Scalable topology optimization with the kernel-independent fast multipole method

Igor Ostanin, Ivan Tsybulin, Mikhail Litsarev, Ivan Oseledets, Denis Zorin

Research output: Contribution to journalArticlepeer-review


The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a topological derivative. The numerical solution of the elasticity boundary value problem at every iteration is performed with the boundary element formulation and the kernel-independent fast multipole method. Providing excellent single node performance and scalable parallelization, our method is among the fastest optimization tools available today. The performance of our approach is studied on few illustrative examples, including the optimization of engineered constructions for the minimum compliance and the optimization of the microstructure of a metamaterial for the desired macroscopic tensor of elasticity.

Original languageEnglish (US)
Pages (from-to)123-132
Number of pages10
JournalEngineering Analysis with Boundary Elements
StatePublished - Oct 2017


  • Boundary element method
  • Kernel-independent fast multipole method
  • Topology optimization

ASJC Scopus subject areas

  • Analysis
  • General Engineering
  • Computational Mathematics
  • Applied Mathematics


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