Green's kernels for transmission problems in bodies with small inclusions

TL;DR

This paper develops uniform asymptotic approximations for Green's kernels in transmission problems involving small inclusions, providing error estimates and numerical validation for antiplane shear scenarios.

Contribution

It introduces a novel asymptotic method for Green's kernels in domains with small inclusions, including explicit remainder estimates.

Findings

Effective approximation of Green's kernels demonstrated

Numerical simulations confirm accuracy and applicability

Provides explicit error bounds for approximations

Abstract

The uniform asymptotic approximation of Green's kernel for the transmission problem of antiplane shear is obtained for domains with small inclusions. The remainder estimates are provided. Numerical simulations are presented to illustrate the effectiveness of the approach.