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Reduced-order modeling for complex systems
Max Gunzburger
Mathematics and School of Computational Science, Florida State University
Abstract:
The computational approximation of solutions of complex systems suchas the Navier-Stokes equations is often a formidable task. Forexample, in feedback control settings where one often needs solutionsof the complex systems in real time, it would be impossible to uselarge-scale finite element or finite-volume or spectral codes. Forthis reason, there has been much interest in the development of low-dimensional models that can accurately be used to simulate andcontrol complex systems. We review some of the existing reduced-ordermodeling approaches, including reduced-basis methods and especiallymethods based on proper orthogonal decompositions techniques. We alsodiscuss a new approach based on centroidal Voronoi tessellations. Wediscuss the relative merits and deficiencies of the differentapproaches and also the inherent limitations of reduced-ordermodeling in general.
Thursday, May 17, 2007
4:00PM AP&M 6402
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Randolph E. Bank
Philip E. Gill
Michael Holst
Administrative Contact:
[ Click to Send Email ]
Max Gunzburger
Mathematics and School of Computational Science, Florida State University
Abstract:
The computational approximation of solutions of complex systems suchas the Navier-Stokes equations is often a formidable task. Forexample, in feedback control settings where one often needs solutionsof the complex systems in real time, it would be impossible to uselarge-scale finite element or finite-volume or spectral codes. Forthis reason, there has been much interest in the development of low-dimensional models that can accurately be used to simulate andcontrol complex systems. We review some of the existing reduced-ordermodeling approaches, including reduced-basis methods and especiallymethods based on proper orthogonal decompositions techniques. We alsodiscuss a new approach based on centroidal Voronoi tessellations. Wediscuss the relative merits and deficiencies of the differentapproaches and also the inherent limitations of reduced-ordermodeling in general.
Thursday, May 17, 2007
4:00PM AP&M 6402