6 citations · 9 across the 2 of their papers we have counts for
3 papers
math.NA2020★ 3 cited
Efficient, positive, and energy stable schemes for multi-D Poisson-Nernst-Planck systems
Hailiang Liu, Wumaier Maimaitiyiming
In this paper, we design, analyze, and numerically validate positive and energy-dissipating schemes for solving the time-dependent multi-dimensional system of Poisson-Nernst-Planck…
math.NA2019
Positive and free energy satisfying schemes for diffusion with interaction potentials
Hailiang Liu, Wumaier Maimaitiyiming
In this paper, we design and analyze second order positive and free energy satisfying schemes for solving diffusion equations with interaction potentials. The semi-discrete scheme…
math.NA2019★ 6 cited
Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system
Hailiang Liu, Wumaier Maimaitiyiming
The Poisson-Nernst-Planck (PNP) system is a widely accepted model for simulation of ionic channels. In this paper, we design, analyze, and numerically validate a second order uncon…