## Research interests

### Active (in no particular order)

- Uncertainty quantification
- numerical methods for partial differential equations with random inputs
- analyses, numerical analyses
- high-dimensional approximation
- sparse grids
- sampling
- reduced-order modeling
- application to fluids, structures, and other settings

- Nonlocal and fractional derivative models
- mechanics
- subdifussion and superdifussion
- bounded domains
- reduced-order modeling
- wave problems
- nonlocal models with random inputs
- multiscale implementations
- nonlocal calculus
- fractional derivative models as special cases of nonlocal models
- control and optimization problems
- obstacle problems
- jump processes

- Climate modeling
- ocean
- ice sheets
- regional modeling
- variable resolution grid generation
- component coupling
- spatially dependent time stepping
- finite volume methods

- Reduced-order modeling
- proper orthogonal decomposition
- reduced basis, including greedy algorithms
- clustering approaches
- ROM for bifurcation problems
- ROM for uncertainty quantification
- ROM for control and optimization

- Centroidal Voronoi tessellations
- grid generation
- image processing
- reduced-order modeling
- improved CVT construction algorithms
- other applications

- Control and optimization
- PDE constrained
- adjoint methods
- flow control
- application to uncertainty quantification

- Finite element methods
- Least-squares finite element methods
- Navier-Stokes equations
- Boundary condition treatment
- Stabilized finite element methods
- Compatible finite element methods
- Discontinuous Galerkin
- Hyperbolic equations
- Superconductivity, MHD, other applications

### Somewhat active (in no particular order)

- Subsurface flows including karst aquifers
- Superconductivity including two-band superconductors
- Multiscale material modeling

### Dormant but never dead (in no particular order)

- Finite volume, spectral, wavelet, and other numerical methods for PDEs
- Partial differential equations
- Domain decomposition
- Coupled multiphysics problems
- Multiscale multiphysics problems
- Other general numerical analysis and methods
- Fluid and solid mechanics
- Mesh generation
- Multidisciplinary simulation and optimization
- Quasicontinuum methods
- Atomistic to continuum coupling
- Linear algebra
- Fluid dynamics and acoustics
- Financial mathematics
- Image processing
- Computational biology
- Multiscale viscosity methods
- Gas centrifuges and isotope separation

Last updated: August 24, 2016 by Max Gunzburger