Efficient Analytical and Numerical Treatment of High Contrast Composites
Yuliya Gorb, University of Houston

Abstract:

This talk reviews numerical and asymptotic analysis methods for models that describe heterogeneous or composite materials. In particular, we focus on high contrast two-phase composites that are described by PDEs with rough coefficients, e.g. the case of highly conducting particles that are distributed in the matrix of finite conductivity. In our numerical studies, we assume that particles are located at distances comparable with their sizes, while in our asymptotic methods, we consider densely packed composites where particles are almost touching one another. The proposed numerical procedure yields robust iterative method whose number of iterations is independent of the contrast parameter and the discretization scale. Discrete models constructed using our asymptotic procedures are used for capturing and characterizing various blow-up phenomena that occur in dense high contrast materials.