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Multi-level hp-finite cell method for embedded interface problems with application in biomechanics

  • This work presents a numerical discretization technique for solving 3-dimensional material interface problems involving complex geometry without conforming mesh generation. The finite cell method (FCM), which is a high-order fictitious domain approach, is used for the numerical approximation of the solution without a boundary-conforming mesh. Weak discontinuities at material interfaces are resolved by using separate FCM meshes for each material sub-domain and weakly enforcing the interface conditions between the different meshes. Additionally, a recently developed hierarchical hp-refinement scheme is used to locally refine the FCM meshes to resolve singularities and local solution features at the interfaces. Thereby, higher convergence rates are achievable for nonsmooth problems. A series of numerical experiments with 2- and 3-dimensional benchmark problems is presented, showing that the proposed hp-refinement scheme in conjunction with the weak enforcement of the interface conditionsThis work presents a numerical discretization technique for solving 3-dimensional material interface problems involving complex geometry without conforming mesh generation. The finite cell method (FCM), which is a high-order fictitious domain approach, is used for the numerical approximation of the solution without a boundary-conforming mesh. Weak discontinuities at material interfaces are resolved by using separate FCM meshes for each material sub-domain and weakly enforcing the interface conditions between the different meshes. Additionally, a recently developed hierarchical hp-refinement scheme is used to locally refine the FCM meshes to resolve singularities and local solution features at the interfaces. Thereby, higher convergence rates are achievable for nonsmooth problems. A series of numerical experiments with 2- and 3-dimensional benchmark problems is presented, showing that the proposed hp-refinement scheme in conjunction with the weak enforcement of the interface conditions leads to a significant improvement of the convergence rates, even in the presence of singularities. Finally, the proposed technique is applied to simulate a vertebra-implant model. The application showcases the method's potential as an accurate simulation tool for biomechanical problems involving complex geometry, and it demonstrates its flexibility in dealing with different types of geometric description.show moreshow less

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Metadaten
Author:Mohamed Elhaddad, Nils Zander, Tino Bog, László Kudela, Stefan Kollmannsberger, Jan Kirschke, Thomas Baum, Martin Ruess, Ernst Rank
Qualitätssicherung:peer reviewed
Fachbereich/Einrichtung:Hochschule Düsseldorf / Fachbereich - Maschinenbau und Verfahrenstechnik
Document Type:Article
Year of Completion:2018
Language of Publication:English
Publisher:Wiley
Parent Title (English):International Journal for Numerical Methods in Biomedical Engineering
Volume:34
Issue:4
Article Number:e2951
Related URL:http://www.ncbi.nlm.nih.gov/pubmed/29265715
DOI:https://doi.org/10.1002/cnm.2951
ISSN:2040-7947
Funding institution:DFG
Funding institution:European Research Council
Funding number:RA 624/26-1
Funding number:ERC-2014-StG 637164
Dewey Decimal Classification:6 Technik, Medizin, angewandte Wissenschaften / 62 Ingenieurwissenschaften / 620 Ingenieurwissenschaften und zugeordnete Tätigkeiten
Licence (German):keine Lizenz - nur Metadaten
Release Date:2021/07/16
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