Schwarz’s alternating method in a matrix form and its applications to composites

V. Mityushev, W. Nawalaniec, D. Nosov and E. Pesetskaya

Applied Mathematics and Computation, 2019, vol. 356, issue C, 144-156

Abstract: Two-phase composites with n equal non-overlapping inclusions randomly embedded in the matrix are investigated. It is considered the case when the inclusions are bounded by some Lyapunov’s boundary curve. The problem is reduced to a vector-matrix problem of dimension n for one inclusion. The generalized alternating method of Schwarz applied to the vector-matrix problem is decomposed onto n scalar problems for one inclusion which are solved numerically by the method of integral equations for any smooth shape of the inclusions. A symbolic computation method is developed to solve the same problem by means of conformal mapping and functional equations. As a purpose, the effective conductivity of such models is exactly expressed through all geometrical and mechanical properties of its components.

Keywords: Fractured 2D media; Effective conductivity; Random composites; The generalized method of Schwarz; Integral equations; Multiply connected domain (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:356:y:2019:i:c:p:144-156

DOI: 10.1016/j.amc.2019.03.032

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