Octree-based integration scheme with merged sub-cells for the finite cell method: Application to non-linear problems in 3D
Fictitious domain methods, such as the Finite Cell Method (FCM), allow for an efficient and accurate simulation of complex geometries by utilizing higher-order shape functions and an unfitted discretization based on rectangular elements. Since the mesh does not conform to the geometry, cut elements...
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| Published in | Computer methods in applied mechanics and engineering Vol. 401; p. 115565 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.11.2022
Elsevier BV |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0045-7825 1879-2138 1879-2138 |
| DOI | 10.1016/j.cma.2022.115565 |
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| Abstract | Fictitious domain methods, such as the Finite Cell Method (FCM), allow for an efficient and accurate simulation of complex geometries by utilizing higher-order shape functions and an unfitted discretization based on rectangular elements. Since the mesh does not conform to the geometry, cut elements arise that are intersected by domain boundaries. For optimal convergence rates and the efficiency of the simulation in general, special integration schemes have to be used in such elements. In this contribution, the often used, robust octree-decomposition-based integration scheme is enhanced by a novel approach reducing the computational effort when evaluating the discontinuous integrals. This is realized by introducing an additional step, in which the local integration mesh is simplified using data compression techniques leading to fewer integration domains/points. An important advantage of the proposed method is that it can be added in a modular fashion to already existing codes. While it inherits all desired properties of the octree-decomposition-based integration scheme, it significantly reduces the number of integration points and has hardly any negative effect on the simulation accuracy. In this paper, the proposed integration scheme is introduced in detail, and investigated by means of numerical examples in the context of 3D non-linear problems. |
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| AbstractList | Fictitious domain methods, such as the Finite Cell Method (FCM), allow for an efficient and accurate simulation of complex geometries by utilizing higher-order shape functions and an unfitted discretization based on rectangular elements. Since the mesh does not conform to the geometry, cut elements arise that are intersected by domain boundaries. For optimal convergence rates and the efficiency of the simulation in general, special integration schemes have to be used in such elements. In this contribution, the often used, robust octree-decomposition-based integration scheme is enhanced by a novel approach reducing the computational effort when evaluating the discontinuous integrals. This is realized by introducing an additional step, in which the local integration mesh is simplified using data compression techniques leading to fewer integration domains/points. An important advantage of the proposed method is that it can be added in a modular fashion to already existing codes. While it inherits all desired properties of the octree-decomposition-based integration scheme, it significantly reduces the number of integration points and has hardly any negative effect on the simulation accuracy. In this paper, the proposed integration scheme is introduced in detail, and investigated by means of numerical examples in the context of 3D non-linear problems. |
| ArticleNumber | 115565 |
| Author | Petö, Márton Duvigneau, Fabian Garhuom, Wadhah Eisenträger, Sascha Düster, Alexander Juhre, Daniel |
| Author_xml | – sequence: 1 givenname: Márton orcidid: 0000-0002-4373-2848 surname: Petö fullname: Petö, Márton email: marton.petoe@ovgu.de organization: Institute of Mechanics, Otto von Guericke University, Magdeburg, Germany – sequence: 2 givenname: Wadhah surname: Garhuom fullname: Garhuom, Wadhah organization: Hamburg University of Technology, Germany – sequence: 3 givenname: Fabian surname: Duvigneau fullname: Duvigneau, Fabian organization: Institute of Mechanics, Otto von Guericke University, Magdeburg, Germany – sequence: 4 givenname: Sascha surname: Eisenträger fullname: Eisenträger, Sascha organization: Technical University of Darmstadt, Germany – sequence: 5 givenname: Alexander surname: Düster fullname: Düster, Alexander organization: Hamburg University of Technology, Germany – sequence: 6 givenname: Daniel surname: Juhre fullname: Juhre, Daniel organization: Institute of Mechanics, Otto von Guericke University, Magdeburg, Germany |
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| Keywords | Embedded domain methods Octree integration Non-linear mechanics Finite cell method Discontinuous integrals |
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| SubjectTerms | Data compression Decomposition Discontinuous integrals Domains Embedded domain methods Finite cell method Finite element method Non-linear mechanics Octree integration Octrees Robustness (mathematics) Shape functions Simulation |
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| Title | Octree-based integration scheme with merged sub-cells for the finite cell method: Application to non-linear problems in 3D |
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