## 1 Introduction  
The near-field electromagnetic interaction between components has become an issue in high-frequency complex electronic systems, where it is highly likely to generate phenomena that affect the system performance, such as unwanted electromagnetic interference (EMI) or crosstalk noise. An accurate knowledge of the near-field distribution is mandatory in the design and verification of cable harnesses, integrated circuits, printed circuit boards, and Radio-Frequency (RF) systems. The near-field analysis allows, for instance, the location of hot spots and possible noise sources, or the estimation of the currents induced on the scatterers [1]. Specifically, facing both the emission and immunity issues related to unwanted scattering has become a major challenge for high-frequency systems in vehicles, aircraft, ships, and buildings. This problem poses many challenges both in experimental characterization (e.g., [2, 3]) and in numerical modeling, usually based on full-wave or hybrid models (e.g., [4, 5, 6, 7, 8]). The study of the electromagnetic scattering from objects is a classical problem whose numerical solution can be obtained by using either integral or differential formulations [9; 10; 11]. In this paper, we focus on differential formulations solved by means of the finite element method (FEM). The final numerical model must be of course solved in a bounded solution domain, whereas the original problem is definite in an unbounded one (the whole space). Therefore, the unbounded domain must be truncated by an artificial boundary containing all the scatterers, and proper conditions must be imposed on such a boundary to avoid spurious reflections. Non-reflecting conditions can be classified into two main classes: non-reflective boundary conditions and non-reflective boundary layers. In the first class, the impinging waves are absorbed at the artificial boundary, as for instance when using the classical absorbing boundary conditions (ABC) [12]. In the second approach, the waves are absorbed in an extra layer, as in the case of perfectly matched layer (PML) [13]. A comprehensive review of low- and high-order non-reflecting boundary conditions may be found in [14]. The approximation introduced by the absorbing conditions is not the only issue when a scattering problem is solved in an artificially truncated domain: Another issue arises when a near-field analysis is required. Indeed, the absorbing conditions are usually matched on the structure of the far field, hence they are more efficient if the artificial boundary is placed in the far-field region, rather than in the near-field region. As a consequence, in order to achieve a given accuracy, the computational cost of a near-field simulation increases as the boundary is put closer to the scatterer. These two issues may be solved if exact boundary conditions are imposed in the truncating boundary. This can be done by using the so-called Dirichlet-to-Neumann (DtN) operator on the artificial boundary. In this way, the \"inner\" problem (inside the artificial boundary) is decoupled from the \"outer\" one (outside the artificial boundary). Since the boundary conditions are exact, the boundary may be placed at any position, even in close proximity to the scattering object, thus reducing the computational domain (and hence the cost). This approach has been previously proposed for problems in acoustics, photonics, and electromagnetics, see [15; 16; 17]. Recently, it has been adopted for electromagnetic scattering problems applied to conducting cylinders [18], and composite materials [19]. An extension to the multiple scattering problems is also provided in [20]. The treatment of periodic structures, as those arising from arrays of conductors or Photonic Crystals, can be found in [21; 22; 23; 24], based on the use of a semi-analytical DtN. A DtN-related approach can also be found in modeling atomic and molecular physics [25]. In this paper, the DtN approach is used to solve the scattering problem of a bundled cable illuminated by an external field.