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

Mohamed Elhaddad1, Nils Zander1, Tino Bog1

  • 1Chair for Computation in Engineering, Technische Universität München, Arcisstrasse 21,, 80333 München, Germany.

International Journal for Numerical Methods in Biomedical Engineering
|December 22, 2017
PubMed
Summary

This study introduces a novel numerical method for complex 3D material interface problems. The finite cell method with hierarchical hp-refinement improves convergence rates for simulations, even with singularities.

Keywords:
domain couplingembedded interface problemsfinite cell methodhigh-order finite elementshp adaptivityvertebra-implant model

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Area of Science:

  • Computational mechanics
  • Numerical analysis
  • Material science

Background:

  • Solving 3D material interface problems with complex geometries is challenging.
  • Traditional methods often require conforming mesh generation, which is difficult for intricate shapes.
  • Accurate simulation of discontinuities at material interfaces is crucial for many engineering applications.

Purpose of the Study:

  • To present a numerical discretization technique for 3D material interface problems.
  • To develop a method that avoids conforming mesh generation for complex geometries.
  • To enhance convergence rates for problems with singularities and local solution features.

Main Methods:

  • Utilizing the finite cell method (FCM), a high-order fictitious domain approach.
  • Employing separate FCM meshes for each material sub-domain.
  • Weakly enforcing interface conditions between different meshes.
  • Implementing a hierarchical hp-refinement scheme for local mesh refinement.

Main Results:

  • The proposed method effectively handles complex geometries without conforming meshes.
  • Weak enforcement of interface conditions combined with hp-refinement significantly improves convergence rates.
  • The technique successfully resolves singularities and local solution features at interfaces.
  • Numerical experiments on 2D and 3D benchmark problems validate the method's effectiveness.

Conclusions:

  • The developed technique provides an accurate and flexible simulation tool for 3D material interface problems.
  • The combination of FCM and hierarchical hp-refinement offers superior convergence for nonsmooth problems.
  • The method shows significant potential for biomechanical simulations, such as vertebra-implant analysis.