Publications [#372916] of Jian-Guo Liu

Papers Published

1. Gao, Y; Liu, JG, Random Walk Approximation for Irreversible Drift-Diffusion Process on Manifold: Ergodicity, Unconditional Stability and Convergence, Communications in Computational Physics, vol. 34 no. 1 (January, 2023), pp. 132-172 [doi] [reputed journal]
   (last updated on 2025/07/03)

   Abstract:
   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.