Computing the principal eigenelements of some linear operators using a branching Monte Carlo method

Lejay, Antoine; Maire, Sylvain

doi:10.1016/j.jcp.2008.07.018

Cited by 6 publications

(4 citation statements)

References 31 publications

(31 reference statements)

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“…With Remark 2, it can provide the law of the exit time from the domain, which is crucial in the computation of the principal eigenelements of the operator by means of Monte Carlo methods [28,29]. In a recent work [5] it has also been used successfully for solving the Poisson-Boltzmann equation of molecular electrostatics for which the finite differences method was originally designed.…”

Section: Resultsmentioning

confidence: 99%

Simulating diffusions with piecewise constant coefficients using a kinetic approximation

Lejay

Maire²

2010

Computer Methods in Applied Mechanics and Engineering

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Abstract. Using a kinetic approximation of a linear diffusion operator, we propose an algorithm that allows one to deal with the simulation of a multi-dimensional stochastic process in a media which is locally isotropic except on some surface where the diffusion coefficient presents some discontinuities. Basic numerical examples are given in dimensions one to three on PDEs or stochastic PDEs with or without source terms. Finally, we compute the hydrodynamic load in a porous media in the nuclear waste context.

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Section: Resultsmentioning

confidence: 99%

Simulating diffusions with piecewise constant coefficients using a kinetic approximation

Lejay

Maire²

2010

Computer Methods in Applied Mechanics and Engineering

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“…Computing λ 1 and λ 2 directly from a discretization of the elliptic operator L is intractable for all but the lowest dimensional systems. Instead, one must use Monte Carlo methods, such as those found in [11,12,17,18,23]. However, these studies, some of which use branching particles processes like Fleming-Viot (discussed below), only yield λ 1 .…”

Section: Numerical Parameters and Eigenvaluesmentioning

confidence: 99%

Numerical analysis of parallel replica dynamics

Simpson¹,

Luskin²

2013

ESAIM: M2AN

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Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of their time about the minima of the underlying potential, occasionally transitioning into different basins of attraction. The essential idea of parallel replica dynamics is that the exit time distribution from a given well for a single process can be approximated by the minimum of the exit time distributions of N independent identical processes, each run for only 1/N -th the amount of time.While promising, this leads to a series of numerical analysis questions about the accuracy of the exit distributions. Building upon the recent work in [4], we prove a unified error estimate on the exit distributions of the algorithm against an unaccelerated process. Furthermore, we study a dephasing mechanism, and prove that it will successfully complete.

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“…The algorithm stops when the proportion of still running particles is smaller than a given threshold. This approach can be used, for example, for long time simulation, or to estimate rare events, as, for example, in [6,9,10,23]. 4.6.…”

Section: Population Monte Carlomentioning

confidence: 99%

Simulation of diffusions by means of importance sampling paradigm

Deaconu¹,

Lejay²

2010

Ann. Appl. Probab.

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The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with importance sampling techniques. The first interest of this approach is that the weights can be easily computed from the density of the one-dimensional Brownian motion. Compared to the Euler scheme this method allows one to obtain a more accurate approximation of diffusions when one has to consider complex boundary conditions. The method provides also an interesting alternative to performing variance reduction techniques and simulating rare events.Comment: Published in at http://dx.doi.org/10.1214/09-AAP659 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Computing the principal eigenelements of some linear operators using a branching Monte Carlo method

Abstract: International audienceno abstrac

Cited by 6 publications

References 31 publications

Simulating diffusions with piecewise constant coefficients using a kinetic approximation

Simulating diffusions with piecewise constant coefficients using a kinetic approximation

Numerical analysis of parallel replica dynamics

Simulation of diffusions by means of importance sampling paradigm

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