A Liouville type theorem for higher order Hardy–Hénon equation in R^n
Tingzhi Cheng and Shuang Liu
Journal of Mathematical Analysis and Applications 444, no. 1 (2016): 370-389. Download
Invasive behaviour under competition via a free boundary model: a numerical approach
Kamruzzaman Khan, Shuang Liu, Timothy M. Schaerf, and Yihong Du
Journal of Mathematical Biology 83, no. 3 (2021): 1-43. Download
A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem
Shuang Liu, Qi Tang, and Xian-Zhu Tang
SIAM Journal on Scientific Computing 43, no. 6 (2021): B1198-B1225. Download
Cell Polarity and Movement with Reaction-Diffusion and Moving Boundary: Rigorous Modeling and Robust Simulations
Shuang Liu, Li-Tien Cheng, and Bo Li
Submitted to SIAM Journal on Applied Mathematics. arXiv
Numerical PDE's, Free Boundary Problems
Numerical methods for a class of reaction-diffusion equations with free boundaries
Shuang Liu, Yihong Du, and Xinfeng Liu
International Journal of Computer Mathematics 97, no. 5 (2020): 959-979. Download
Numerical methods for a two-species competition-diffusion model with free boundaries
Shuang Liu and Xinfeng Liu
Mathematics 2018, 6, 72. Download
Krylov implicit integration factor method for a class of stiff reaction-diffusion systems with moving boundaries
Shuang Liu and Xinfeng Liu
Discrete & Continuous Dynamical Systems-B 25, no. 1 (2020): 141-159. Download
Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness
Zhichao Peng, Daniel Appelö, and Shuang Liu
Submitted to Journal of Scientific Computing. arXiv
Integration factor combined with level set method for reaction-diffusion systems with free boundary in high spatial dimensions
Shuang Liu and Xinfeng Liu
Submitted to Communications on Applied Mathematics and Computation. arXiv
Biomolecular Modeling and Simulations
Explicit-Solute Implicit-Solvent Molecular Simulation with Binary Level-Set, Adaptive-Mobility, and GPU.
Shuang Liu, Zirui Zhang, Li-Tien Cheng, and Bo Li
Journal of Computational Physics (accepted). arXiv