| Issue |
ESAIM: M2AN
Volume 41, Number 2, March-April 2007
Special issue on Molecular Modelling
|
|
|---|---|---|
| Page(s) | 189 - 213 | |
| DOI | https://doi.org/10.1051/m2an:2007017 | |
| Published online | 16 June 2007 | |
Diffusion Monte Carlo method: Numerical Analysis in a Simple Case
ENPC-CERMICS, 6-8 avenue Blaise Pascal, Cité
Descartes, Champs sur Marne, 77455 Marne-la-Vallée Cedex 2, France. makrimo@cermics.enpc.fr; jourdain@cermics.enpc.fr; lelievre@cermics.enpc.fr
Received:
30
September
2005
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example, we prove the convergence of the method for a fixed number of reconfigurations when the number of walkers tends to +∞ while the timestep tends to 0. We confirm our theoretical rates of convergence by numerical experiments. Various resampling algorithms are investigated, both theoretically and numerically.
Mathematics Subject Classification: 81Q05 / 65C35 / 60K35 / 35P15
Key words: Diffusion Monte Carlo method / interacting particle systems / ground state / Schrödinger operator / Feynman-Kac formula.
© EDP Sciences, SMAI, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.