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Multi‐level h p ‐finite cell method for embedded interface problems with application in biomechanics
Author(s) -
Elhaddad Mohamed,
Zander Nils,
Bog Tino,
Kudela László,
Kollmannsberger Stefan,
Kirschke Jan,
Baum Thomas,
Ruess Martin,
Rank Ernst
Publication year - 2018
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.2951
Subject(s) - polygon mesh , discretization , finite element method , classification of discontinuities , interface (matter) , convergence (economics) , boundary (topology) , computer science , mathematics , gravitational singularity , domain (mathematical analysis) , boundary value problem , algorithm , mesh generation , geometry , topology (electrical circuits) , mathematical analysis , structural engineering , bubble , maximum bubble pressure method , parallel computing , engineering , economics , economic growth , combinatorics
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 h p ‐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 h p ‐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.