# Multilevel domain decomposition for electronic structure calculations

## Abstract

We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and density functional theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of domain decomposition methods. Using this approach, calculations have been successfully performed on several linear polymer chains containing up to 40,000 atoms and 200,000 atomic orbitals. Both the computational cost and the memory requirement scale linearly with the number of atoms. Additional speed-up can easily be obtained by parallelization. We show that this domain decomposition method outperforms the density matrix minimization (DMM) method for poor initial guesses. Our method provides an efficient preconditioner for DMM and other linear scaling methods, variational in nature, such as the orbital minimization (OM) procedure.

- Authors:

- EDF R and D, 1 avenue du General de Gaulle, 92141 Clamart Cedex (France) and CERMICS, Ecole Nationale des Ponts et Chaussees, 6 and 8, Avenue Blaise Pascal, Cite Descartes, 77455 Marne-La-Vallee Cedex 2 (France). E-mail: maxime.barrault@edf.fr
- CERMICS, Ecole Nationale des Ponts et Chaussees, 6 and 8, Avenue Blaise Pascal, Cite Descartes, 77455 Marne-La-Vallee Cedex 2 (France). E-mail: cances@cermics.enpc.fr
- Department of Mathematics, University of Florida, Gainesville, FL 32611-8105 (United States). E-mail: hager@math.ufl.edu
- CERMICS, Ecole Nationale des Ponts et Chaussees, 6 and 8, Avenue Blaise Pascal, Cite Descartes, 77455 Marne-La-Vallee Cedex 2 (France). E-mail: lebris@cermics.enpc.fr

- Publication Date:

- OSTI Identifier:
- 20991560

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 222; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2006.06.049; PII: S0021-9991(06)00318-4; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; DENSITY FUNCTIONAL METHOD; DENSITY MATRIX; ELECTRONIC STRUCTURE; MATHEMATICAL MODELS; MINIMIZATION; POLYMERS

### Citation Formats

```
Barrault, M., Cances, E., Hager, W.W., and Le Bris, C..
```*Multilevel domain decomposition for electronic structure calculations*. United States: N. p., 2007.
Web. doi:10.1016/j.jcp.2006.06.049.

```
Barrault, M., Cances, E., Hager, W.W., & Le Bris, C..
```*Multilevel domain decomposition for electronic structure calculations*. United States. doi:10.1016/j.jcp.2006.06.049.

```
Barrault, M., Cances, E., Hager, W.W., and Le Bris, C.. Thu .
"Multilevel domain decomposition for electronic structure calculations". United States.
doi:10.1016/j.jcp.2006.06.049.
```

```
@article{osti_20991560,
```

title = {Multilevel domain decomposition for electronic structure calculations},

author = {Barrault, M. and Cances, E. and Hager, W.W. and Le Bris, C.},

abstractNote = {We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and density functional theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of domain decomposition methods. Using this approach, calculations have been successfully performed on several linear polymer chains containing up to 40,000 atoms and 200,000 atomic orbitals. Both the computational cost and the memory requirement scale linearly with the number of atoms. Additional speed-up can easily be obtained by parallelization. We show that this domain decomposition method outperforms the density matrix minimization (DMM) method for poor initial guesses. Our method provides an efficient preconditioner for DMM and other linear scaling methods, variational in nature, such as the orbital minimization (OM) procedure.},

doi = {10.1016/j.jcp.2006.06.049},

journal = {Journal of Computational Physics},

number = 1,

volume = 222,

place = {United States},

year = {Thu Mar 01 00:00:00 EST 2007},

month = {Thu Mar 01 00:00:00 EST 2007}

}