@Article{CSIAM-AM-3-1,
author = {Huangxin, Chen and Leng, Haitao and Wang, Dong and Xiao-Ping, Wang},
title = {An Efficient Threshold Dynamics Method for Topology Optimization for Fluids},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2022},
volume = {3},
number = {1},
pages = {26--56},
abstract = {<p style="text-align: justify;">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 prove mathematically that the iterative algorithm has the total energy decaying
property. The proposed algorithm is simple and easy to implement. Extensive numerical experiments in both two and three dimensions show that the proposed iteration
algorithm converges in much fewer iterations and is more efficient than many existing
methods. In addition, the numerical results show that the algorithm is very robust and
insensitive to the initial guess and the parameters in the model.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2021-0007},
url = {https://global-sci.com/article/82309/an-efficient-threshold-dynamics-method-for-topology-optimization-for-fluids}
}