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Diffusion Monte Carlo method: Numerical Analysisin a Simple Case

Published online by Cambridge University Press:  16 June 2007

Mohamed El Makrini
Affiliation:
ENPC-CERMICS, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne-la-Vallée Cedex 2, France. [email protected]; [email protected]; [email protected]
Benjamin Jourdain
Affiliation:
ENPC-CERMICS, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne-la-Vallée Cedex 2, France. [email protected]; [email protected]; [email protected]
Tony Lelièvre
Affiliation:
ENPC-CERMICS, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne-la-Vallée Cedex 2, France. [email protected]; [email protected]; [email protected]
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Abstract


The Diffusion Monte Carlo method is devoted to the computation ofelectronic ground-state energies of molecules. In this paper, we focus onimplementations of this method which consist in exploring theconfiguration space with a fixed number of random walkers evolvingaccording to a stochastic differential equation discretized in time. Weallow stochastic reconfigurations of the walkers to reduce thediscrepancy between the weights that they carry. On a simpleone-dimensional example, we prove the convergence of the method for afixed number of reconfigurations when the number of walkers tends to+∞ while the timestep tends to 0. We confirm our theoreticalrates of convergence by numerical experiments. Various resamplingalgorithms are investigated, both theoretically and numerically.


Type
Research Article
Copyright
© EDP Sciences, SMAI, 2007

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