I will teach MATH 5545, Calculus of Variations and Optimal Control in the fall of 2014.
5545: The first semester of the Calculus of Variations and Optimal Control sequence. This semester introduces the necessary and sufficient conditions for an important class of minimization problems.
In the spring semester, I am scheduled to teach MATH 3054 (Programming and Mathematical Problem Solving) and 5546 (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:
- Convergence Theory Based on Asymptotic Consistency,
- Forebody Simulator Design Problem,
- Parameter Estimation
- 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.