Asymptotic modelling of conductive thin sheets
Asymptotic modelling of conductive thin sheets
复制标题
导电薄片的渐近建模
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
S. Tordeux
中科院分区：
文献类型：
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作者：
K. Schmidt;S. Tordeux
我们推导并分析了将二维小厚度ε导电片缩小到一个界面的模型，并通过该界面上的条件近似其屏蔽行为。为此，我们考虑一个电导率与厚度ε成反比的模型问题，这导致ε→0的非平凡极限解。展开式的函数按层次定义，即按顺序定义。我们的分析表明，对于光滑的薄片，模型对于任何阶都定义良好，并且具有最佳收敛性，这意味着具有N项的展开的h1建模误差在薄片的外部以O（εN+1）为界，在薄片的内部以O（εN+1/2）为界。我们明确地说明了0阶、1阶和2阶的模型。变曲率板的数值实验验证了理论结果。
We derive and analyse models which reduce conducting sheets of a small thickness ε in two dimensions to an interface and approximate their shielding behaviour by conditions on this interface. For this we consider a model problem with a conductivity scaled reciprocal to the thickness ε, which leads to a nontrivial limit solution for ε → 0. The functions of the expansion are defined hierarchically, i.e. order by order. Our analysis shows that for smooth sheets the models are well defined for any order and have optimal convergence meaning that the H1-modelling error for an expansion with N terms is bounded by O(εN+1) in the exterior of the sheet and by O(εN+1/2) in its interior. We explicitly specify the models of order zero, one and two. Numerical experiments for sheets with varying curvature validate the theoretical results.