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Session Chair: Gerhard Starke, Universität Duisburg-Essen
Location:Auditorium Wolfsburg
Presentations
Improved Integration in the Finite Cell Method using Merged Sub-Cells and Boolean Operations
Daniel Juhre1, Márton Petö1, Fabian Duvigneau1, Sascha Eisenträger2
1Otto von Guericke University Magdeburg, Germany; 2TU Darmstadt, Germany
The Finite Cell Method (FCM) is a powerful tool for efficient and accurate simulation of complex geometries using higher-order shape functions and an unfitted discretization [1]. A widely used approach for the computation of the cut cell matrices intersected by the immersed boundaries is based on a quadtree/octree-decomposition of the cell domain into smaller integration domains called sub-cells. While the main advantage of this method is its robustness and simplicity, evaluating discontinuous integrals with this method can be computationally expensive if high accuracy is demanded. In this contribution, two novel approaches addressing this issue are presented, which inherit all the desired properties of the recursive sub-division-based integration schemes, however, they significantly reduce the computational effort while maintaining the same integration accuracy. The first approach is based on merging the sub-cells using data compression techniques to form larger blocks and thereby reducing their number by a significant amount. An additional convenient feature of this approach lies in its modularity, as it can be simply added to FCM software without any major modification of the code. The proposed method has been investigated by numerical examples in the context of linear problems in 2D and non-linear problems in 3D. The results show a saving in computational time by up to 50% while yielding basically the same accuracy and stability of the simulation [2]. The second approach is an extension of the already existing Boolean FCM concept to multi-material problems. Here, the key idea lies in utilizing an overlapping structure of the integration sub-cells and using Boolean operations during the numerical integration to achieve a significantly more efficient distribution of the integration points. The proposed approach is combined with the local enrichment technique to accurately capture the weak discontinuity of the displacement field along material interfaces. The results show a significant reduction in the number of integration points and computational time by 70-80%, while maintaining the same accuracy as the standard quadtree/octree-based integration scheme [3].
References
[1] Parvizian, J., Düster, A. and Rank E. Finite cell method: h- and p-extension for embedded domain problems in solid mechanics. Computational Mechanics (2007) 41: 121–133. [2] M. Petö, W. Garhuom, F. Duvigneau, S. Eisenträger, A. Düster, and D. Juhre. Octreebased integration scheme with merged sub-cells for the finite cell method: Application to non-linear problems in 3D. Computer Methods in Applied Mechanics and Engineering (2022) 401: 115565. [3] M. Petö, S. Eisenträger, F. Duvigneau, and D. Juhre. Boolean finite cell method for multi-material problems including local enrichment of the ansatz space. Computational Mechanics (2023).
