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Volume . Symbolic-Numerical Analysis of 2D Composites and Porous Material

Published: 1st October 2017 Authors: Simon Gluzman Vladimir Mityushev Wojciech Nawalaniec

Computational analysis of Structured Media presents a generalized convergent method of Schwarz and functional equations yield for use in symbolic-numeric computations relevant to the effective evaluation of 2D composite properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis and their applications to composites and porous media. Symbolic-numerical computations are widely used to deduce new formulae interesting for mathematiciains and engineers. The main line of presentation is the investigation of two-phase composites with non-overlapping inclusions randomly embedded in matrices. A direct approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value problems are solved for all locations of inclusions, i.e., for all events of the considered probabilistic space C by the generalized method of Schwarz. Second, the effective properties are calculated in analytical form and averaged over C. This is related to the classic method based on the average probabilistic values involving the $n$-point correlation functions. However, the authors avoid computation of the correlation functions and compute their weighted moments of high orders by an indirect method which does not address to the correlation functions. The effective properties are exactly expressed through these moments. It is proved that the generalized method of Schwarz converges for an arbitrary multiply connected doubly periodic domain and for an arbitrary contrast parameter. Similar techniques are applicable to porous media. The proposed method yields effective algorithm in symbolic-numeric form.

Additional volumes

Volume 197. Inequalities for Differential and Integral Equations

Published: 12th November 1997 Series Volume Editor: B. Pachpatte