@Article{CiCP-34-1,
author = {Yuan, Gao and Liu, Jian-Guo},
title = {Random Walk Approximation for Irreversible Drift-Diffusion Process on Manifold: Ergodicity, Unconditional Stability and Convergence},
journal = {Communications in Computational Physics},
year = {2023},
volume = {34},
number = {1},
pages = {132--172},
abstract = {<p style="text-align: justify;">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 structure-preserving 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0021},
url = {https://global-sci.com/article/79363/random-walk-approximation-for-irreversible-drift-diffusion-process-on-manifold-ergodicity-unconditional-stability-and-convergence}
}