Research
Areas of Interest
Numerical Methods for Parabolic PDE and Interface Problems
I develop and analyze numerical methods for nonlinear PDE and interface problems, with particular attention to stability, accuracy, and efficient solvers.
- diffuse-interface approximation methods
- discontinuous Galerkin (DG) and finite element methods
- energy- and entropy-stable methods
- positivity-preserving methods
- adaptive mesh refinement
- multigrid methods and fast solvers
Complex Fluids
I study thermodynamically consistent models for complex fluids, phase transitions, and coupled transport processes.
- interfaces
- multiphase flows
- phase transitions
- non-isothermal models
- thermodynamically consistent models
- polymeric flows
- kinetic equations
Nonlinear PDE
My analytical work concerns fundamental properties of nonlinear PDE and their singular limits.
- properties of solutions
- singular perturbation problems
- asymptotic methods
- gamma convergence
- existence, uniqueness, and regularity
Biological Growth
I use mathematical models to investigate growth, progression, and membrane dynamics in biological systems.
- developmental biology
- spatiotemporal cancer-progression models
- membrane dynamics
Materials Science
I develop phase-field models and computational methods for structural evolution in complex materials.
- ionic materials
- phase-field and phase-field-crystal (PFC) methods
- crystallization
- material anisotropy
- structural phase transitions