• 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

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

• 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

CV (pdf file)