Because of their superior absorption characteristics, the Perfectly Matched Layer (PML) absorbers are used in truncating finite element domains. However, their implementation is equivalent to imposing active elements inside the main mesh. Consequently, the condition number of the resulting systems deteriorates. In this work, an efficient preconditioned generalized minimal residual (GMRES) iterative solver is developed and applied to systems truncated by PML absorbers. This iterative scheme is implemented and tested for different cases representing actual structures.