1：Experimental Design and Method Selection:

The study employs the hierarchical cascading algorithm for FEM simulations, utilizing periodic structure partitioning and Schur complement techniques. It includes the use of perfectly matched layers (PMLs) for open boundary conditions, with variants like C-PML and M-PML. An iterative hierarchical cascading method is introduced for 3D simulations to reduce degrees-of-freedom.

2：Sample Selection and Data Sources:

Simulations are performed on specific SAW device geometries, such as synchronous resonators and coupled-resonator filters on substrates like 42°YX-cut LiTaO3 and 128°YX-cut LiNbO3, with defined parameters like pitch, metallization ratio, and electrode thickness.

3：List of Experimental Equipment and Materials:

The implementation uses a custom mesh generation algorithm and an in-house FEM engine on the commercial Matlab platform. Substrates include piezoelectric materials like LiTaO3 and LiNbO3, with aluminum and copper electrodes.

4：Experimental Procedures and Operational Workflow:

The device geometry is partitioned into unit blocks, simulated with FEM, and cascaded hierarchically. For 3D, an iterative method with modal B-matrices is used. Simulations are run at harmonic frequencies, and results are validated against reference methods like FEM/BEM.

5：Data Analysis Methods:

Data analysis involves evaluating electric responses (e.g., admittance), field distributions (e.g., mechanical displacement and power flow), and convergence of iterative methods. Tools include custom algorithms in Matlab for cascading and post-processing.