methods for Solving the Hartree-Fock Equations of Diatomic Molecules I JO - Communications in Computational Physics VL - 5 SP - 959 EP - 985 PY - 2009 DA - 2009/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7773.html KW - AB -

The theory of domain decomposition is described and used to divide the variable domain of a diatomic molecule into separate regions which are solved independently. This approach makes it possible to use fast Krylov methods in the broad interior of the region while using explicit methods such as Gaussian elimination on the boundaries. As is demonstrated by solving a number of model problems, these methods enable one to obtain solutions of the relevant partial differential equations and eigenvalue equations accurate to six significant figures with a small amount of computational time. Since the numerical approach described in this article decomposes the variable space into separate regions where the equations are solved independently, our approach is very well-suited to parallel computing and offers the long term possibility of studying complex molecules by dividing them into smaller fragments that are calculated separately. 

John C. Morrison, Scott Boyd, Luis Marsano, Bernard Bialecki, Thomas Ericsson & Jose Paulo Santos. (2020). Numerical Methods for Solving the Hartree-Fock Equations of Diatomic Molecules I. Communications in Computational Physics. 5 (5). 959-985. doi:
Copy to clipboard
The citation has been copied to your clipboard