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Volume 33, Issue 4
An Iterative Thresholding Method for the Minimum Compliance Problem

Luyu Cen, Wei Hu, Dong Wang & Xiaoping Wang

DOI: 10.4208/cicp.OA-2023-0010

Commun. Comput. Phys., 33 (2023), pp. 1189-1216.

Published online: 2023-05

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  • Abstract

In this paper, we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance problem. The material domain is implicitly represented by its characteristic function, and the problem is formulated into a minimization problem by the principle of minimum complementary energy. We prove that the energy is decreasing in each iteration. Two effective continuation schemes are proposed to avoid trapping into the local minimum. Numerical results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.

  • Keywords

Minimum compliance, convolution, thresholding, linear elasticity.

  • AMS Subject Headings

65K10, 74B05, 74P15, 35K08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-33-1189, author = {Cen , LuyuHu , WeiWang , Dong and Wang , Xiaoping}, title = {An Iterative Thresholding Method for the Minimum Compliance Problem}, journal = {Communications in Computational Physics}, year = {2023}, volume = {33}, number = {4}, pages = {1189--1216}, abstract = {

In this paper, we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance problem. The material domain is implicitly represented by its characteristic function, and the problem is formulated into a minimization problem by the principle of minimum complementary energy. We prove that the energy is decreasing in each iteration. Two effective continuation schemes are proposed to avoid trapping into the local minimum. Numerical results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0010}, url = {http://global-sci.org/intro/article_detail/cicp/21689.html} }
TY - JOUR T1 - An Iterative Thresholding Method for the Minimum Compliance Problem AU - Cen , Luyu AU - Hu , Wei AU - Wang , Dong AU - Wang , Xiaoping JO - Communications in Computational Physics VL - 4 SP - 1189 EP - 1216 PY - 2023 DA - 2023/05 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2023-0010 UR - https://global-sci.org/intro/article_detail/cicp/21689.html KW - Minimum compliance, convolution, thresholding, linear elasticity. AB -

In this paper, we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance problem. The material domain is implicitly represented by its characteristic function, and the problem is formulated into a minimization problem by the principle of minimum complementary energy. We prove that the energy is decreasing in each iteration. Two effective continuation schemes are proposed to avoid trapping into the local minimum. Numerical results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.

Cen , LuyuHu , WeiWang , Dong and Wang , Xiaoping. (2023). An Iterative Thresholding Method for the Minimum Compliance Problem. Communications in Computational Physics. 33 (4). 1189-1216. doi:10.4208/cicp.OA-2023-0010
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