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Computational Analysis of Structured Media - 1st Edition - ISBN: 9780128110461, 9780128110478

Computational Analysis of Structured Media

1st Edition

Authors: Simon Gluzman Vladimir Mityushev Wojciech Nawalaniec
Paperback ISBN: 9780128110461
eBook ISBN: 9780128110478
Imprint: Academic Press
Published Date: 11th September 2017
Page Count: 328
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Table of Contents

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


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.

Key Features

  • 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


Applied mathematicians at graduate level and above and mathematically advanced engineers interested in macroscopic property analysis in deterministic and random composites for scientific or industrial ends.


No. of pages:
© Academic Press 2018
11th September 2017
Academic Press
Paperback ISBN:
eBook ISBN:


"In conclusion, the treatise is very interesting and well written. The computational analysis of composites is given by using the classical analytic formulae in the complex domain. The analysis may be readily extended to special geometry, motion, material and alike of structured media. The treatise can be used even as a “basic reference” for teaching a graduate course, and it is highly recommended to researchers in applied mathematics and computational mechanics." --Zentralblatt MATH

Ratings and Reviews

About the Authors

Simon Gluzman

Simon Gluzman is presently an Independent Researcher (Toronto, Canada) and formerly a Research Associate at PSU in Applied Mathematics. He is interested in Re-summation methods in theory of random and regular composites and the method of self-similar and rational approximants.

Affiliations and Expertise

Independent Researcher, Toronto, Canada

Vladimir Mityushev

Vladimir Mityushev is the head of the modeling and simulation laboratory at the department of computer science and computational methods at the Pedagogical University of Kraków, Poland, a leader of the research group He is interested in mathematical modeling and computer simulations, Industrial mathematics and boundary value problems and their applications.

Affiliations and Expertise

Head of Modeling and Simulation Laboratory, Institute of Computer Science, Pedagogical University, Krakow, Poland

Wojciech Nawalaniec

Wojciech Nawalaniec is an Associate Professor in applied mathematics at Pedagogical University of Cracow, Kraków. He is interested in Computational methods, such as symbolic computation, mathematical modeling and algorithms.

Affiliations and Expertise

Associate Professor, Applied Mathematics, Pedagogical University of Cracow, Krakow, Poland