(untitled) (Journal of Computational Mathematics, 2018)
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 ±12 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 Neumann-Poincaré operator, in terms of δ and m, and we check that we recover the estimates obtained in [10].