EIGENVALUES OF THE NEUMANN-POINCAR(E) OPERATOR FOR TWO INCLUSIONS WITH CONTACT OF ORDER m:A NUMERICAL STUDY

• 来源期刊: 计算数学（英文版）
• 关键词: Elliptic equations Eigenvalues Numerical approximation
• 年，卷（期）: 2018,（1）
• 页码范围: 17-28
• 页数: 12页
• 语种: 英文
• DOI: 10.4208/jcm.1607-m2016-0543

摘要

In a composite medium that contains close-to-touching inclusions,the pointwise values of the gradient of the voltage potential may blow up as the distance δ between some inclusions tends to 0 and as the conductivity contrast degenerates.In a recent paper [9],we showed that the blow-up rate of the gradient is related to how the eigenvalues of the associated Neumann-Poincaré operator converge to ±2/1 as δ → 0,and on the regularity of the contact.Here,we consider two connected 2-D inclusions,at a distance δ ＞ 0 from each other.When δ =0,the contact between the inclusions is of order m ≥ 2.We numerically determine the asymptotic behavior of the first eigenvalue of the NeumannPoincaré operator,in terms of δ and m,and we check that we recover the estimates obtained in [10].