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

Grégoire Allaire (1, 2) , Charles Dapogny (3, 4) , Pascal Frey (3)

1 DeFI - Shape reconstruction and identification
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 LJLL - Laboratoire Jacques-Louis Lions
4 Technocentre Renault [Guyancourt]

An approach for structural optimization is proposed, which combines the versatility 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 this 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.

Mots clés: Local mesh modifications.; Geometry and topology optimization; Level set method; Local mesh modifications

Domaines: Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Grégoire Allaire, Charles Dapogny, Pascal Frey. A mesh evolution algorithm based on the level set method for geometry and topology optimization. Structural and Multidisciplinary Optimization, 2013, 48 (4), pp.711-715. ⟨10.1007/s00158-013-0929-2⟩. ⟨hal-00801704⟩