On Field Concentration Between Nearly-Touching Multiscale Inclusions in the Quasi-Static Regime (Advances in Applied Mathematics and Mechanics, 2024)
Strong field concentration may occur between two nearly-touching high-contrast material inclusions due to an incident field. The degree of concentration ischaracterised by the blowup rate of the underlying gradient field. This phenomenonhas received considerable attention in the literature due to its practical implicationsin the theory of composite materials. However, most of the existing studies are concerned with the static cases. In this paper, we present a comprehensive numericalinvestigation of this intriguing phenomenon associated to the Helmholtz system inthe quasi-static frequency regime. On the one hand, we present extensive numericalresults to corroborate the theoretical findings in [16], and on the other hand, we derive new findings that cannot be handled by the theoretical analysis yet. Our focus ison the static effect, frequency effect, the geometric (curvature) effect to the gradientestimates.