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.
- 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
- eBook ISBN:
- Paperback 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
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.
Research Associate, PSU in Applied Mathematics. He held in the past held various research positions in Industry and Academia
Vladimir Mityushev is the head of modeling and simulation laboratory at the department of computer science and computational methods at Pedagogical University of Cracow, Kraków, Poland. He is interested in Mathematical modeling and computer simulations, Industrial mathematics and boundary value problems and their applications.
Head of Modeling and Simulation Laboratory, Department of Computer Science and Computational Methods, Pedagogical University of Cracow, Kraków, Poland
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.
Associate Professor, Applied Mathematics, Pedagogical University of Cracow, Kraków, Poland