静电学
分段
多极展开
电介质
计算机科学
离散化
迭代法
材料科学
计算科学
数学分析
数学
物理
算法
光电子学
量子力学
作者
Leslie Greengard,Monique Moura
出处
期刊:Acta Numerica
[Cambridge University Press]
日期:1994-01-01
卷期号:3: 379-410
被引量:60
标识
DOI:10.1017/s0962492900002464
摘要
A classical problem in electrostatics is the determination of the effective electrical conductivity in a composite material consisting of a collection of piecewise homogeneous inclusions embedded in a uniform background. We discuss recently developed fast algorithms for the evaluation of the potential and electrostatic fields induced in multiphase composites by an applied potential, from which the desired effective properties may be easily obtained. The schemes are based on combining a suitable boundary integral equation with the Fast Multipole Method and the GMRES iterative method; the CPU time required grows linearly with the number of points in the discretization of the interface between the inclusions and the background material. A variety of other questions in electrostatics, magnetostatics and diffusion can be formulated in terms of interface problems. These include the evaluation of electrostatic fields in the presence of dielectric inclusions, the determination of magnetostatic fields in media with variable magnetic permeability, and the calculation of the effective thermal conductivity of a composite material. The methods presented here apply with minor modification to these other situations as well.
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