ENUMATH 2017 Conference
Plenary talk

Model Order Reduction for Component-to-System Analysis of Parametrized Partial Differential Equations

by Anthony T. Patera (Massachusetts Institute of Technology, USA)

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, classification and monitoring, 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 a posteriori error estimators for adaptivity and verification. The method is also well-suited for parallel calculation in both the offline and online stages.

We provide examples in acoustics, linear elasticity, and nonlinear solid mechanics, with applications from musical instruments to shiploaders.