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...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.展开更多
In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the heat transfer problem.The material domain is implicitly represented by its characteristic function,and the problem is for...In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the heat transfer problem.The material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimum-minimum problem.We prove that the energy is decreasing in each iteration.Numerical experiments for two types the heat transfer problems(volume to point and volume to sides)are performed to demonstrate the effectiveness of the proposed methods.展开更多
基金support from National Natural Science Foundation of China(NSFC)grant(No.12271461)the key project of NSFC(No.12131010)+4 种基金the Hong Kong Research Grants Council GRF(GRF grants 16308421,16305819,16303318)the University Development Fund from The Chinese University of Hong Kong,Shenzhen(UDF01002028)support from National Natural Science Foundation of China grant(Grant No.12101524)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515012199)Shenzhen Science and Technology Innovation Program(Grant No.JCYJ20220530143803007,RCYX20221008092843046).
文摘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.
基金support from National Natural Science Foundation of China(NSFC)grant(No.12271461)the key project of NSFC(No.12131010)+1 种基金the Hong Kong Research Grants Council GRF(GRF grants Nos.16308421,16305819,16303318)the University Development Fund from The Chinese University of Hong Kong,Shenzhen(UDF01002028).
文摘In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the heat transfer problem.The material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimum-minimum problem.We prove that the energy is decreasing in each iteration.Numerical experiments for two types the heat transfer problems(volume to point and volume to sides)are performed to demonstrate the effectiveness of the proposed methods.
