# Diffusion Monte Carlo method: Numerical Analysis in a Simple Case

Mohamed El Makrini; Benjamin Jourdain; Tony Lelièvre

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 2, page 189-213
- ISSN: 0764-583X

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topEl Makrini, Mohamed, Jourdain, Benjamin, and Lelièvre, Tony. "Diffusion Monte Carlo method: Numerical Analysis in a Simple Case." ESAIM: Mathematical Modelling and Numerical Analysis 41.2 (2007): 189-213. <http://eudml.org/doc/250054>.

@article{ElMakrini2007,

abstract = {
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.
},

author = {El Makrini, Mohamed, Jourdain, Benjamin, Lelièvre, Tony},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Diffusion Monte Carlo method; interacting particle systems;
ground state; Schrödinger operator; Feynman-Kac formula.},

language = {eng},

month = {6},

number = {2},

pages = {189-213},

publisher = {EDP Sciences},

title = {Diffusion Monte Carlo method: Numerical Analysis in a Simple Case},

url = {http://eudml.org/doc/250054},

volume = {41},

year = {2007},

}

TY - JOUR

AU - El Makrini, Mohamed

AU - Jourdain, Benjamin

AU - Lelièvre, Tony

TI - Diffusion Monte Carlo method: Numerical Analysis in a Simple Case

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/6//

PB - EDP Sciences

VL - 41

IS - 2

SP - 189

EP - 213

AB -
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.

LA - eng

KW - Diffusion Monte Carlo method; interacting particle systems;
ground state; Schrödinger operator; Feynman-Kac formula.

UR - http://eudml.org/doc/250054

ER -

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