3054: Emphasizes basic programming skills in Matlab motivated by solving some basic mathematical problems. This course is helpful background for Introduction to Numerical Analysis, Mathematical Modeling, and many other upper level math courses.
5546: The second semester of the Calculus of Variations and Optimal Control sequence. This semester builds upon the minimization 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.
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,
- Applications to 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.