CAAM 699 - Section 2

Math Sciences VIGRE Seminar
Topics in Model Reduction

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.