## 2 Electromagnetic Simulation  
The boundary conditions (Figure 2) aimed to investigate the interaction of a plane wave with the considered sample. The generation of plane wave characteristics of the electromagnetic field was determined by choosing the conditions of the electric wall (x\({}_{\rm min}\) and x\({}_{\rm max}\)) and magnetic wall (y\({}_{\rm min}\) and y\({}_{\rm max}\)). The conditions for the input and output ports are labeled \"open\". The generation of the interaction of the analyzed structure with a plane type wave is presented in Figure 3. Details about the procedure and related conditions can be found in [29]. Figure 1: Equivalent permittivity of a composite material (with polystyrene matrix). The polymer matrix that will host the inserts was low-density polyethylene (LDPE), for which CST Studio Suite software [27] does not have models in its own library. As a  
Figure 3: Plane wave configuration: Electric and magnetic field lines at the entrance port. Figure 2: Boundary conditions. result, a new model was made based on 1 st-order Debye Equation (2) (where \(\omega\) represents the angular velocity), and on the physical characteristics of LDPE, listed in Table 1.  
\[\varepsilon^{*}(\omega)=\varepsilon_{\infty}+\frac{\varepsilon_{S}-\varepsilon_{ \infty}}{1+j\cdot\omega\cdot\tau} \tag{2}\]  
As regards the metal inserts (iron and aluminum) the software has predefined models in libraries, as presented in Table 2.  
This study analyzed the electromagnetic energy loss enhanced by the presence of inserts inside the polymer matrix. For this, the SAR (specific absorption rate) was calculated by integrating the entire volume of the considered domain (matrix and particles), at various frequencies in the microwave domain. The modeling is more accurate if considering quasi-cubic/parallelepipedal particles, equating the volume of particles of different shapes, because, in the case of metallic materials, we expect the electromagnetic energy losses to be superficial rather than volumetric. As a result, in all the following stages of the simulation, parallelepipedal particles equivalent to spheres with radii of 50 nm and 800 nm, respectively, were taken into account, the mathematical equating methodology being largely described in [29; 30]. The edge of the reference cubic particle with the same volume as the ideal spherical particle will be R\({}_{\text{ref}}\) = R\(\cdot\)(4\(\pi\)/3)\({}^{1/3}\). To account for detected irregularities in the size of the nanoparticles, we allow every side of every cube to variate between half and twice the reference cubical edge, resulting in a randomly shaped parallelepipedal particle, also randomly placed. By decreasing the dimensions of the inserts, a limitation of the capacity of the computing systems may be reached relatively quickly if working with larger simulated volumes. A reasonable solution adopted was to reduce the total volume of the structure as the particle size decreases, so that the total number of particles is approximately constant for both particle dimensions, at around 500 (variations appear due to their random distribution). \begin{table}
\begin{tabular}{c c} \hline \hline
**Matrix** & **LDPE** \\ \hline Model type & Normal \\ \hline Thermal conductivity & 0.48 [W/K/m] \\ \hline Density & 945 kg/m\({}^{3}\) \\ \hline Electrical permittivity \(\varepsilon_{\infty}\) & 2.2 \\ \hline Electrical permittivity \(\varepsilon_{\text{S}}\) & 4 \\ \hline Relaxation time & 0.2 s \\ \hline Magnetic permeability & 1 \\ \hline Specific heat & 1.9 kJ/K/kg \\ \hline \hline \end{tabular}
\end{table} 
Table 1: LDPE matrix properties.