Xiaochuan Tian

I am an Associate Professor in the Department of Mathematics at UC San Diego. My research focuses on mathematical modeling, applied analysis, and numerical methods for partial differential and integro-differential equations, with a particular interest in nonlocal modeling and meshfree approaches for solving PDEs/IDEs.

My current research topics include:

  • Calculus of variations, Theory of nonlocal function spaces, Asymptotic analysis, Γ-convergence
  • High order numerical methods, Meshfree methods, Petrov-Galerkin methods, Multiscale and Adaptive methods, Asymptotic compatible schemes
  • Nonlocal modeling in continuum mechanics

Research

My research interests include numerical analysis, applied PDEs, nonlocal models, fractional PDEs and multiscale modeling.

Group

Zhaolong Han
PhD. Candidate
Research Interests: Nonlocal Vector Calculus, Bourgain-Bresiz-Mironescu type Compactness, Asymptotically Compatible Schemes, Petrov-Galerkin Methods, Optimal Control

Qihao Ye
PhD. Candidate
Research Interests: Meshfree Methods, Fast Algorithms, Data-driven Discovery of Stochastic Dynamics, Reinforcement Learning

Yimeng Zhang
PhD. Candidate
Research Interests: Machine Learning Approach in Parameterized Dynamical Systems, Biochemical Reaction Systems, Neural Network Approximation Theory

Teaching

"A unique human capacity, separating people from animals, is the ability to pass information and knowledge from one generation to the next. "

Fall 2024: MATH 272A Numerical Partial Differential Equations