In this paper, a localized version of the method of fundamental solutions (MFS) named as the localized MFS (LMFS) is applied to two-dimensional (2D) harmonic elastic wave problems. Due to the dense and ill-conditioned coefficient matrices, the traditional MFS is computationally expensive and time-consuming to solve the above-mentioned problems which require a large amount number of nodes to obtain excellent numerical results. In the LMFS, the domain is divided into small subdomains, in which the traditional MFS is applied to represent the physical variables as linear combinations of the fundamental solution. A sparse and banded system of linear equations is yielded in this method, so that it is attractive to solve large-scale problems. A numerical example demonstrates the effectiveness and accuracy of the proposed LMFS.

在本文中，将基本解法（MFS）的本地化版本（称为本地化MFS（LMFS））应用于二维（2D）谐波弹性波问题。由于稠密且病态的系数矩阵，传统的MFS解决上述问题需要大量节点才能获得出色的数值结果，因此在计算上既昂贵又费时。在LMFS中，将域划分为小子域，在该子域中，传统MFS被应用为将物理变量表示为基本解的线性组合。该方法产生了一个稀疏的带状线性方程组，因此吸引人们去解决大规模问题。数值算例说明了所提出的LMFS的有效性和准确性。