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Volume 13, Issue 6
Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory

Yan Gu, Chia-Ming Fan & Zhuojia Fu

Adv. Appl. Math. Mech., 13 (2021), pp. 1520-1534.

Published online: 2021-08

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  • Abstract

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.

  • AMS Subject Headings

62P30, 65M32, 65K05

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COPYRIGHT: © Global Science Press

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@Article{AAMM-13-1520, author = {Gu , YanFan , Chia-Ming and Fu , Zhuojia}, title = {Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {6}, pages = {1520--1534}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0134}, url = {http://global-sci.org/intro/article_detail/aamm/19433.html} }
TY - JOUR T1 - Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory AU - Gu , Yan AU - Fan , Chia-Ming AU - Fu , Zhuojia JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1520 EP - 1534 PY - 2021 DA - 2021/08 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0134 UR - https://global-sci.org/intro/article_detail/aamm/19433.html KW - Method of fundamental solutions, meshless method, large-scale simulations, elasticity problems. AB -

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.

Yan Gu, Chia-Ming Fan & Zhuojia Fu. (1970). Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory. Advances in Applied Mathematics and Mechanics. 13 (6). 1520-1534. doi:10.4208/aamm.OA-2020-0134
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