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Numerical solution of a nonlinear eigenvalue problem arising in optimal insulation
Interfaces and Free Boundaries ( IF 1 ) Pub Date : 2019-05-09 , DOI: 10.4171/ifb/414
Sören Bartels 1 , Giuseppe Buttazzo 2
Affiliation  

The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of corresponding eigenfunctions that determine the optimal layer thickness are addressed. Corresponding numerical experiments confirm the theoretical observation that a symmetry breaking occurs for the case of small available insulation masses and provide insight in the geometry of optimal films. An experimental shape optimization indicates that convex bodies with one axis of symmetry have favorable insulation properties.

中文翻译:

最优绝缘中非线性特征值问题的数值解

通过可变厚度的薄膜对导热体的最佳绝缘可以表述为不可微分的非局部特征值问题。解决了确定最佳层厚度的相应特征函数的可靠计算的离散化和迭代解决方案。相应的数值实验证实了理论观察结果,即在可用绝缘质量较小的情况下发生对称破坏,并提供对最佳薄膜几何形状的洞察。实验形状优化表明具有一个对称轴的凸体具有良好的绝缘性能。
更新日期:2019-05-09
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