Abstract
We consider to solve numerically the shape optimization problems of Dirichlet Laplace eigenvalues subject to volume and perimeter constraints. By combining a level set method with the relaxation approach, the algorithm can perform shape and topological changes on a fixed grid. We use the volume expressions of Eulerian derivatives in shape gradient descent algorithms. Finite element methods are used for discretizations. Two and three-dimensional numerical examples are presented to illustrate the effectiveness of the algorithms.
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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
The work was supported by the National Natural Science Foundation of China (grant 12071149) and the Science and Technology Commission of Shanghai Municipality (Grant Numbers 19ZR1414100, 18dz2271000, and 21JC1402500). The authors thank Xindi Hu in East China Normal University for many helpful comments in numerical experiments.
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Qian, M., Zhu, S. A level set method for Laplacian eigenvalue optimization subject to geometric constraints. Comput Optim Appl 82, 499–524 (2022). https://doi.org/10.1007/s10589-022-00371-1
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DOI: https://doi.org/10.1007/s10589-022-00371-1