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Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2022

A uniformly accurate scheme for the numerical integration of penalized Langevin dynamics

Résumé

In molecular dynamics, penalized overdamped Langevin dynamics are used to model the motion of a set of particles that follow constraints up to a parameter $\varepsilon$. The most used schemes for simulating these dynamics are the Euler integrator in $\mathbb{R}^d$ and the constrained Euler integrator. Both have weak order one of accuracy, but work properly only in specific regimes depending on the size of the parameter $\varepsilon$. We propose in this paper a new consistent method with an accuracy independent of $\varepsilon$ for solving penalized dynamics on a manifold of any dimension. Moreover, this method converges to the constrained Euler scheme when $\varepsilon$ goes to zero. The numerical experiments confirm the theoretical findings, in the context of weak convergence and for the invariant measure, on a torus and on the orthogonal group in high dimension and high codimension.
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Dates et versions

hal-04347712 , version 1 (15-12-2023)

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Paternité

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Adrien Laurent. A uniformly accurate scheme for the numerical integration of penalized Langevin dynamics. SIAM Journal on Scientific Computing, 2022, 44 (5), pp.A3217-A3243. ⟨10.1137/21M1455188⟩. ⟨hal-04347712⟩
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