About Me

I am a professor of Mathematics in the College of Science at Virginia Tech. I am also a member of the Interdisciplinary Center for Applied Mathematics.

I am on sabbatical for the 2015-2016 academic year.

My research is in the development and analysis of computational tools for optimal design and control of nonlinear PDEs (for example, active and passive control of fluid flows modeled by the Navier-Stokes equations). This research requires developments in a wide range of mathematical topics. A partial list is given below.

  • Sensitivity Analysis:
    • Adaptive Finite Element Calculations,
    • Automatic Differentiation,
    • Local Improvements in Reduced-Order Models,
    • Nearby Solutions,
    • Stability Analysis,
    • Uncertainty Quantification
  • Optimal Design Algorithms:
  • Computational Methods for Control of PDEs:
    • Approximation to PDE Riccati Equations,
    • Data Assimilation,
    • Optimal Actuator and Sensor Placement
  • Model Reduction Methods:
    • Principal Interval Decomposition,
    • Proper Orthogonal Decomposition,
    • Extensions to Parameter Dependent Models,
    • Extensions to Complex Turbulent Flows,
    • Applications to Fluid Flow Control
  • Applied Mathematics / Computational Science:
    • Design of Energy Efficient Buildings,
    • Computational Fluid Dynamics,
    • Modeling for Ventilation in Mines,
    • Optimal Zonation for Groundwater Models

A more complete description of my research can be found here.