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Sparse basis pursuit for compliance minimization in the vanishing volume ratio limit
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-06-07 , DOI: 10.1002/zamm.202000008
Anton Evgrafov 1 , Ole Sigmund 1
Affiliation  

We consider a non‐smooth convex variational problem appearing as a formal limit of compliance minimization in the vanishing volume ratio limit. The problem has a classical basis pursuit form, and several successful algorithms have been utilized to solve problems of this class in other application contexts. We discuss the well‐posedness and regularity of solutions to these problems, possible solution algorithms, and their discretizations as relevant in this mechanical engineering context. We then test the algorithms on a few benchmark problems with available analytical solutions.

中文翻译:

稀疏的基础上寻求在消失的体积比限制中最小化合规性

我们认为不光滑的凸变分问题出现在消失的体积比极限中作为最小化合规性的形式极限。该问题具有经典的基础追求形式,并且已经使用了几种成功的算法来解决其他应用程序上下文中此类的问题。我们讨论了这些问题的解决方案的适定性和规律性,可能的解决方案算法以及与该机械工程环境相关的离散化。然后,我们使用可用的分析解决方案针对一些基准问题测试算法。
更新日期:2020-06-07
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