WIAS Preprint No. 1902, (2013)

Multi-material phase field approach to structural topology optimization


  • Blank, Luise
  • Farshbaf Shaker, Mohammad Hassan
    ORCID: 0000-0003-0543-5938
  • Garcke, Harald
  • Rupprecht, Christoph
  • Styles, Vanessa

2010 Mathematics Subject Classification

  • 49Q10 74P05 74P15 90C52 65K15


  • shape and topology optimization, phase field approach, shape sensitivity analysis, gradient projection method




Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An efficient numerical method based on an H1-gradient projection method is introduced and finally several numerical results demonstrate the applicability of the approach.

Appeared in

  • Trends in PDE Constrained Optimization, G. Leugering, P. Benner et al., eds., vol. 165 of International Series of Numerical Mathematics, Birkhäuser, Basel et al., 2014, pp. 231--246

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