Topological Derivative for PDEs on Surfaces

Peter Gangl, Kevin Sturm

Research output: Contribution to journalArticlepeer-review


In this paper we study the problem of the optimal distribution of two materials on C2 submanifolds M of dimension d-1 in Rd by means of the topological derivative. We consider a class of shape optimization problems which are constrained by a linear partial differential equation on the surface. We examine the configurational perturbation of the differential operator and material coefficients and derive the corresponding topological derivative. Finally, we show how the topological derivative in conjunction with a level set method on the surface can be used to solve the topology optimization problem numerically.

Original languageEnglish
Pages (from-to)81–103
Number of pages23
JournalSIAM Journal on Control and Optimization
Issue number1
Publication statusPublished - 2022


  • asymptotic analysis
  • topological derivative
  • topology optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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