An exponential timestepping algorithm for diffusion with discontinuous coefficients

Abstract : We present a new Monte Carlo algorithm to simulate diffusion processes in presence of discontinuous convective and diffusive terms. The algorithm is based on the knowledge of close form analytic expressions of the resolvents of the diffusion processes which are usually easier to obtain than close form analytic expressions of the density. In the particular case of diffusion processes with piecewise constant coefficients, known as Skew Diffusions, such close form expressions for the resolvent are available. Then we apply our algorithm to this particular case and we show that the approximate densities of the particles given by the algorithm replicate well the particularities of the true densities (discontinuities, bimodality, ...) Besides, numerical experiments show a quick convergence.
Type de document :
Pré-publication, Document de travail
2018
Liste complète des métadonnées

https://hal.inria.fr/hal-01806465
Contributeur : Antoine Lejay <>
Soumis le : samedi 2 juin 2018 - 20:45:55
Dernière modification le : mercredi 10 octobre 2018 - 10:09:36
Document(s) archivé(s) le : lundi 3 septembre 2018 - 15:59:13

Fichier

simulation_exponential_time_st...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01806465, version 1

Citation

Antoine Lejay, Lionel Lenôtre, Géraldine Pichot. An exponential timestepping algorithm for diffusion with discontinuous coefficients. 2018. 〈hal-01806465〉

Partager

Métriques

Consultations de la notice

235

Téléchargements de fichiers

68