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Diffusion Monte Carlo method: numerical analysis in a simple case | | Tony Lelievre
; Mohamed El Makrini
; Benjamin Jourdain
; | | Date: |
14 Mar 2007 | | Subject: | Numerical Analysis | | 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 {f 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 $+infty$ 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 | | Source: | arXiv, math/0703407 | | Services: | Forum | Review | PDF | Favorites | |
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