Data-based model reduction and reanalysis

In many applications in Computer Aided Engineering, like parametric studies, structural optimization or virtual material design, a large number of almost similar models have to be simulated. Although individual simulation results may differ only marginally in both space and time, the same effort is invested for every single new simulation with no account for experience and knowledge from previous simulations. This projects aims towards further developing methods to use simulation data to significantly accelerate computations in many query contexts within the framework of structural dynamics. The idea is to combine concepts of data-based model order reduction and computational reanalysis to a technology that systematically and automatically reduces computational expense by reusing simulation data. While model order reduction allows reducing model fidelity in space and time without significantly deteriorating accuracy, reanalysis uses results from previous computations as a predictor or preconditioner. Particular challenges emanate from the nature of the envisaged applications, involving path-dependence, dissipative effects and non-smooth non-linearities. As a sample problem, the upper arm model investigated in project PN 7-1 can be mentioned.

The key questions can be summarized as follows:

1. How can reanalysis methods be further developed and extended to meet the requirements of challenging problems, like contact, non-linear material models as well as instability and bifurcation problems
2. How can reanalysis and model order reduction be combined to a “reduced model reanalysis” approach?
3. How can smooth, spline-based discretization techniques be used to construct reduced bases and setup a hierarchy of low-fidelity and high-fidelity models?
4. Which data from previous simulations are needed to extract reduced models or perform reanalyses and how can they be obtained?