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 Introduction to Numerical Analysis and MATH 5465, Numerical Analysis in the fall of 2012.
4445: The first semester of the Introduction to Numerical Analysis course analyzes computational approaches to systems of linear and nonlinear algebraic equations. Numerical solutions to eigenvalue problems are also covered.
5465: The first semester of Numerical Analysis emphasizes error analysis for numerical linear algebra including linear systems and eigenvalue problems.
I taught MATH 3054 (current number 4984), Programming and Mathematical Problem Solving in the spring of 2012.
3054: Emphasizes basic programming skills in Matlab and is helpful in Introduction to Numerical Analysis, Mathematical Modeling, and other upper level math courses.
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.
