SIAM Conference on Control and its Applications, July 11-14, 2001, Town and Country Resort Hotel, San Diego, CA


Short Course: Flow Control and Optimization

Half day short course: July 10, 2001, Town and Country Resort Hotel, San Diego, California

Organizer and Instructor:

Max D. Gunzburger
Iowa State University


The development, implementation, and analysis of computational algorithms for flow control and optimization are presented. The developmental aspects are first presented in abstract settings that make generalizations easy; then, they are presented in concrete settings which serve to illustrate and reinforce the abstract development. Difficulties encountered (and methods for overcoming them) in practical implementations of the algorithms are discussed through a series of illustrative examples. Analytical methods and results are discussed not only to see what possibilities exist for the rigorous analyses of flow control and optimization problems and algorithms, but also to illustrate the practical implications of such analyses. Wherever possible, comparisons and value judgements are made between different available methodologies.


The goals of the course are to introduce how to develop computational algorithms for flow control and optimization problems, how to determine which methodologies are best suited for a specific setting, how to overcome potential implementation pitfalls, and how such problems and algorithms can be analyzed.

Level of Material

25% introductory; 50% intermediate; 25% advanced

Recommended Background

4/5 of the course will be easily accessible to someone with knowledge of vector calculus as well as some knowledge of fluid mechanics and computational fluid mechanics. The majority of the course will be accessible to someone with knowledge of just one of these. A small portion (less than 1/5) of the analysis aspects of the course requires, for a full understanding, substantial familiarity with advanced mathematical concepts; however, others with less mathematical sophistication will still benefit from the theoretical material presented in the course. Both novices and all but the most experienced practitioners can benefit from some or all of the course materials.

Who Should Attend?

Industrial, laboratory, and academic engineers who want to learn about how to develop and apply computational algorithms for solving practical flow control and optimization problems. Such problems are ubiquitous in industry including, among many others, the aerospace, automotive, computer, chemical, environmental, metals, petroleum, semiconductor, and weather forecasting industries. There are many application to military systems as well. Applied mathematicians interested in applications should be equally interested in the course. Furthermore, many of them would also have interest in the theoretical aspects of the course.

About the Instructor

Max D. Gunzburger is a Professor and Chair of the Department of Mathematics at Iowa State University. His research interests include; flow control (and other control problems for partial differential equations), least-squares finite element methods, superconductivity, centroidal Voronoi tessellations, and domain decomposition, to name a few. In the flow control and optimization setting, he has been a leading contributor to the development of computational algorithms and analytic theories for flow control and optimization. He has studied sensitivity and adjoint-based methods applied to value control and shape design problems. His books include; Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice and Algorithms; Academic, Boston, 1989, Incompressible Computational Fluid Dynamics: Trends and Advances; Cambridge, Cambridge, 1993; edited with R. Nicolaides, Optimal Control and Design; Birkhauser, Boston, 1995; edited with J. Borggaard, J. Burkardt, and J. Peterson, and Flow Control; Springer, New York, 1995; edited.

Course Outline (subject to change)

1. A very brief history of flow control and optimization
2. Three approaches to optimal control and optimization problems
2.1 One-shot methods
2.2 Sensitivity-based optimization methods
2.3 Adjoint-based optimization methods
2.4 Time-dependent problems
2.5 Different types of controls
3. Illustration of sensitivity-based optimization methods
3.1 An optimization problem for Euler flows
4. Illustration of adjoint-based optimization methods
4.1 A drag minimization problem for time-dependent, incompressible, viscous flows
4.2 Uncoupling of the optimality system
5. Discretize then differentiate vs. differentiate then discretize
6. Questions of accuracy and consistency
6.1 Insensitive functionals, inconsistent gradients, spurious minima, and regularized functionals
6.2 Sensitivities for flows with discontinuities
7. Reducing the costs of optimization and control calculations
7.1 Storage savings schemes for time-dependent adjoint- based optimizations
7.2 Reduced order methods
7.3 Regularization of the cost functional
8. Theoretical aspects
8.1 Analysis of control and optimization problems for the Navier-Stokes system
8.2 Analysis of algorithms for flow control and optimization


Seats are limited. Please register before the deadline. To register, please submit the Preregistration Form. Submit completed form with registration payment to reach SIAM on or before June 7, 2001. Registration fee includes coffee breaks and lunch on Sunday, July 10.

©2001, Society for Industrial and Applied Mathematics
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