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 will teach MATH 5546, Calculus of Variations and Optimal Control in the spring of 2014.

5546: The second semester of the Calculus of Variations and Optimal Control sequence. This semester builds upon the minimizations problems studied in the first semester and extends them to optimal control problems such as time optimal control and ultimately covers introductory theory of the control of distributed parameter systems and computational aspects.

In the fall semester, I am scheduled to teach MATH 5545 (Calculus of Variations and Optimal Control).

My research is in the development and analysis of computational tools for optimal design and control of nonlinear PDEs (usually Navier-Stokes equations). This covers a wide range of areas. A partial list is given below.

  • Sensitivity Analysis:
    • Adaptive Finite Element Calculations,
    • Automatic Differentiation,
    • Nearby Solutions,
    • 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,
    • Fluid Flow Control
  • Applied Mathematics / Computational Science:
    • Design of Energy Efficient Buildings,
    • Optimal Zonation for Groundwater Models

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