## 1 Introduction  
Lamb waves are waves whose material boundary is constrained and generated by the specimen's elastic micro-deformations, which propagate in parallel plate-like structures at ultrasonic frequencies with wavelengths \(\lambda\), generally greater than the plate-thickness [1]. These waves have been of great interest in recent years in the field of nondestructive testing (NDT) [2; 3; 4], surface corrosion damage in plates [5; 6], Structural Health Monitoring (SHM) [7], Lamb wave interaction with defects [8], and materials characterization [9]. It is possible to inspect over long distances, covering the entire cross-section of the plate from a single probe position, including isolated or embedded areas, which are of interest in many engineering applications for corrosion monitoring [10], monitoring stress levels [11], or aerospace composites [12]. Multiple symmetric _Sn_ or antisymmetric _An_ (\(n=0,\,1,\,2,\,\dots\) ) modes are generated for specific plate thicknesses, frequency ranges, and material properties [13]. Despite this, there are difficulties related to interpreting the information of the reflected waves given the discontinuities and the limited scanning distance covered by the wave with good sensitivity [14]. The high attenuation of guided waves occurs mainly because the propagated wave is highly dispersive, producing wave packets that spread out in space and time through plate structures. Physically, the dispersions of the ultrasonic pulse as a consequence of the spectral components propagate at different phase velocities [15]. Thus, according to [1], this causes the attenuation of the pulse due to the dispersion or leakage of energy, and increases the complexity of the received signal due to the multiple mode generation [16; 17; 18]. Most of the Lamb wave problems are associated with obtaining appropriate dispersion curves and corresponding wave structures [19; 20]. There are different analytic and semi-analytic approaches for dispersion curve generation, all of them with different implementation complexities and limitations [20]. This information provided by the dispersion curves includes phase and group velocities, wave number, cut-off frequencies, and the modes with the highest and lowest associated dispersion, among other properties for different propagation modes. Dispersion curves can be obtained experimentally [21; 22; 23; 24; 25], numerically [26; 27], analytically, and semi-analytical. For instance, the Semi-Analytical Scaled Boundary Finite Element Method (SBFEM) [27; 28] is one of the latest approaches defined in the literature. SBFEM is versatile, accurate, and computationally efficient [29]. In the case of the semi-analytic scheme, the waveguide is discretized along the cross-section by using different finite elements and shape functions, while an analytical solution is adopted in the wave propagation direction [30; 31]. The spectral elements in the study of guided waves have already been proposed in the literature. [PERSON] et al. [32; 33; 34; 35] investigated the propagation of guided waves in metallic, composite, and sandwich strips with the time-domain spectral finite element method (TDSFE). See [36; 37; 38], for instance, which discusses the application of spectral elements as an approach to the study of guided wave propagation. The application of the SBFEM method to estimate dispersion curves is based on the fact that only the boundary of the computational domain is discretized with finite elements. As indicated in Figure 1, the appropriate one-dimensional functions \(N\) are defined by the coordinate \(\eta\). Few studies on using SBFEM for guided waves' dispersion curve estimations have been reported [36]. The main concerns related to the algorithm's implementation are the associated computational costs and the accuracy for high-order and isoparametric interpolation approaches.