Location: Heizkraftwerk (Toaster), Hörsaal 1132|603 - HKW5, from 3 pm - 4 pm

Prof. Anthony Patera, Ph.D. - Parametrized Partial Differential Equations: Mathematical Models, Computational Methods, and Applications

Ford Professor of Engineering and Professor of Mechanical Engineering
Department of Mechanical Engineering, Massachusetts Institute of Technology, USA


Parametrized partial differential equations (pPDEs) play an important role in many physical disciplines and a wide variety of engineering applications. We first discuss the interplay between mathematical model and subsequent numerical treatment. We next describe two mathematical features of pPDEs which inform associated computational methods: low-dimensionality, as suggested by the parametric manifold; parameter spatial localization, as suggested by evanescence. We then consider several computational perspectives: user interfaces and apps; model reduction, in particular the reduced basis method
and the reduced basis component method; data assimilation and classification. Finally, we present applications from a range of disciplines: acoustics — mufflers and woodwinds; structures — from microtrusses to infrastructure digital twins; fluid mechanics and heat transfer — culinary natural convection. We also take advantage of pPDEs to illustrate the remarkable advances in algorithms, architectures, and processing power over the past four decades.