In situ adaptive reduction of nonlinear multiscale structural dynamics models
Abstract
Conventional offline training of reduced‐order bases in a predetermined region of a parameter space leads to parametric reduced‐order models that are vulnerable to extrapolation. This vulnerability manifests itself whenever a queried parameter point lies in an unexplored region of the parameter space. This article addresses this issue by presenting an in situ, adaptive framework for nonlinear model reduction where computations are performed by default online and shifted offline as needed. The framework is based on the concept of a database of local reduced‐order bases (ROBs), where locality is defined in the parameter space of interest. It achieves accuracy by updating on‐the‐fly a precomputed ROB and approximating the solution of a dynamical system along its trajectory using a sequence of most appropriate local ROBs. It achieves efficiency by managing the dimension of a local ROB and incorporating hyperreduction in the process. While sufficiently comprehensive, the framework is described in the context of dynamic multiscale computations in solid mechanics. In this context, even in a nonparametric setting of the macroscale problem and when all offline, online, and adaptation overhead costs are accounted for, the proposed computational framework can accelerate a single three‐dimensional, nonlinear, multiscale computation by an order of magnitude, without compromising accuracy.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 16, 2020
- Source ID
- 10.1002/nme.6505
Entities
People
- Charbel Farhat
- Philip Avery
- Wanli He
Organizations
- Air Force Office of Scientific Research
- King Abdulaziz City for Science and Technology
- National Aeronautics and Space Administration
- Stanford University