## 3 Numerical Simulations  
The acoustic information of the structure such as sound pressures and normal velocities are acquired in the simulations, and the process could be accomplished in COMSOL Multiphysics (a commercial software based on FEM). The sound radiation model for a structure in the free field and half-space are shown in Figure 3. The non-reflecting boundary condition is simulated by the technology of the perfect matched layer (PML), and the thickness of every layer should not be larger than \(1/15\) of the wavelength.  
The vibration of the structure should be acquired in advance as the input of the prediction methods. Meanwhile, the vibration information of the structure could be regarded as the references of vibration reconstruction in VR-ESM. However, it is often difficult to obtain the vibration of a structure in the fluid, especially when reflection boundaries exist to reinforce the acoustic-solid coupling effect. Luckily, in COMSOL, it is convenient to solve the problem as the FEM algorithm is the basic of the software. Especially, at low frequencies, the vibration could be obtained via FEM with a tiny computational cost.  
To acquire the vibration of the structure when the parameters of the fluid, the structure, and the excitations are given out in advance, the structural FEM equation and the acoustical FEM equation should be solved simultaneously. The coupling relationship between the two equations is expressed by the continuity of the structural normal velocity and the particle velocity of the fluid on the structural surface. Then, the structural vibration and the sound field could be computed easily in the solution domain as all the computational processes are completed inside the software. Moreover, the structural modal analysis could also be carried out with FEM. The development of the method is introduced in detail in the study [15].  
As FEM-BEM is a mature algorithm for sound prediction, the prediction results of FEM-BEM are considered as the references of the other prediction methods in the following extent. The computational process of FEM relies on the meshing of structure and the fluid domain, making it computational costly to complete the sound prediction at a long distance with FEM. Therefore, scholars take advantage of BEM in saving computation to complete the sound prediction at arbitrary positions in the sound field [7]. BEM is based on the Helmholtz integral equation as Equation (27):  
\[C(P)p(P)=\int_{S}\left[P(P_{S})\frac{\partial G(P,P_{S})}{\partial n_{s}}- \mathrm{j}\rho_{0}\Omega_{0}v_{n}G(P,P_{S})\right]dS \tag{27}\]  
where \(C(P)\) is a coefficient that is related to the position with the sound field point \(P\). When \(P\) is outside the structure, \(C(P)=1\). \(P_{S}\) represents the integral points on the structural surface and \(v_{n}\) is the normal velocity at \(P_{S}\)[3]. It could be found that \(P(P_{S})\) and \(v_{n}\) has been obtained in the process of FEM. Thus, the computation of BEM could be completed. From the above introductions, FEM could be combined with BEM to utilize the advantages of the two methods. As the acoustical input of the other prediction methods such as ESM, CMESM, and VR-ESM is the normal velocities on the structure, the operation is the same as the abovementioned introduction.  
Figure 3: The sound radiation model for a structure: (**a**) free field and (**b**) half-space.