Dimensional Reduction and Hyper Reduction of Parametric Nonlinear Structural Dynamics Models for Real-Time Computing: SEMM Seminar
Seminar | April 24 | 12-1 p.m. | 502 Davis Hall
Charbel Farhat, Professor, Department of Aeronatics and Astronautics, Department of Mechanical Engineering and Institute for Computational and Mathematical Engineering, Stanford University
Model reduction is a tool in applied mathematics that is rapidly becoming indispensable for computational-based design and optimization, stochastic analysis for uncertainty quantification, embedded computing, and online optimal control. It is also essential for what-if engineering scenarios and other parametric studies where dramatically faster if not real-time simulation responses are desired. This is because in many engineering applications, high-dimensional, time-dependent, numerical simulations remain so computationally intensive that they cannot be performed routinely, or even as often as needed. For example, this is the case for the simulation of the blast-induced fracture of thin shells, and the numerical prediction of large shear deformations in soft tissues. During the last decade, both theoretical and algorithmic aspects of linear model reduction have been addressed and matured. Their impact on practical and important applications has also been successfully demonstrated in many engineering fields. Unfortunately, this is not yet the case for nonlinear model reduction, where problems with large displacements and rotations, large deformations, material yielding, contact, and evolving domains and discontinuities raise significant barriers. This lecture will present a data-driven framework for nonlinear model reduction that addresses these issues. This computational framework is based on a concept of local reduced-order bases where the data can be high-dimensional surrogate data, where locality pertains to the regimes of the solution manifold rather than spatial or temporal considerations, and which incorporates elements of machine learning. It will also present a structure-preserving hyper reduction approach for accelerating time-to- solution. Significant results obtained for the application of this nonlinear model reduction framework to the simulation in real time of the response of a V-hull vehicle to under-body blasts and the failure analysis of underwater structures will be reported and discussed.