Computational Analysis of Structured Media

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 mediaTheory of Representative Volume ElementCombines exact results, Monte-Carlo simulations and Resummation techniques under one umbrellaContains new analytical formulae obtained in the last ten years and it combines different asymptotic methods with the corresponding computer implementations

1. Introduction 2. Complex potentials and R-linear problem 3. Constructive Homogenization 4. From basic sums to effective conductivity and RVE 5. Introduction to the method of Self-Similar Approximants 6. Conductivity of Regular Composite. Square Lattice 7. Conductivity of Regular Composite. Hexagonal Array 8. Effective Conductivity of 3D Regular Composites 9. Random 2D Composites 10. Elastic problem 11. Table of the main analytical formulae