论文标题
应用基于域分解的Legendre搭配方法来计算水平分层环境中的水下声音传播
Applying a Legendre collocation method based on domain decomposition to calculate underwater sound propagation in a horizontally stratified environment
论文作者
论文摘要
传统上，使用普通模式计算了水平分层环境中声波的传播，这是海洋声学中的经典问题。大多数基于正常模式模型的程序使用有限差异方法（FDM）离散化。在本文中，提出了基于域分解的Legendre搭配方法（LCM）来解决此问题。一组搭配点不能穿透多层介质，因此需要域分解和使用多组套在一起点。该方法的解决方案过程完全在物理空间中进行，要求在搭配点严格确定原始的微分方程。因此，形成了密集的矩阵特征值系统，可以直接从中获得水平波数和模式的解。提出了数值实验，以证明该方法的有效性和适用性。与其他方法的比较表明，本文提出的LCM比FDM更准确，并且与其他类型的光谱方法相比，计算速度的准确性大致相同。
The propagation of sound waves in a horizontally stratified environment, a classic problem in ocean acoustics, has traditionally been calculated using normal modes. Most programs based on the normal mode model are discretized using the finite difference method (FDM). In this paper, a Legendre collocation method (LCM) based on domain decomposition is proposed to solve this problem. A set of collocation points cannot penetrate multiple layers of media, thus necessitating domain decomposition and the use of multiple sets of collocation points. The solution process of this method proceeds entirely in physical space, requiring that the original differential equation be strictly established at the collocation points; thus, a dense matrix eigenvalue system is formed, from which the solution for the horizontal wavenumbers and modes can be directly obtained. Numerical experiments are presented to demonstrate the validity and applicability of this method. A comparison with other methods shows that the LCM proposed in this article is more accurate than the FDM and offers roughly the same accuracy as but a faster calculation speed than other types of spectral methods.
