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.

翻译：在分子动态中,受抑制过量的兰埃文动力学被用于模拟一组粒子的动作,这些粒子的动作是紧随一个参数($varepsilon$)的制约。模拟这些动态的最常用方案是以$mathb{R ⁇ d$为单位的Euler集成器和受限制的Euler集成器。两者的精度顺序都比较弱,但只有在取决于参数($\varepsilon$)大小的特定制度下才能正常工作。我们在本文件中提出了一个新的一致方法,其精确度不以$\varepslon$为单位,用于解决任何层面的受罚动态。此外,当$\varepslon$为零时,这种方法会与受限制的Euler制成法相汇合。数字实验证实了理论结论,即在衰弱的趋同环境中,以及异性测量,在高维度和高共度和高共度的横形组之间。