Commun. Comput. Phys., 5 (2009), pp. 959-985. |
Numerical Methods for Solving the Hartree-Fock Equations of Diatomic Molecules I John C. Morrison ^{1*}, Scott Boyd ^{1}, Luis Marsano ^{1}, Bernard Bialecki ^{2}, Thomas Ericsson ^{3}, Jose Paulo Santos ^{4} 1 Department of Physics, University of Louisville, Louisville, KY, 40292, USA.2 Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401-1887, USA. 3 Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Gothenburg, Sweden. 4 Department of Physics, New University of Lisbon, Lisbon, Portugal. Received 22 February 2008; Accepted (in revised version) 9 July 2008 Available online 14 October 2008 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. AMS subject classifications: 65N35, 65N22, 65F10Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164 Key words: Fast Krylov methods, splines, Hartree-Fock equations, diatomic molecules, eigenvalue problem. *Corresponding author. Email: johnc@erdos.math.louisville.edu (J. C. Morrison), bbialeck@mines.edu (B. Bialecki), thomas@math.chalmers.se (T. Ericsson), jps@fct.unl.pt (J. P. Santos) |