In many applications in Computer Aided Engineering (CAE), 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.
The idea is to combine concepts of data-based Model Order Reduction (MOR) and computational Reanalysis to a technology that systematically and automatically reduces computational expense by reusing simulation data. While MOR allows to reduce model fidelity in space and time without significantly deteriorating accuracy, reanalysis uses results from previous computations as a predictor or preconditioner.
The aim of the project is to develop methods for systematic reuse of simulation data to accelerate time- and resource-critical simulations in non-linear structural dynamics. Existing reanalysis methods will be further developed and extended to meet the requirements of challenging problem classes as specified below. Reanalysis and MOR will be combined to a "reduced model reanalysis" approach. One idea is to use smooth, spline-based discretization techniques to construct reduced bases and setup a hierarchy of low- and high-fidelity models. In this context, it has to be determined which data from previous simulations are needed to extract reduced models or perform reanalyses.
Challenging problem classes are contact scenarios, non-linear material behaviour and, instability and bifurcation. Standard and isogeometric finite elements are used for discretization in space. The expected overarching scientific innovation is a better establishing of the yet scarcely pursued idea to reuse simulation data to accelerate computations.
State of current work and results
Together with project PN 7-6 "Reusage and Reanalysis of Simulation Data in Structural Dynamics", a data-based "reduced model reanalysis" method that combines MOR techniques and reanalysis to accelerate repeated simulations of almost similar systems was developed. So far, this method was applied to nonlinear stability problems to treat the above-mentioned problem class instability and bifurcation. In particular, this method enables acceleration of the exact computation of critical points, such as limit and bifurcation points, by the method of extended systems for systems that depend on a set t of design parameters, such as material or geometric properties. Such critical points are of utmost engineering significance due to the special characteristics of the structural behavior in their vicinity. Using classical reanalysis methods, like the fold line analysis the computation of critical points of almost similar systems can also be accelerated. A major drawback of this technology is that only small parameter variations are possible. Otherwise, the algorithm may not converge to the correct solution or fail to converge. The newly developed, data-based "reduced model reanalysis" method overcomes this problem. It combines the idea of reanalysis with the nonlinear, nonintrusive model reduction approach for structural mechanical systems from PN 7-6.
The reduced model reanalysis was verified and validated for a couple of numerical examples, including standard and isogeometric finite element models. The speedup is strongly application-dependent, but at least one order of magnitude is mostly achievable. In the case of buckling of a thin plate, the method was able to learn smooth functions (critical load) as well as non-smooth functions (buckling mode) in the parameter spaces from the training data to obtain good enough predictors for the method of extended systems.
Data-based model reduction and reanalysis
(Project PN 3-2 of project network 3)
German Research Foundation (DFG), Cluster of Excellence EXC 2075 "Data-integrated Simulation Science (SimTech)", GEPRIS project number 390740016
apl. Prof. Dr.-Ing. Jörg Fehr, Institute of Engineering and Computational Mechanics (ITM), Universität Stuttgart