Research

“The purpose of computation is insight, not numbers.” — Richard Hamming

My academic training is rooted in pure mathematics, with a strong focus on theoretical rigor. That foundation continues to inform my approach. However, in recent years, I have become increasingly drawn to computational mathematics as a bridge between mathematical insight and real-world complexity.

I am particularly interested in problems where high-level theory meets practical need—especially in the context of large-scale simulation, engineering-driven modeling, and high-performance computing. My work centers on the development of high-order numerical methods, such as discontinuous Galerkin schemes, and their application to complex coupled systems.

I believe that effective mathematical research balances depth and purpose. I value approaches that go beyond technical intricacy for its own sake, aiming instead for clarity, efficiency, and relevance in both design and application.

Research Interests:

• Numerical solutions of partial differential equations (PDEs): Focus on high-order discretization methods such as the discontinuous Galerkin (DG) method for hyperbolic and convection-dominated problems.
• Superconvergence and accuracy enhancement: Rigorous theoretical analysis and development of post-processing techniques to improve solution accuracy and computational efficiency.
• High-performance computing (HPC): Scalable solvers, parallel-in-time algorithms, and integration with industrial simulation software for large-scale scientific computing.
• Machine learning in numerical methods: Incorporating deep learning for data-driven acceleration, adaptive modeling, and hybrid PDE-ML frameworks to enhance performance and predictive capability.
• Coupled multi-physics simulations: Design and analysis of robust and efficient numerical algorithms for complex multi-physics systems, emphasizing the synergy between mathematical modeling, numerical analysis, and HPC-driven implementation in engineering and scientific applications.

Talks

For international applicants: Please demonstrate your academic competence, research potential, and alignment with my research focus. All candidates, including Chinese applicants, will be evaluated using the same academic criteria, and selection will be based on overall merit.