Hesford Andrew J, Waag Robert C
Department of Electrical and Computer Engineering, University of Rochester, Rochester NY 14642-8648 USA.
J Comput Phys. 2010 Oct 20;229(21):8199-8210. doi: 10.1016/j.jcp.2010.07.025.
The fast multipole method (FMM) is applied to the solution of large-scale, three-dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid. The grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques. The regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the FMM, both of which scale linearly with the number of scattering elements. In particular, the use of fast Fourier transforms to compute Green's function convolutions required for neighboring interactions lowers the often-significant cost of finest-level FMM computations and helps mitigate the dependence of FMM cost on finest-level box size. Numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest-level box is increased.
快速多极子方法（FMM）被应用于求解涉及定义在规则网格上的非均匀物体的大规模三维声学散射问题。这种网格排列特别适合散射几何形状事先未知的应用，并且可以使用迭代逆散射算法或其他成像技术在规则网格上进行重建。未知散射元素的规则结构有助于显著减少FMM所需的存储量和计算量，这两者都与散射元素的数量呈线性比例关系。特别是，使用快速傅里叶变换来计算相邻相互作用所需的格林函数卷积，降低了最精细级别FMM计算中通常很高的成本，并有助于减轻FMM成本对最精细级别盒子大小的依赖性。数值结果表明，随着每个最精细级别盒子中散射元素数量的增加，复合方法的效率得以体现。
