ASYMPTOTIC APPROXIMATION OF THE DIRICHLET TO NEUMANN MAP OF HIGH CONTRAST CONDUCTIVE MEDIA

作者：Borcea Liliana^*; Gorb Yuliya; Wang Yingpei

来源：Multiscale Modeling and Simulation, 2014, 12(4): 1494-1532.

DOI：10.1137/140960761

• Dirichlet to Neumann map
• high contrast
• discrete network
• boundary layer

We present an asymptotic study of the Dirichlet to Neumann map of high contrast composite media with perfectly conducting inclusions that are close to touching. The result is an explicit characterization of the map in the asymptotic limit of the distance between the particles tending to zero. Known homogenization results state that the effective conductivity of the high contrast composites is determined by resistor networks with topology defined by the geometric distribution of the inclusions. The result in this paper is stronger than homogenization because it applies to arbitrary boundary conditions. In particular, it accounts for the coupling of boundary current flow induced by oscillatory boundary potentials and the flow in the network.

• 出版日期2014