Research Projects & Outcomes

Research Interests

• Design, analysis, and implementation of numerical methods for partial differential equations.
• Computational mathematics with high-performance computing for interdisciplinary multi-physics and multi-scale real-world problems. In particular, focus on subsurface applications.
• Free-boundary multiphase problems using projection methods for Navier-Stokes and level set methods with adaptive finite elements. Video
• Analysis and computation of physics preserving (local mass conservation, locking free, maximum principle, and so on) enriched Galerkin methods for coupling flow and transport in porous media.
• Multi physical and multi scale problems in porous pedia, including fracture systems; phase-field fracture with Biot thermo-hydro-mechanic-chemical coupling.
• Employing machine learning / deep learning / neural networks for solving inverse problems, and data assimilation problems based on physical partial differential equations.