<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">J. C. Morrison</style></author><author><style face="normal" font="default" size="100%">S. Boyd</style></author><author><style face="normal" font="default" size="100%">L. Marsano</style></author><author><style face="normal" font="default" size="100%">B. Bialecki</style></author><author><style face="normal" font="default" size="100%">T. Ericsson</style></author><author><style face="normal" font="default" size="100%">J P Santos</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Numerical methods for solving the Hartree-Fock equations of diatomic molecules I.</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Computational Physics</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">diatomic molecules</style></keyword><keyword><style  face="normal" font="default" size="100%">eigenvalue problem.</style></keyword><keyword><style  face="normal" font="default" size="100%">Fast Krylov methods</style></keyword><keyword><style  face="normal" font="default" size="100%">Hartree-Fock equations</style></keyword><keyword><style  face="normal" font="default" size="100%">splines</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.global-sci.com/issue/abstract/readabs.php?vol=5&amp;page=959&amp;issue=5&amp;ppage=985&amp;year=2009</style></url></web-urls></urls><number><style face="normal" font="default" size="100%">5</style></number><volume><style face="normal" font="default" size="100%">5</style></volume><pages><style face="normal" font="default" size="100%">959-985</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">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.</style></abstract><notes><style face="normal" font="default" size="100%">AMS subject classifications: 65N35, 65N22, 65F10</style></notes></record></records></xml>