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 Focus:

• Numerical methods and error analysis for PDEs: Developing and analyzing high-order discretizations for hyperbolic, wave-propagation, and convection-dominated problems, with particular experience in discontinuous Galerkin methods.

• Quantity-of-interest (QoI)-oriented output enhancement: Recovering useful information from the error structures of existing numerical approximations through low-cost, non-intrusive reconstruction and post-processing, with particular emphasis on superconvergence analysis and SIAC filtering.

• Scalable scientific computing: Designing and evaluating numerical algorithms under realistic computational and software constraints, with experience in scalable solvers, parallel-in-time methods, and large-scale simulation software.

Emerging and Collaborative Directions

• Learning-assisted numerical methods for PDEs: Exploring data-driven components for tasks where fixed analytical models or heuristic rules are limiting, including feature detection, adaptive numerical decisions, and hybrid PDE–ML methods, with emphasis on robustness, cost, and comparison with strong conventional baselines.

• Industrial and multiphysics scientific computing: Contributing mathematical modeling, numerical algorithms, and HPC expertise to coupled engineering simulations, with attention to heterogeneous scales, software integration, parallel performance, and verification in realistic computational workflows.

For Students