基本解方法解水下刚性目标三维Helmholtz外散射问题

The method of fundamental solutions for 3D Helmholtz exterior problem of underwater rigid objects

运用基本解方法求解水下刚性目标三维Helmholtz外散射问题。研究了源点位置分布和数目对基本解方法计算结果的影响,比较了最小二乘配点法和等额配点法的计算精度。结果表明,当源点构成的形状与目标边界的形状差异大时,计算精度差,增加源点的数量可提高计算精度,运用较少的源点也可获得令人满意的精度,从而提高计算效率,但源点不宜距离目标边界过远;最小二乘配点法的计算精度较等额配点法高些。

Three-dimensional Helmholtz exterior scattering problem of underwater rigid objects is solved by using the method of fundamental solutions （MFS）. Influences of position distribution and the number of source points to the computational results are studied, and computational accuracy of least square collocation method and that of equivalent collocation method is compared. The results show that computational accuracy gets worse when the distinction between the shape composed of source points and boundary shape of object is more appreciable. It can be improved by increasing the number of source points. Satisfied computational accuracy could obtain from less of the number of source points thus the computational efficiency is gained. However, the source points should not be far from the boundary of object. Computational accuracy of least square collocation method is higher than that of equivalent collocation method.