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

作　　者：Yuan Gao Jian-Guo Liu 

机构地区：[1]Department of Mathematics,Purdue University,West Lafayette,IN,USA [2]Departments of Mathematics and Physics,Duke University,Durham,NC,USA

出　　处：《Communications in Computational Physics》2023年第6期132-172,共41页计算物理通讯（英文）

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.

摘　　要：Irreversible drift-diffusion processes are very common in biochemical reactions.They have a non-equilibrium stationary state(invariant measure)which does not satisfy detailed balance.For 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 measure.Both 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 estimates.Based 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 conducted.These two structurepreserving schemes also give a natural random walk approximation for a generic irreversible drift-diffusion process on a manifold.This makes them suitable for adapting to manifold-related computations that arise from high-dimensional molecular dynamics simulations.

关 键 词：Symmetric decomposition non-equilibrium thermodynamics enhancement by mixture exponential ergodicity structure-preserving numerical scheme 

分 类 号：O17[理学—数学]