Nearly Singular Fields: Electrostatics and Elastostatics of Composite Materials

Leslie Greengard
Courant Institute
New York University

Abstract: A longstanding area of research in materials science has been the study of electrostatic, magnetic and elastic fields in composites with densely packed inclusions whose material properties differ markedly from those of the background. While powerful tools exist for dilute suspensions, accurate calculations in the close-to-touching case have been carried out largely by asymptotic methods and only for simple geometries such as regular arrays of cylinders or spheres. In this talk, we will describe some new algorithms for the evaluation of electrostatic and elastostatic fields in composite materials with complex geometry.