## 2 Materials and Methods
### Numerical Models
The random structure of defects (Figure 3) was created with certain assumptions:  
Figure 2: Modeled samples: (**a**) a sample without any defects (NDS); (**b**) a sample with one defect located in the center of the epoxy layer (CDS); (**c**) a sample with the defects simulating the ageing process located at the rim of the epoxy and composite layers (ADS); (**d**) a sample with both: ageing defects and central defect (CADS). * The radius of each defect varies randomly between 0.1 and 1 cm. The height of the defect is either 0.01 cm (for 30% of defects) or 0.015 cm (for the remaining 70% of defects). In the first case, the entire defect is within the adhesive layer, while in the latter, it partially extends into the composite layer (Figure 3a);
* The defects were located exclusively at the periphery of the composite reinforcement, with their centers randomly distributed along a 1 cm margin encompassing the entire composite (Figure 3b);
* The total count of cylindrical defects is 100;
* Overlapping defects are allowed, but their logical sum will be taken into account. The whole structure is presented in Figure 3c with the magnification of the chosen region. Figure 4a presents the whole geometry designed for one of the scenarios, specifically a sample exhibiting a defect in the form of non-adherence, together with defects presented on the borders of the composite layer (CADS). The system accurately replicates the physical laboratory setup, considering the precise location of the sample in relation to the antenna. An adequate angle was chosen to rotate the sample in relation to the antenna, allowing for the surface to be observed using a thermal imaging camera. The angular placement of  
Figure 3: Designing the defects simulating the ageing process (dimensions in mm): (**a**) the model of two possible depths of the defect—the defect located within the epoxy and composite layers and the defect located only in the epoxy layer; (**b**) marked frame at the reinforcement surface showing the localization of all the generated defects related to ageing; (**c**) the visualization of the effect of the defects generation in COMSOL. the sample in relation to the antenna significantly impacts the final result of microwave heating. In our particular situation, the choice of this angle was arbitrarily, but it is worth investigating the selection of an angle that allows for both the viewing of the sample while it is being heated and the establishment of a potentially even temperature distribution throughout its surface. The accuracy of the solution in the finite element method is significantly affected by the quality of the mesh. Figure 4b presents the mesh configuration of the system under analysis. Figure 4b illustrates an instance where the total number of finite tetrahedral elements was 776,410. The meshing process was carried out in a customized manner, with the maximum size of each element set to 1/10 of the wavelength. This criterion was applied to the regions encompassing the antenna and the surrounding sample, where the heat transfer problem was not handled. In the sample domain regions, where the heat transfer was resolved, especially in the thin layers of epoxy and carbon composite, as well as in the surrounding of the small aging defects, the elements number was noticeably increased, as depicted in the Figure 4c. The walls of the simulated antenna were subjected to an impedance boundary condition, which was defined as follows [53]:  
\[\sqrt{\frac{\mu}{e-j\sigma/\omega}}\mathbf{n}\times\mathbf{H}=\mathbf{n}\times \mathbf{E}, \tag{4}\]  
where \(\mathbf{H}\) is the magnetic field strength vector. The walls of the air-filled region enclosing the sample are subjected to a scattering boundary condition [54]:  
\[\mathbf{n}\times(\
abla\times\mathbf{E})-j\mathbf{k}\mathbf{n}\times(\mathbf{ E}\times\mathbf{n})=0, \tag{5}\]  
where \(k\) is the wavenumber. A specific wall within the waveguide applies the port boundary condition to produce an electromagnetic wave. The assumed mode, in this case, is \(\mathrm{TE}_{10}\).