EIGENVALUES OF THE NEUMANN-POINCARE OPERATOR FOR TWO INCLUSIONS WITH CONTACT OF ORDER m： A NUMERICAL STUDY

作     者：Eric Bonnetier Faouzi Triki Chun-Hsiang Tsou 

作者机构：Universitd Grenoble-Alpes//CNRS Laboratoire Jean Kuntzraann UMR 5224 Grenoble F-38041 France 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2018年第36卷第1期

页      面：17-28页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the LabEx PERSYVAL-Lab 

主　　题：Elliptic equations Eigenvalues Numerical approximation. 

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 S 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-Poincare operator converge to ±1/2 as δ→ 0, and on the regularity of the contact. Here, we consider two connected 2-D inclusions, at a distance 5 〉 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 Neumann- Poincare operator, in terms of 5 and rn, and we check that we recover the estimates obtained in [10].