Asymptotics and Computation of the Solution to the Conductivity Equation in the Presence of Adjacent Inclusions with Extreme Conductivities

摘要

When inclusions with extreme conductivity (insulator or perfect conductor)are closely located, the gradient of the solution to the conductivity equationcan be arbitrarily large. And computation of the gradient is extremelychallenging due to its nature of blow-up in a narrow region in betweeninclusions. In this paper we characterize explicitly the singular term of thesolution when two circular inclusions with extreme conductivities are adjacent.Moreover, we show through numerical computations that the characterization ofthe singular term can be used efficiently for computation of the gradient inthe presence adjacent inclusions.