In this paper two domain decomposition formulations are presented for the solution of large-scale problems in solid and structural mechanics. In the first approach a PCG method is applied to the interface problem after eliminating the internal d.o.f. For this Schur complement implementation, a Subdomain-by-Subdomain (SBS) preconditioner is proposed based on the local Schur complement of each subdomain. The approximate inverse of the global Schur complement, which acts as a preconditioner, is expressed by a truncated Neumann series resulting in an additive form local preconditioner. The second approach operates on the global subdomain problem and the PCG iterations are performed on a SBS global basis. The innovative aspect of this formulation is focused on the handling and implementation of the preconditioning matrix. An internal PCG algorithm is applied to solve the preconditioning problem. These internal PCG iterations are performed on a totally uncoupled problem with the introduction of Lagrange multipliers.

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