A Heuristic Method Using Hessian Matrix for Fast Flow Topology Optimization

Kazuo Yonekura () and Yoshihiro Kanno ()
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Kazuo Yonekura: IHI Corporation
Yoshihiro Kanno: University of Tokyo

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 2, No 16, 681 pages

Abstract: Abstract 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.

Keywords: Topology optimization; Lattice Boltzmann method; Hessian; Sensitivity analysis; 76D55; 76M25; 49M15 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-1404-4

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