Structural and Multidisciplinary Optimization

, Volume 48, Issue 4, pp 711–715 | Cite as

A mesh evolution algorithm based on the level set method for geometry and topology optimization

  • Grégoire AllaireEmail author
  • Charles Dapogny
  • Pascal Frey
Brief Note


We propose an approach for structural optimization which combines the flexibility of the level set method for handling large deformations and topology changes with the accurate description of the geometry provided by an exact mesh of the shape. The key ingredients of our method are efficient algorithms for (i) moving a level set function on an unstructured mesh, (ii) remeshing the surface corresponding to the zero level set and (iii) simultaneously adaptating the volumic mesh which fits to this surfacic mesh.


Geometry and topology optimization Level set method Local mesh modifications 



This work has been supported by the RODIN project (FUI AAP 13). G. A. is a member of the DEFI project at INRIA Saclay Ile-de-France.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Grégoire Allaire
    • 1
    Email author
  • Charles Dapogny
    • 2
    • 3
  • Pascal Frey
    • 2
  1. 1.Centre de Mathématiques Appliquées (UMR 7641)École PolytechniquePalaiseauFrance
  2. 2.UMR 7598, Laboratoire J.-L. LionsUPMC Univ Paris 06ParisFrance
  3. 3.Renault DREAM-DELT’AGuyancourtFrance

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