二维海洋波导中Helmholtz方程外问题数值解的有限元方法

A Finite Element Method for the Exterior Problem of the Helmholtz Equation in an Ocean Waveguide

研究了二维海洋波导中声波与散射体相互作用的问题.基于伽辽金变分原理和DtN映射方法,发展了这类声散射问题的一种有限元数值求解方法,提出了有效的数值实现手段.考察了海洋波导中声波与散射体相互作用的回声结构特性,包括海洋界面的多重反射效应对回声结构特性的影响.数值计算结果表明,所建立的有限元理论方法是有效和实用的,而且数值实现速度较快.

The interaction of acoustic waves with the scattering object in an oceanic waveguide was examined. A finite element method was developed to solve numerically the acoustic scattering problem based on the Galerkin variational principle and the DtN mapping method. The results show that the proposed meth od is valid and its numerical implementation is very fast. Moreover, the echo characteristics of the scatter ing wave by an obstacle in an oceanic waveguide and multiple scattering effects between the obstacle and the waveguide boundaries were considered.