In this paper, we discuss a domain decomposition method to solve linear elasticity problems in complicated 2-D geometries $Omega$. We describe in details algebraic system corresponding to Dirichlet-Neumann and Schwarz methods. The alternating iterative algorithm obtained is numerically implemented using the boundary element method. The stopping and accuracy criteria, and two type of domain are investigated which confirm that the iterative algorithm produces a convergent and accurate numerical solution with respect to the number of iterations.
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