Physics

Channel (broadcasting)

Finite element method

Spectral method

Computer network

Mathematics

Method of fundamental solutions

Economic growth

Singular boundary method

Elasticity (physics)

Mathematical optimization

Mathematical analysis

Boundary value problem

Economics

Convergence (economics)

Computer science

Numerical analysis

Discretization

Applied mathematics

Rate of convergence

Boundary element method

Thermodynamics

Advances in Applied Mathematics and Mechanics

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.

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