Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory

A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed.