Random Walk Approximation for Irreversible Drift-Diffusion Process on Manifold:Ergodicity,Unconditional Stability and Convergence

作     者：Yuan Gao Jian-Guo Liu 

作者机构：Department of MathematicsPurdue UniversityWest LafayetteINUSA Departments of Mathematics and PhysicsDuke UniversityDurhamNCUSA 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2023年第33卷第6期

页      面：132-172页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Jian-Guo Liu was supported in part by NSF under awards DMS-2106988 by NSF RTG grant DMS-2038056 Yuan Gao was supported by NSF under awards DMS-2204288 

主　　题：Symmetric decomposition non-equilibrium thermodynamics enhancement by mixture exponential ergodicity structure-preserving numerical scheme 

摘      要：Irreversible drift-diffusion processes are very common in biochemical *** have a non-equilibrium stationary state(invariant measure)which does not satisfy detailed *** the corresponding Fokker-Planck equation on a closed manifold,using Voronoi tessellation,we propose two upwind finite volume schemes with or without the information of the invariant *** schemes possess stochastic Q-matrix structures and can be decomposed as a gradient flow part and a Hamiltonian flow part,enabling us to prove unconditional stability,ergodicity and error *** on the two upwind schemes,several numerical examples–including sampling accelerated by a mixture flow,image transformations and simulations for stochastic model of chaotic system–are *** two structurepreserving schemes also give a natural random walk approximation for a generic irreversible drift-diffusion process on a *** makes them suitable for adapting to manifold-related computations that arise from high-dimensional molecular dynamics simulations.