Parametrized Model Order Reduction for Component-to-System Synthesis and Analysis

Anthony T. Patera

Massachusetts Institute of Technology

Thursday, July 20, 9:00 am

Abstract:

In this talk we describe and demonstrate a model order reduction methodology for efficient solution of partial differential equations characterized by many (spatially distributed) parameters. The approach is relevant in many-query and real-time contexts such as design, shape and topology optimization, parameter estimation and classification, and reconditioning. The numerical approach comprises four principal ingredients: component-to-system synthesis, formulated as a static-condensation procedure; model order reduction, informed by evanescence arguments at component interfaces (port reduction) and low-dimensional parametric manifolds in component interiors (reduced basis techniques); offline-online computational decomposition strategies; and parallel calculation, implemented in a cloud environment. We provide examples in acoustics, linear elasticity, and nonlinear solid mechanics, with applications from musical instruments to shiploaders.

Biography:

Anthony T. Patera is Ford Professor of Engineering and Professor of Mechanical Engineering at the Massachusetts Institute of Technology (MIT), and Co-Director of the MIT Center for Computational Engineering. In 2013-2014 Professor Patera also held a Research Chair from the Paris Foundation for Mathematical Sciences hosted at the University Pierre and Marie Curie. His research interests include partial differential equations, variational techniques, computational methods, numerical analysis, model order reduction, a posteriori error estimation, real-time simulation, data assimilation and classification, fluid dynamics, heat transfer, and acoustics and continuum mechanics. Professor Patera has undergraduate and graduate degrees in Mechanical Engineering from MIT and a doctoral degree in Applied Mathematics also from MIT.