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.
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The study of the second author is partially supported by JSPS KAKENHI 17K06633.
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Ilio Galligani.
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Yonekura, K., Kanno, Y. A Heuristic Method Using Hessian Matrix for Fast Flow Topology Optimization. J Optim Theory Appl 180, 671–681 (2019). https://doi.org/10.1007/s10957-018-1404-4
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DOI: https://doi.org/10.1007/s10957-018-1404-4