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CAAM 699 - Section 2
Math Sciences VIGRE Seminar Fall 2008 |
About this Course
Model reduction seeks to replace a large-scale system of differential or difference equations by a system of substantially lower dimension that has nearly the same response characteristics. There are extensive applications in circuit simulation, fluid dynamics, structural dynamics, climate modeling and many others.
CAAM 699 (section 2) is a research seminar on model reduction.
Seminar participation will consist of reading, discussing, and presenting
current research and survey papers in various aspects of model reduction.
Time and Room
Fridays 3:00pm-4:00pm, DH2014
Talks
| Aug. 29 | Organizational Meeting |
| Sept. 05 | Saifon Chaturantabut: Proper Orthogonal Decomposition (POD) Slides Additional Reading: S. Volkwein, Model Reduction using Proper Orthogonal Decomposition. Lecture Notes, 41 pages. |
| Sept. 12 | no seminar |
| Sept. 19 | Timo Reis: Model Reduction of Electrical Circuits Slides . |
| Sept. 26 | Saifon Chaturantabut: The Empirical Interpolation Method Slides |
| Oct 3 | Danny Sorensen: Applications and Implementation of the Empirical Interpolation Method |
| Oct 10 | Danny Sorensen: Why the Empirical Interpolation Method works |
| Oct 24 | Timo Reis: Towards Model Reduction for Nonlinear Electrical Circuits |
| Oct 31 | no seminar |
| Nov 7 | Matthias Heinkenschloss: Model Reduction for Systems with Local Nonlinearities |
| Nov 14 | Timo Reis: Circuit Synthesis - An MNA Approach Slides . |
| Nov 21 | no seminar |
| SPECIAL LECTURE: Wednesday Nov 26, 2pm, DH1064 | Shervin Bagheri (Department of Mechanics, Royal Institute of Technology (KTH), Stockholm) Linear Stability and Control of Fluid Flows: Coping with High-Dimensional Discretizations Abstract: The systems that arise in fluid mechanics are inevitably too complex to meet expediency requirements of standard stability analysis, optimization and control. Recent advances in computational methods have enabled global stability analyses of flows with nearly arbitrary complexity and have furnished the possibility to assess fully two- and three-dimensional base flows as to their stability and response behavior to general three-dimensional perturbations. Specifically, the combination of new efficient methods for computing steady-state solutions (such as the selective frequency damping) and for treating very large eigenvalue problems (such as the Arnoldi method implemented in the software package ARPACK) based on only minimal modifications of existing numerical simulation codes has provided the necessary tools for an encompassing study of the disturbance behavior in complex flows. At the same time, many powerful linear systems and control theoretical tools that have been out of reach for the fluid mechanics community are now available due to the recent advances of matrix-free methods (such as snapshot-based balanced truncation). In this talk, stability analysis and model reduction for control design of the linearized Navier/Stokes equations are shown to results in various very large eigenvalue problems. The techniques discussed to solve these problems share a common methodology: only snapshots of flow fields at different points in time are used and no large matrices are stored. Therefore the main tool is a numerical code that time integrates the forward and adjoint governing equations. |
Participants
| Saifon Chaturantabut | E-mail: saifon.chaturantabut AT rice.edu |
| Bosen Du | E-mail: Bosen.Du AT rice.edu |
| Matthias Heinkenschloss | E-mail: heinken AT caam.rice.edu |
| Kun Liu | E-mail: Kun.Liu AT rice.edu |
| Ryan Nong | E-mail: ryannong AT caam.rice.edu |
| Timo Reis | E-mail: Timo.Reis AT rice.edu | Danny C. Sorensen | E-mail: sorensen AT rice.edu |
Note on Disability Based Accommodations
If you have a documented disability that will impact your work in this class, please contact me to discuss your needs. Additionally, you will need to register with the Disability Support Services Office in the Ley Student Center.This web page is located at http://www.caam.rice.edu/~caam699-2 and maintained by Matthias Heinkenschloss.