Application of a Chebyshev Collocation Method to Solve a Parabolic Equation Model of Underwater Acoustic Propagation

2021 ◽  
Author(s):  
Yongxian Wang ◽  
Houwang Tu ◽  
Wei Liu ◽  
Wenbin Xiao ◽  
Qiang Lan
Keyword(s):  
Parabolic Equation ◽  
Collocation Method ◽  
Acoustic Propagation ◽  
Equation Model ◽  
Chebyshev Collocation Method ◽  
Underwater Acoustic ◽  
Chebyshev Collocation

scholarly journals A Spectral Method for Two-Dimensional Ocean Acoustic Propagation

2021 ◽  
Vol 9 (8) ◽  
pp. 892
Author(s):  
Xian Ma ◽  
Yongxian Wang ◽  
Xiaoqian Zhu ◽  
Wei Liu ◽  
Qiang Lan ◽  
...  
Keyword(s):  
Numerical Calculation ◽  
Spectral Method ◽  
Collocation Method ◽  
Approximation Error ◽  
Sound Field ◽  
Acoustic Propagation ◽  
Two Dimensional ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation ◽  
Wide Range

The accurate calculation of the sound field is one of the most concerning issues in hydroacoustics. The one-dimensional spectral method has been used to correctly solve simplified underwater acoustic propagation models, but it is difficult to solve actual ocean acoustic fields using this model due to its application conditions and approximation error. Therefore, it is necessary to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation without using simplified models. Here, two commonly used spectral methods, Chebyshev–Galerkin and Chebyshev–collocation, are used to correctly solve the two-dimensional Helmholtz model equation. Since Chebyshev–collocation does not require harsh boundary conditions for the equation, it is then used to solve ocean acoustic propagation. The numerical calculation results are compared with analytical solutions to verify the correctness of the method. Compared with the mature Kraken program, the Chebyshev–collocation method exhibits higher numerical calculation accuracy. Therefore, the Chebyshev–collocation method can be used to directly solve the representative two-dimensional ocean acoustic propagation equation. Because there are no model constraints, the Chebyshev–collocation method has a wide range of applications and provides results with high accuracy, which is of great significance in the calculation of realistic ocean sound fields.

scholarly journals A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1227
Author(s):  
Xian Ma ◽  
Yongxian Wang ◽  
Xiaoqian Zhu ◽  
Wei Liu ◽  
Wenbin Xiao ◽  
...  
Keyword(s):  
Collocation Method ◽  
High Efficiency ◽  
Sound Field ◽  
Acoustic Propagation ◽  
Collocation Methods ◽  
Two Dimensional ◽  
Chebyshev Collocation Method ◽  
Application Range ◽  
Chebyshev Collocation ◽  
The Galerkin Method

The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness.

An embedded formula of the Chebyshev collocation method for stiff problems

2017 ◽  
Vol 351 ◽  
pp. 376-391 ◽  
Author(s):  
Xiangfan Piao ◽  
Sunyoung Bu ◽  
Dojin Kim ◽  
Philsu Kim
Keyword(s):  
Collocation Method ◽  
Stiff Problems ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation
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