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

Author

Listed:
  • Mityushev, V.
  • Nawalaniec, W.
  • Nosov, D.
  • Pesetskaya, E.

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.

Suggested Citation

  • Mityushev, V. & Nawalaniec, W. & Nosov, D. & Pesetskaya, E., 2019. "Schwarz’s alternating method in a matrix form and its applications to composites," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 144-156.
    • Handle: RePEc:eee:apmaco:v:356:y:2019:i:c:p:144-156
    DOI: 10.1016/j.amc.2019.03.032
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