On the convergence of diffusion Monte Carlo in non-Euclidean spaces. I. Free diffusion

The Journal of Chemical Physics
E Curotto, Massimo Mella

Abstract

We develop a set of diffusion Monte Carlo algorithms for general compactly supported Riemannian manifolds that converge weakly to second order with respect to the time step. The approaches are designed to work for cases that include non-orthogonal coordinate systems, nonuniform metric tensors, manifold boundaries, and multiply connected spaces. The methods do not require specially designed coordinate charts and can in principle work with atlases of charts. Several numerical tests for free diffusion in compactly supported Riemannian manifolds are carried out for spaces relevant to the chemical physics community. These include the circle, the 2-sphere, and the ellipsoid of inertia mapped with traditional angles. In all cases, we observe second order convergence, and in the case of the sphere, we gain insight into the function of the advection term that is generated by the curved nature of the space.

References

Oct 15, 2005·The Journal of Chemical Physics·E Curotto
Nov 23, 2006·The Journal of Chemical Physics·P HåkanssonMarta Patrone
Mar 17, 2007·The Journal of Chemical Physics·P Håkansson, M Mella
Mar 29, 2007·The Journal of Physical Chemistry. a·Michael W Avilés, E Curotto
Nov 18, 2009·The Journal of Chemical Physics·E AsareJ D Doll
Mar 1, 2012·The Journal of Chemical Physics·K RobertsE Curotto
May 17, 2013·The Journal of Chemical Physics·Grégoire GuillonPierre-Nicholas Roy
Oct 5, 2013·The Journal of Chemical Physics·Massimo Mella, E Curotto
Jun 9, 2014·The Journal of Chemical Physics·Pavel Castro-VillarrealSendic Estrada-Jiménez
Mar 23, 2015·The Journal of Chemical Physics·E Curotto, Massimo Mella

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Citations

Mar 23, 2015·The Journal of Chemical Physics·E Curotto, Massimo Mella
May 10, 2016·The Journal of Chemical Physics·H M ChristensenE Curotto
Mar 17, 2018·The Journal of Chemical Physics·E Curotto, M Mella
Apr 21, 2021·Physical Chemistry Chemical Physics : PCCP·O A Ramírez-GarzaP González-Mozuelos

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