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For the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous 3-D objects, a previously published one-way domain decomposition method (DDM) is considered: the computational domain is partitioned into concentric subdomains on the interfaces of which Robin-type transmission conditions (TCs) are prescribed, with an integral equation (IE) on the outer boundary of the computational domain (DDM-IE). On account of the large computing time required by the solution of the isolated IE system, in this paper the IE is replaced by the integral representations (IRs) of the fields that requires only a few matrix-vector products (adaptive absorbing boundary condition: AABC). The IRs necessitate the calculation of the electric and magnetic currents on some inner surface S that is chosen to be the interface between the last two subdomains. Taking advantage of the TCs, the unknown current on S (here the magnetic current) is obtained via a change of bases H(rot) to H(div) that allows the accurate computation of the IR integrals involving the surface divergence terms, and permits the separate solution of the FE systems in the last two subdomains. The matrix-vector products in the AABC are performed only once per DDM iteration. Numerical results are presented that illustrate the accuracy of the DDM-AABC and its superiority, in terms of computing time, over the DDM-IE. Also, some indications are given on how to estimate numerically the convergence rate of the DDM-AABC.