AE 4803/8803 NUM/QNU -- Numerical Analysis and Algorithms
Description: This course covers fundamental algorithms used in computational analysis and design of engineering systems. Topics include numerical integration of ODEs, numerical solution of PDEs, uncertainty quantification, and learning/fitting models to data. Students will both implement these algorithms and analyze their behavior theoretically. Model problems will be drawn from applications in aerospace engineering. Primary audience is advanced aerospace undergraduates, graduate students interested in the material are welcome.
Pre-requisites: (1) introductory programming course or equivalent experience: you should be proficient with for loops, if/else statements, logical operators (and/or), and array indexing. (2) Undergraduate math through multivariable calculus and differential equations (MATH 1551, 1552, 1553, 2551, 2552).
CSE/AE 8803 MOR -- Model Reduction [Draft syllabus, accessible with GT login]
Description: Advanced graduate-level topics course introducing projection-based model reduction methods for surrogate modeling of high-dimensional systems arising from PDEs. Topics covered include proper orthogonal decomposition, reduced basis methods, system-theoretic methods including rational interpolation and balanced truncation, nonlinear model reduction, and data-driven model reduction. Homeworks will primarily involve implementing methods on model problems. The second part of the course will consist of a guided student-led reading group/journal club.
Pre-requisites: (1) graduate coursework in the numerical solution of PDEs, e.g. MATH 6640 a graduate-level CFD or finite element course. Numerical linear algebra and linear control theory helpful but not required. (2) scientific computing programming proficiency - you should be able to implement simple PDE solvers without help. Interested students unsure if they satisfy the pre-requisites can email me to discuss.
ACM 11 -- Introduction to Computational Science and Engineering: Spring 2021, Spring 2022 terms. *Received a 2021-2022 ASCIT Teaching Award from the Associated Students of Caltech.
ACM 213 -- Numerical Optimization: Spring 2022
ACM 270 -- Model Reduction for Large Scale Simulations: Winter 2021
16.s685 -- A Hands-on Introduction to Computational Engineering: co-instructor in Spring 2018, Spring 2019 terms
16.003 -- Unified Engineering: Fluid Dynamics: TA in Spring 2018
Other teaching activities