An efficient threshold dynamics method for topology optimization for fluids

Huangxin Chen Xiamen University Haitao Leng The Hong Kong University of Science and Technology Dong Wang University of Utah Xiao-Ping Wang The Hong Kong University of Science and Technology

Optimization and Control mathscidoc:1908.27001

2018.12
We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power in the fluid and the perimeter approximated by nonlocal energy, subject to a fluid volume constraint and the incompressibility condition. We show that the minimization problem can be solved with an iterative scheme in which the Stokes equation is approximated by a Brinkman equation. The indicator functions of the fluid-solid regions are then updated according to simple convolutions followed by a thresholding step. We demonstrate mathematically that the iterative algorithm has the total energy decaying property. The proposed algorithm is simple and easy to implement. A simple adaptive time strategy is also used to accelerate the convergence of the iteration. Extensive numerical experiments in both two and three dimensions show that the proposed iteration algorithm is quite robust and converges in much fewer iterations and is more efficient than many existing methods.
Topology optimization, Stokes flow, threshold dynamics method, mixed finite-element method, convolution, fast Fourier transform.
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@inproceedings{huangxin2018an,
  title={An efficient threshold dynamics method for topology optimization for fluids},
  author={Huangxin Chen, Haitao Leng, Dong Wang, and Xiao-Ping Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190820102702776047419},
  year={2018},
}
Huangxin Chen, Haitao Leng, Dong Wang, and Xiao-Ping Wang. An efficient threshold dynamics method for topology optimization for fluids. 2018. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190820102702776047419.
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