Electrostatics and heat conduction in high contrast composite materials

We present a robust integral equation method for the calculation of the electrostatic and thermal properties of systems made of piecewise homogeneous, high contrast materials. By high contrast, we mean that the electrical or thermal conductivity ratios are high. Our approach involves a modification of the standard integral representation using,in electrostatic terms, the polarization charge as an unknown. It is related to the perturbation approach proposed by Tausch and White [J. Tausch, J. White, Capacitance extraction of 3-D conductor systems in dielectric media with high-permittivity ratios, IEEE Trans. Microwave Theory Tech., 47 (1999) 18-26], but based on a simple form of projection rather than on the solution of auxiliary integral equations. Numerical implementation is straightforward in the multiple dielectric case.