# Acoustic Shooting and Bounce Ray Method for Calculating Echoes of Complex Underwater Targets
## 8 Conclusions  
To solve the needs of the accurate simulation of complex underwater target echoes quickly, this paper, based on the derivation of the time-domain Kirchhoff integral formula, first defined the solution vector and used the Stokes formula to reduce the dimension of the two-dimensional integral process, which effectively reduces the computational complexity of the integral and provides a theoretical basis for the parallel solution of the time-domain simulation echo. At the same time, combined with the geometric acoustic method (GA), based on the KD-tree spatial partitioning algorithm, which has mature application in computer graphics, through modeling and analysis of several key problems affecting the calculation of the sound field in the process of the geometric tracking of sound lines, and finally established the efficient parallel characteristics. The acoustic bouncing ray calculation method (TD-ASBR) for the time domain target echo simulation. In the realization of the simulation examples, the TD-ASBR method was used to simulate the angle-intensity and frequency-intensity responses of typical models, such as sphere and cylinder, and the correctness and effectiveness of the method are analyzed and verified. At the same time, the acoustic ISAR imaging method is used to directly prove that TD-ASBR method generates target echo simulation results with more complete target information. The comparison of the echo simulation results of the PA acceleration method shows that TD-ASBR can provide a corresponding simulation solving efficiency under different simulation accuracy conditions. The results of the TD-ASBR method proved to be accurate and reliable. The algorithm can be accelerated by the high-performance parallel computing platform, which has high parallel computing efficiency and is suitable for the broadband fine echo simulation of complex underwater targets.  
It can be seen from the design process of the TD-ASBR method that the algorithm is more suitable for high-frequency acoustic conditions. However, although not to the low frequency under the condition of effective elastic echo simulation, for the calculation of surface acoustical material laying conditions, will be certain to approximate simplified, acoustic pulse is obtained by using the layered medium acoustic spread across the medium state and still use the TD method of ASBR processing, which is a direction for further research.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Entity Model** & **Ball (0.05 \(\lambda\))** & **Column (0.05 \(\lambda\))** & **Standard Boat (0.1 \(\lambda\))** \\ \hline GPU-PA acceleration algorithm & 0.65 & 0.35 & 2.69 \\ GPU-Conventional integral dimension reduction & 4.45 & 1.46 & 9.20 \\ accelerative ratio & 6.84 & 4.17 & 3.42 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the calculation time (unit: seconds).  
**Author Contributions:** Conceptualization, G.Z. and X.W.; methodology, G.Z. and N.S.; software, S.S. and X.W.; validation, W.Z.; formal analysis, G.Z. and X.W.; writing--original draft preparation, G.Z. and X.W.; visualization, N.S.; funding acquisition, X.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was funded in part by the China Postdoctoral Science Foundation (2013M540735); in part by the National Nature Science Foundation of China under Grant 61901388, 61701360; and in part by the Fundamental Research Funds for the Central Universities.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.