A Heuristic Method Using Hessian Matrix for Fast Flow Topology Optimization
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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.
KeywordsTopology optimization Lattice Boltzmann method Hessian Sensitivity analysis
Mathematics Subject Classification76D55 76M25 49M15
The study of the second author is partially supported by JSPS KAKENHI 17K06633.
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