# Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics

1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : Motivated by the development of efficient Monte Carlo methods for PDE models in molecular dynamics, we establish a new probabilistic interpretation of a family of divergence form operators with discontinuous coefficients at the interface of two open subsets of $\mathbb{R}^d$. This family of operators includes the case of the linearized Poisson-Boltzmann equation used to compute the electrostatic free energy of a molecule. More precisely, we explicitly construct a Markov process whose infinitesimal generator belongs to this family, as the solution of a SDE including a non standard local time term related to the interface of discontinuity. We then prove an extended Feynman-Kac formula for the Poisson-Boltzmann equation. This formula allows us to justify various probabilistic numerical methods to approximate the free energy of a molecule. We analyse the convergence rate of these simulation procedures and numerically compare them on idealized molecules models.
Keywords :
Type de document :
Article dans une revue
ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2010, 44 (5), pp.997-1048
Domaine :

Littérature citée [35 références]

https://hal.inria.fr/inria-00459411
Contributeur : Nicolas Champagnat <>
Soumis le : mardi 23 février 2010 - 18:51:15
Dernière modification le : jeudi 15 mars 2018 - 16:56:04
Document(s) archivé(s) le : jeudi 18 octobre 2012 - 15:46:01

### Fichier

HAL-PB.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : inria-00459411, version 1

### Citation

Mireille Bossy, Nicolas Champagnat, Sylvain Maire, Denis Talay. Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2010, 44 (5), pp.997-1048. 〈inria-00459411〉

### Métriques

Consultations de la notice

## 379

Téléchargements de fichiers