Applied Mathematics
Wednesday,
April 19, 2017
11:00 AM - 12:00 PM
Vladimir Druskin
Scientific Advisor at Schlumberger Doll Research
"Geometric interpretations of reduced order models and applications to numerical PDEs and imaging"
Scientific Advisor at Schlumberger Doll Research
"Geometric interpretations of reduced order models and applications to numerical PDEs and imaging"
The reduced order model (ROM) is a small dynamic system that approximates response (transfer function) of a largescale dynamic system. The ROMs are routinely used in control and data-intensive computing. In his seminal work (1952) Mark Krein showed that one important (so-called Stieltjes) class of rational transfer functions can be equivalently realized via strings of point masses and weightless springs. This gave rise to network and finite-difference interpretation of the ROMs for linear dynamic systems, which include parabolic and hyperbolic PDEs with time-independent coefficients and also some elliptic problems. I will review important applications of this approach, such as discretization of exterior problems, solution of multiscale hyperbolic elasticity problems, and present recent results on linearization of inverse hyperbolic problems with multiple scattering via data-driven ROMs.
Contributors: Liliana Borcea, Stefan Guettel, Fernando Guevara Vasquez, Leonid Knizhnerman, Alexander Mamonov, Shari Moskow and Mikhail Zaslavsky.
Host: Guillaume Bal
Contributors: Liliana Borcea, Stefan Guettel, Fernando Guevara Vasquez, Leonid Knizhnerman, Alexander Mamonov, Shari Moskow and Mikhail Zaslavsky.
Host: Guillaume Bal
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