Journal of Optimization Theory and Applications

, Volume 180, Issue 2, pp 671–681 | Cite as

A Heuristic Method Using Hessian Matrix for Fast Flow Topology Optimization

  • Kazuo YonekuraEmail author
  • Yoshihiro Kanno


We propose a heuristic optimization method for a density-based fluid topology optimization using a Hessian matrix. In flow topology optimization, many researches use a gradient-based method. Convergence rate of a gradient method is linear, which means slow convergence near the optimal solution. For faster convergence, we utilize a Hessian matrix toward the end of the optimization procedure. In the present paper, we formulate a fluid optimization problem using the lattice Boltzmann method and heuristically solve the optimization problem with using an approximated sensitivity. In the formulation of a Hessian matrix, we use a heuristic trick in order to formulate it as a diagonal matrix. By the heuristics, the computation cost is decreased drastically. The validity of the method is studied via numerical examples.


Topology optimization Lattice Boltzmann method Hessian Sensitivity analysis 

Mathematics Subject Classification

76D55 76M25 49M15 



The study of the second author is partially supported by JSPS KAKENHI 17K06633.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IHI CorporationYokohamaJapan
  2. 2.University of TokyoBunkyo-kuJapan

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