6 papers
Addressing complex boundary conditions of miscible flow and transport in two and three dimensions with application to optimal control
Yiqun Li, Hong Wang, Xiangcheng Zheng
We investigate complex boundary conditions of the miscible displacement system in two and three space dimensions with the commonly-used Bear-Scheidegger diffusion-dispersion tensor…
An equivalent formulation of Sonine condition
Xiangcheng Zheng
Sonine kernel is characterized by the Sonine condition (denoted by SC) and is an important class of kernels in nonlocal differential equations and integral equations. This work pro…
Understanding high-index saddle dynamics via numerical analysis
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
High-index saddle dynamics (HiSD) serves as a competitive instrument in searching the any-index saddle points and constructing the solution landscape of complex systems. The Lagran…
Local modification of subdiffusion by initial Fickian diffusion: Multiscale modeling, analysis and computation
Xiangcheng Zheng, Yiqun Li, Wenlin Qiu
We propose a local modification of the standard subdiffusion model by introducing the initial Fickian diffusion, which results in a multiscale diffusion model. The developed model…
Semi-implicit method of high-index saddle dynamics and application to construct solution landscape
Yue Luo, Lei Zhang, Pingwen Zhang +2
We analyze the semi-implicit scheme of high-index saddle dynamics, which provides a powerful numerical method for finding the any-index saddle points and constructing the solution…
Mathematical and numerical analysis to shrinking-dimer saddle dynamics with local Lipschitz conditions
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
We present a mathematical and numerical investigation to the shrinkingdimer saddle dynamics for finding any-index saddle points in the solution landscape. Due to the dimer approxim…