## 3 Calculation Simulation and Analysis
### Performance Comparison of Different Methods  
When the time is taken as 1 s and the time step \(\Delta t\) is taken as 0.0001 s, the symmetrization equations expressed in Equation (20) do not converge, and the results of Equation (20) for the first 100 time steps are given in Figures 3 and 4, which shows that both the sound pressure and displacement do not converge with time. This is due to the fact that when the matrix is symmetrized, since there are more degrees of freedom in the elastomer than in the fluid, the term in Equation (20) involves the operation of multiple degrees of freedom, which leads to an incomplete symmetry with the term, while the term in Equation (21) has a better symmetry with the term. Therefore, the GEM and GIM in the later study are both calculated using Equation (21). Figure 3: Calculated results for the first 100 time steps of Equation (20) (sound pressure at reception point 1). In order to facilitate the comparative analysis, the same calculation platform is used, the results are normalized, and the root mean square errors of the five methods are shown in Table 1, where \(p_{1}\) represents the sound pressure at the reception point 1 in Figure 2, \(p_{2}\) represents the sound pressure at the reception point 2, \(u_{3}\) represents the displacement at the reception point 2, and \(u_{4}\) represents the displacement at the reception point 4. As can be seen from Table 1, in terms of stability, all five methods are stable because the selected step sizes satisfy the stability conditions of the explicit methods plus the unconditional stability of the implicit methods. In terms of computational accuracy, IIM and GIM have comparable accuracy because both are based on the implicit method of solving; GEM has a higher accuracy than EEM, which indicates that for the explicit method, the global solution accuracy is better than the partial solution because each iteration introduces numerical errors, and the EEM needs to be iterated in two steps (see Equation (10)), whereas the GEM can be iterated in only one step (see Equation (23)), and therefore the cumulative error of GEM is smaller than that of EEM. The accuracy of EEM is basically the same as that of EIM, which indicates that compared with the explicit-explicit method, the explicit-implicit hybrid method does not significantly improve the computational accuracy, which is due to the fact that in each iteration of EIM, the results computed by the explicit method (the first equation of Equation (19)) will be introduced to the implicit method (the second equation of Equation (19)), and the iteration of the two is nested within each other, which makes the advantage of implicit method not obvious. The advantage of the implicit method is not apparent. In terms of computational efficiency, EEM is the fastest. GEM is also an explicit method, but it involves more matrix degrees of freedom than the partial solution and takes nearly twice as long as EEM. The IIM method takes the longest time, which is about twice as long as EEM; this is because according to Equation (19), the implicit solution requires six equations to be iterated at the same time, whereas according to Equation (10), the explicit solution requires only three equations to be iterated at the same time. The time consumed by GEM and GIM is comparable, which indicates that for the global solution, the explicit method has no apparent advantage in terms of computational efficiency, because according to Equations (23) and (24), ignoring the computation of matrix summation, both GEM and GIM need to multiply large matrices once. In order to more conveniently and intuitively show the results of the wavefield calculations, Figures 5-8 give the results of the comparison between the GIM and