ME 397 (unique number = 17778)
CAM 397 (unique number = 63613)

Computational Optimization of Systems Governed by Partial Differential
Equations

Instructor: Omar Ghattas (omar@ices.utexas.edu; www.cs.cmu.edu/~oghattas)

Meeting time: Tues/Thurs, 9 to 11am (not a typo)
Office hours: Tues/Thurs 11am-noon, plus feel free to email or call to
set up an appointment for other times

Location: ETC 5.130

Description:

This course provides an introduction to the numerical solution of
nonlinear optimization problems that are governed by systems of
partial differential equations (PDEs), i.e. "PDE-constrained
optimization." The focus of the course is on regularization,
variational formulations, finite element approximation, direct and
adjoint sensitivity analysis, control and state inequalities, and
large-scale optimization algorithms. Settings covered include inverse
problems and parameter estimation, optimal design (including shape
optimization), and optimal control. Students will develop numerical
implementations and solutions of model problems in each of these
problem classes using a high-level finite element toolkit.
Applications to problems in continuum fluid, solid, and biomechanics
and transport.

Prerequisites:

Graduate standing or consent of instructor. Some background in
numerical linear algebra, finite element methods, and nonlinear
optimization is desirable; however, much of the required mathematical
background will be covered at the beginning of the course, albeit
quickly. If in doubt, contact me.