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

Elhaddad, M., Zander, N., Bog, T., Kudela, L., Kollmannsberger, S., Kirschke, J. S., Baum, T., Ruess, M. and Rank, E. (2018) Multi-level hp-finite cell method for embedded interface problems with application in biomechanics. International Journal for Numerical Methods in Biomedical Engineering, 34(4), e2951. (doi: 10.1002/cnm.2951) (PMID:29265715)

Abstract

This work presents a numerical discretization technique for solving three-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 employed to locally refine the FCM meshes in order to resolve singularities and local solution features at the interfaces. Thereby, higher convergence rates are achievable for non-smooth problems. A series of numerical experiments with two- and three-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.

• Item Type: Articles
• Additional Information: The authors gratefully acknowledge the financial support of the German Research Foundation (DFG) under Grant RA 624/26-1, and of the European Research Council under Grant ERC-2014- StG 637164.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ruess, Dr Martin
• Authors: Elhaddad, M., Zander, N., Bog, T., Kudela, L., Kollmannsberger, S., Kirschke, J. S., Baum, T., Ruess, M., and Rank, E.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal for Numerical Methods in Biomedical Engineering
• Publisher: Wiley
• ISSN: 2040-7939
• ISSN (Online): 2040-7947
• Published Online: 19 December 2017
• Copyright Holders: Copyright © 2017 John Wiley and Sons, Ltd.
• First Published: First published in International Journal for Numerical Methods in Biomedical Engineering 34(4):e2951
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher