Key, F., von Danwitz, M., Ballarin, F., & Rozza, G. (2023). Model Order Reduction for Deforming Domain Problems in a Time-Continuous Space-Time Setting. arXiv. https://doi.org/10.48550/arXiv.2303.16662
E317-01 - Forschungsbereich Leichtbau E317 - Institut für Leichtbau und Struktur-Biomechanik
Model Order Reduction; Continuous Space-Time Approach; Finite Element Method; Deforming Domain Problems
In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with changes in the domain topology, need to be tackled appropriately. The second challenge arises when computational resources and the time for evaluating the model become critical in so-called many query scenarios for parametric problems. For example, these problems occur in optimization, uncertainty quantification (UQ), or automatic control and using highly resolved full-order models (FOMs) may become impractical. To address both types of complexity, we present a novel projection-based model order reduction (MOR) approach for deforming domain problems that takes advantage of the time-continuous space-time formulation. We apply it to two examples that are relevant for engineering or biomedical applications and conduct an error and performance analysis. In both cases, we are able to drastically reduce the computational expense for a model evaluation and, at the same time, to maintain an adequate accuracy level. All in all, this work indicates the effectiveness of the presented MOR approach for deforming domain problems taking advantage of a time-continuous space-time setting.
European Union – NextGenerationEU European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Actions INDAM-GNCS
dtec.bw – Digitalization and Technology Research Center of the Bundeswehr under the project RISK.twin 872442 (ARIA) CUP E53C22001930001
Digital Transformation in Manufacturing: 20% Computational Fluid Dynamics: 20% Modeling and Simulation: 60%