研究 / Research

Research & Publications

My research focuses on computational and applied mathematics — developing efficient, energy-stable numerical schemes for phase-field models and interfacial dynamics. I work on both the theoretical foundations (unconditional stability, convergence analysis) and practical algorithms (decoupled solvers, high-order methods).

Publications

2026

Efficient, Decoupled, Second- and Third-Order IMEX-RK Schemes with Original-Form Energy Stability for the Anisotropic Phase-Field Dendritic Growth Model

Jianan Li, Zhaoqing Xu (co-first), Jiang Yang, Xiaofeng Yang · SIAM Journal on Scientific Computing (SISC), 48(2), B233–B261, 2026.

2026

Dihedral-Symmetry-Preserving and Energy-Stable Spectral Schemes for the Two-Dimensional Anisotropic Phase-Field Dendritic Growth Model

Zhaoqing Xu (co-first), Jianan Li, Jiang Yang, Xiaofeng Yang · Under review at Computer Methods in Applied Mechanics and Engineering (CMAME), 2026.

2026

Unconditional Original Energy-Dissipative and MBP-Preserving Second-Order IMEX-RK Schemes for the Allen–Cahn Equation with Degenerate Mobility

Jianan Li, Tao Tang, Zhaoqing Xu, Jiang Yang · Submitted to SIAM Journal on Numerical Analysis (SINUM), 2026.

Manuscripts in Preparation

—

A Sticky Particle Method for the Euler-Alignment System

Alina Chertock, Changhui Tan, Zhaoqing Xu · In preparation.

—

Symmetrized Transferable Neural Network Collocation Methods for the Allen–Cahn and Cahn–Hilliard Equations

Zhaoqing Xu, Lili Ju, Xiaofeng Yang · In preparation.

Presentations

2026

North American High Order Methods Conference (NAHOMCon)

Contributed Talk — Efficient, decoupled IMEX-RK schemes for the anisotropic phase-field dendritic growth model · Santa Fe, NM, June 2026.

Selected Topics

  • Energy stability — original-form energy laws, unconditional dissipation, maximum bound principle (MBP)
  • High-order IMEX methods — second- and third-order Runge–Kutta, spectral collocation
  • Structure preservation — dihedral symmetry, positivity, volume conservation
  • Dendritic growth — anisotropic phase-field models, solidification dynamics

Full CV available here. Code and preprints will be linked as they are released.