A volume-controlled level-set method for topology optimization
Abstract
Topology optimization typically involves a geometric volume/mass constraint due to the limited use of material. As a popular technique for topology optimization, the level-set method typically employs the Lagrange method, the penalty method, or the augmented Lagrangian approach to address the volume constraint. This requires careful parameter tuning and may lead to non-monotonic changes in the objective. In this paper, we present a new volume-controlled level-set method for topology optimization. By imposing a scalar weighted volume?compatibility constraint in a modified Stokes-type extension-regularization problem, the velocity is made volume compatible at the beginning of each frozen transport interval. At the continuous level, we prove that the initial rate of change of the regularized volume vanishes and that the subsequent frozen-velocity drift is of order T2; under a narrow-band assumption, the corresponding constant is independent of the smoothing parameter. For the discontinuous Galerkin spatial semi-discretization of the level-set transport equation, we derive a quantitative regularized-volume drift estimate that displays the dependence on the smoothing parameter, spatial mesh size, transport time, and discrete velocity. The effectiveness of the present algorithm is demonstrated through the minimum compliance problem for linear elasticity, the eigenfrequency maximization for structural vibration, and the minimum energy dissipation problem for Stokes flows.
Related
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BibTeX
@misc{gong2026volumecontrolled,
title = {{A volume-controlled level-set method for topology optimization}},
author = {Wei Gong and Zhenmin Zhang and Shengfeng Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12922},
eprint = {2610.12922},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12922},
}
RIS
TY - UNPB
TI - A volume-controlled level-set method for topology optimization
AU - Wei Gong
AU - Zhenmin Zhang
AU - Shengfeng Zhu
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.12922
UR - https://arxiv.org/abs/2610.12922
AB - Topology optimization typically involves a geometric volume/mass constraint due to the limited use of material. As a popular technique for topology optimization, the level-set method typically employs the Lagrange method, the penalty method, or the augmented Lagrangian approach to address the volume constraint. This requires careful parameter tuning and may lead to non-monotonic changes in the objective. In this paper, we present a new volume-controlled level-set method for topology optimization. By imposing a scalar weighted volume?compatibility constraint in a modified Stokes-type extension-regularization problem, the velocity is made volume compatible at the beginning of each frozen transport interval. At the continuous level, we prove that the initial rate of change of the regularized volume vanishes and that the subsequent frozen-velocity drift is of order T^2; under a narrow-band assumption, the corresponding constant is independent of the smoothing parameter. For the discontinuous Galerkin spatial semi-discretization of the level-set transport equation, we derive a quantitative regularized-volume drift estimate that displays the dependence on the smoothing parameter, spatial mesh size, transport time, and discrete velocity. The effectiveness of the present algorithm is demonstrated through the minimum compliance problem for linear elasticity, the eigenfrequency maximization for structural vibration, and the minimum energy dissipation problem for Stokes flows.
ER -