## 3 Method
### Algorithmic Implementation
Upon selecting an appropriate discretization method, an external meshing software, such as gmsh [81], can be used to model the domain. If a complex structure and/or various damage configurations are present, this can become a tedious and time-intensive task, which can render automatized damage-detection algorithms infeasible. With this, as well

Figure 6: An infinite plate with one feature and one sensor. Possible travel paths for propagating \(S_{0}\) and \(A_{0}\) modes. Thin lines: \(S_{0}\) mode. Fat lines: \(A_{0}\) mode. Dashed: \(S_{0}\) and \(A_{0}\) modes, stemming from mode conversion at the feature. (**a**) Possible travel paths. (**b**) Tree corresponding to the rays in (**a**). as other meshing-related issues, in mind, several enhancements of the aforementioned methods have been proposed, which enable supplementing the mesh with additional geometrical definitions, thus easing the reliance on the performance of meshing software. In the present contribution, the SEM was supplemented with a mesh-independent representation of voids, whose influence on Equation (2) is accounted for via customized space integration rules. This approach, known as the Spectral Cell Method [82; 83; 84; 85; 86], allows for maintaining a level of efficiency that is on par with the SEM; however, it also leads to a loss of the diagonal mass matrix property for elements that are intersected by voids. To mitigate this issue, several alternatives have been proposed, including diagonal scaling [87], or moment fitting [88] schemes, as well as the use of implicit-explicit solvers [89; 90]. In this contribution, we have adopted the latter approach, implemented in the C++ language. The corresponding code has been validated by comparison against a numerical implementation adopting shell elements [91], against benchmark analytical solutions for simple setups [88], as well as corroborated using Laser Doppler Vibrometer (LDV) experimental measurements [86]. ### Plate Configuration

For all given results, a 2 mm aluminum plate with its material properties displayed in Table 1 is examined. As previously described, a regular mesh is used for all simulations, with features modeled as voids via customized integration. Each element of the mesh is 3 mm \(\times\) 3 mm \(\times\) 2 mm with slightly smaller elements for sections whose dimensions are not a perfect multiple of 3 mm. Fourth-order spectral elements are utilized, and cut elements are described in [88]. To avoid boundary reflections, Absorbing Layers using Increasing Damping (ALID) are applied. The ALID scheme refers to several layers of elements at the boundary of the domain, with each layer comprising a higher damping coefficient as the distance from the plate increases, which allows for absorption of the incoming waves. Here, we apply ALID through 30 layers, each with a width of one element, and an increasing mass proportional damping. The damping coefficients are determined through a quadratic function, with the maximum damping coefficient assigned as \(10^{7}\) in the 30 th layer, following the recommendations in [92]. ### Excitation

The excitation in the given examples stems from two point loads applied at the top and the bottom of the plate in different locations. This introduces some practical questions. If both loads comprise the same magnitude and are oriented to the same or opposite direction, the plate is, in theory, excited purely anti-symmetrically or symmetrically, respectively. However, it should be noted that even in a frequency range, where only the fundamental Lamb wave modes (\(S_{0}\) and \(A_{0}\)) are propagating, shear horizontal modes are activated. In the shown example, this introduces negligible error and is, therefore, ignored. If the shear horizontal modes are of interest, it should be possible to excite these in a targeted manner and consequently treat them similarly to Lamb wave modes. We acknowledge that point loads are not thoroughly depicting realistic excitation sources within an actual monitoring setup.