ECCOMAS 2024

Reduced Model Reanalysis – Combining Data-Based Model Reduction and Reanalysis to Accelerate Structural Analysis

  • Strauß, Anika (University of Stuttgart)
  • Kneifl, Jonas (University of Stuttgart)
  • Fehr, Jörg (University of Stuttgart)
  • Bischoff, Manfred (University of Stuttgart)

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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 the individual scenarios may differ only slightly 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. Therefore, we have developed a method that combines data-based Model Order Reduction (MOR) and reanalysis, thus exploiting knowledge from previous simulation runs to accelerate computations in multi-query contexts. While MOR allows reducing model fidelity in space and time without significantly deteriorating accuracy, reanalysis uses results from previous computations as a predictor or preconditioner. The workflow of our method, named Reduced Model Reanalysis (RMR), is divided into an offline and online phase. In the offline phase, data is generated to cover a wide range of the parameter space. From this data, a surrogate model is learned in a reduced space using regression algorithms from the field of machine learning. The models are learned in a reduced space due to the prohibitively large number of degrees of freedom of the full finite element model. The reduced subspaces are obtained via a snapshot POD. In the online phase, approximations of all relevant solution quantities are obtained from the surrogate model. Their projection to the full space provides predictors that allow for an accelerated solution of the system in comparison to a standard structural mechanics computation. In the case of nonlinear stability analysis, this method can, for example, be used to accelerate the exact computation of critical points by the method of extended systems [1]. Further potential application fields of RMR are general nonlinear static and transient problems, with particular challenges when path-dependence comes into play. REFERENCES [1] P. Wriggers , W. Wagner and C. Miehe. A quadratically convergent procedure for the calculation of stability points in finite element analysis. Computer Methods in Applied Mechanics and Engineering 1988; 70(3): 329-347.