In this master thesis I investigate the case of solving linear systems which correspond to mechanical problems with the use of Deflated Preconditioned Conjugate Method (DPCG), where the creation of the preconditioner is based on Additive Schwarz method (ASM). This approach allows us to perform several computation steps in parallel, which leads to a faster solution of the problem. Also, the use of ASM implies that we need to decompose the domain. There are plenty of ways to do it. In this Master Thesis I perform a decomposition based on the material types, i.e. each distinguishable consistent area of one material type is taken as a subdomain for the decomposition.