For students
If you are an undergraduate or graduate student interested in working with me, take a look at the research areas below. If any of these topics interest you and you would like to explore a possible research project, feel free to reach out to me.
Projects can range from introductory computational work to more advanced research problems, depending on your background and interests.
Helpful preparation includes linear algebra, numerical analysis, and scientific programming.
Reading group
Weekly research reading group at SDU
I organize a weekly research reading group at SDU University. We study foundational ideas in computational mathematics and fluid dynamics and discuss recent papers and developments related to our research interests.
Location: TBD
Book for Fall 2026: Steven L. Brunton and J. Nathan Kutz,
Data-Driven Science and Engineering
Current directions
Research themes
- Finite element methods: fitted and unfitted discretizations for PDEs on complex, moving, and evolving domains.
- Computational fluid dynamics: numerical methods for the Navier–Stokes equations, Shallow Water Equations, and coupled or multiphysics PDE systems.
- Reduced-order modeling: Proper Orthogonal Decomposition (POD), Reduced Order Models (ROMs), and related data-driven reduction techniques.
- Scientific machine learning: machine learning for fluid dynamics, data-driven modeling of dynamical systems, and efficient surrogate models for PDE simulations.
Recommended reading
Books and notes
- Steven L. Brunton and J. Nathan Kutz, Data-Driven Science and Engineering
- Bernd R. Noack and Steven L. Brunton, Data-Driven Fluid Mechanics
- Stephen Boyd and Lieven Vandenberghe, Convex Optimization
- Lloyd N. Trefethen and David Bau III, Numerical Linear Algebra
- Gene H. Golub and Charles F. Van Loan, Matrix Computations
- Yousef Saad, Iterative Methods for Sparse Linear Systems
- John K. Hunter and Bruno Nachtergaele, Applied Analysis
- Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri, Numerical Mathematics
Software to explore
Scientific computing tools
Finite element methods
- FEniCSx — a Python-friendly platform for automated finite element methods.
- deal.II — a comprehensive C++ finite element library with extensive tutorials.
- Netgen/NGSolve — high-performance multiphysics finite element software with Python and C++ interfaces.
Linear algebra and solvers
- PETSc — scalable parallel solvers, preconditioners, and scientific-computing data structures.
- Trilinos — a collection of C++ packages for linear algebra, nonlinear solvers, and optimization.
- Eigen — a lightweight C++ library for dense and sparse linear algebra.