605 citations · 1.2k across the 29 of their papers we have counts for
29 papers
Unconditional Optimal Error Estimates and Energy Stability for a Linearly Implicit Mass-Lumped Projection Finite Element Method for the Harmonic Map Flow
Yongyong Cai, Xingwei Yang
We propose and analyze a linearly implicit mass-lumped finite element method for the heat flow of harmonic maps into the unit sphere. The method consists of a linear predictor foll…
Tensor gradient flow for rod-like liquid crystals from molecular model with closure approximation by quasi-entropy
Yongyong Cai, Jie Xu, Haixin Zhang
In tensor dynamics for liquid crystals derived from molecular models, a common problem is closure approximation. For rod-like molecules, the Bingham closure has proved to outperfor…
A robust hybridizable discontinuous Galerkin scheme with harmonic averaging technique for steady state of real-world semiconductor devices
Qingyuan Shi, Yongyong Cai, Chijie Zhuang +4
Solving real-world nonlinear semiconductor device problems modeled by the drift-diffusion equations coupled with the Poisson equation (also known as the Poisson-Nernst-Planck equat…
Revealing Excited States of Rotational Bose-Einstein Condensates
Jianyuan Yin, Zhen Huang, Yongyong Cai +2
Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations. In this study, the ground and excited states of the rotational Bose-Einstein condens…
Stabilized exponential time differencing schemes for the convective Allen-Cahn equation
Yongyong Cai, Lili Ju, Rihui Lan +1
The convective Allen-Cahn equation has been widely used to simulate multi-phase flows in many phase-field models. As a generalized form of the classic Allen-Cahn equation, the conv…
Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation
Weizhu Bao, Yongyong Cai, Feng Yue
Improved uniform error bounds on time-splitting methods are rigorously proven for the long-time dynamics of the weakly nonlinear Dirac equation (NLDE), where the nonlinearity stren…