Interdisciplinary Center for Applied Mathematics


Interdisciplinary Center for
Applied Mathematics

Computation and Analysis of Reduced-Order Models for Distributed Parameter Systems
Project Manager:	Jeff Borggaard (jborggaard@vt.edu)
Phone:	5402317667

Project Description

This project studies the development of reduced-order models. Our emphasis is on linear models for control and new methods for generating nonlinear models arising from fluid flows. We are also concerned with high-performance parallel algorithms for the generation of basis vectors and proposed looking at domain decomposition strategies. This project received support from the Air Force Office of Scientific Research under grant FA9550-05-1-0449 and the National Science Foundation under grant DMS-0513542.

For more information, consult our reduced-order modeling webpage.

Project Affiliates

Beattie, Christopher (Professor)

5402318279

beattie@math.vt.edu

Borggaard, Jeff (Mathematics: Professor)

5402317667

jborggaard@vt.edu

Gugercin, Serkan (Mathematics: Associate Professor)

5402317667

gugercin@math.vt.edu

Iliescu, Traian (Mathematics: Associate Professor)

5402317667

iliescu@math.vt.edu

Stoyanov, Miroslav (Ph.D. 2009)

Publications2010

I. Akhtar, J. Borggaard, and A. Hay, "Shape Sensitivity Analysis in Flow Models using a Finite-Difference Approach," Mathematical Problems in Engineering, 2010.

A. Hay, I. Akhtar, and J. Borggaard, "On the Sensitivity Analysis of Angle-of-Attack in a Model Reduction Setting," in Proc. 48th AIAA Aerospace Sciences Meeting and Exhibit, 2010,

2009

I. Akhtar, A. H. Nayfeh, and C. J. Ribbens, "On the Stability and Extension of Reduced-Order Galerkin Models in Incompressible Flows: A Numerical Study of Vortex Shedding," Theoretical and Computational Fluid Dynamics, vol. 23, iss. 3, pp. 213–237, 2009.

I. Akhtar, A. Hay, and J. Borggaard, "Sensitivity Analysis-Based Reduced-Order Models for Flow Past an Elliptic Cylinder," in Proc. 47th AIAA Aerospace Sciences Meeting and Exhibit, 2009,

2008

J. Borggaard, A. Duggelby, A. Hay, T. Iliescu, and Z. Wang, "Reduced Order Modeling of Turbulent Flows," in Proc. 2008 Mathematical Theory for Networks and Systems, 2008,

I. Akhtar, J. Borggaard, and J. A. Burns, "Reduced-Order Model for Optimal Control of Vortex-Shedding," in Proc. AIAA 4th Flow Control Conference, 2008,

2007

S. Gugercin A.C. Antoulas and C. A. Beattie, "H2 Model Reduction for large-scale dynamical systems," Accepted, SIMAX, 2007.

S. Gugercin, "An iterative SVD-Krylov based method for model reduction of large-scale dynamical systems," Accepted, Linear Algebra and Its Applications, 2007.

S. Gugercin and K. Willcox, "Krylov Projection Framework for Fourier Model Reduction," Automatica, 2007.

C. A. Beattie and S. Gugercin, "Krylov-based minimization for optimal H2 model reduction," in Proc. of the 46th IEEE Conference on Decision and Control, 2007,

2006

C. Beattie, J. Borggaard, S. Gugercin, and T. Iliescu, "A Domain Decomposition Approach to POD," in Proc. of the 45th IEEE Conference on Decision and Control, 2006,

C. A. Beattie and S. Gugercin, "Inexact Solves in Krylov-based Model Reduction," in Proc. of the 45th IEEE Conference on Decision and Control, 2006,

S. Gugercin A.C. Antoulas and C. A. Beattie, "A rational Krylov Iteration for Optimal H2 Model Reduction," in Proc. of MTNS 2006, 2006,

J. Borggaard and T. Iliescu, "Approximate Deconvolution Boundary Conditions for Large Eddy Simulation," Applied Math Letters, vol. 19, pp. 735–740, 2006.

J. Borggaard, "Optimal Reduced-Order Modeling for Nonlinear Distributed Parameter Systems," in Proc. Proc. 2006 American Control Conference, 2006,

2005

C. A. Beattie and S. Gugercin, "Krylov-based model reduction of second-order systems with proportional damping," in Proc. of the 44th IEEE Conference on Decision and Control, 2005,

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