Applied Mathematics Letters ( IF 3.848 ) Pub Date : 2020-09-10 , DOI: 10.1016/j.aml.2020.106759 Weiwei Li
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.