Applied Mathematics and Wave Phenomena
Applied Mathematics and Wave Phenomena focuses on solving problems that are inherently interdisciplinary with direct physical applications to fields that span the sciences and engineering. Such research invariably leads to studying complex behavior that require tools from mathematical modelling, analysis, and numerical simulation to gain a better understanding of the underlying physical phenomena. Application areas include fluid dynamics, plasma physics, fracture mechanics, hydrological chemical reaction networks, transport phenomena, inverse problems, geophysics, and signal processing. Topics of interest include numerical methods for solving partial differential equations, approximation theory, machine learning, wave motion, nonlinear dynamics, qualitative structure and bifurcation theory, complex networks, and optimization, among others.
- Meshfree Approximation Methods
- Radial Basis Functions
- Approximation Theory
- Numerical Solution of PDEs
- Spline Theory
- Computer-Aided Geometric Design
- Forward and inverse acoustic and electromagnetic scattering in 3-D.
- Efficient algorithms for the Stokes and Navier-Stokes equations on rotating surfaces.
- Quadrature finite element methods for elliptic, parabolic and hyperbolic problems.
- Free surface nonlinear evolutionary systems with applications.
Research Groups: Martin Group, CWP, CASERM
- Near-surface, engineering, environmental and urban geophysics
- Analysis of large sensor networks
- Fiber-optic sensing, including distributed acoustic sensing
- Signal processing, imaging, and inverse problems
- Data-intensive high performance computing
- Passive seismic methods
- Scattering, diffraction and propagation of waves
- Waves in anisotropic and inhomogeneous media
- Fracture mechanics; diffraction by cracks
- Integral equations, especially hypersingular equations
- Zeroth-order optimization and applications
- Signal processing, particularly compressed sensing
- Learning-to-optimize for inverse problems
- Nonlinear dimensionality reduction
- First passage percolation
Research Groups: Math Bio, Hydrology Research Group
- Analysis of Partial Differential Equations
- Kinetic Theory
- Chemical Reactions Dynamics
- Lagrangian Numerical Methods for transport phenomena
Samy Wu Fung
- Inverse Problems, Optimization, Deep Learning
- Optimal Control, Mean Field Games