Computational Analysis of Structured Media

presents a systematical approach to analytical formulae for the effective properties of deterministic and random composites. Schwarz''s method and functional equations yield for use in symbolic-numeric computations relevant to the effective properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis, and their applications to composites. Symbolic-numerical computations are widely used to deduce new formulae interesting for applied mathematicians and engineers.

The main line of presentation is the investigation of two-phase 2D composites with non-overlapping inclusions randomly embedded in matrices.

Computational methodology for main classes of problems in structured media

Theory of Representative Volume Element

Combines exact results, Monte-Carlo simulations and Resummation techniques under one umbrella

Contains new analytical formulae obtained in the last ten years and it combines different asymptotic methods with the corresponding computer implementations