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A comparison between the improved element-free Galerkin method and the element-free Galerkin method for 2D potential and elasticity problems

100%

Debbabi I. , Sendi Z. , BelHadjSalah H.

Computer Assisted Methods in Engineering and Science

2016

tom Vol. 23, no. 2/3

87--107

In this paper, a comparison between the improved element-free Galerkin (IEFG) method, based on the improved moving least square (IMLS) approximation, and the element-free Galerkin (EFG) method, based on the moving least square (MLS) approximation, is presented. The IMLS approximation is obtained when an orthogonal basis function with a weight function is used. The IMLS approximation has a greater computational efficiency than the existing MLS approximation and does not lead to an ill-conditioned system of equations. The comparison is made for two-dimensional (2D) potential problems and 2D elastic problems. From these problems, the efficiency of the IEFG method is validated by comparing the results obtained with the IEFG method and EFG method with those obtained analytically.

On efficient evaluation of integrals entering boundary equations of 3D potential and elasticity theory

80%

Rybarska-Rusinek L. , Jaworski D. , Linkov A.

Journal of Mathematics and Applications

2014

tom Vol. 37

85--96

The paper presents recurrent formulae for efficient evaluation of all the integrals needed for colving static 3D potential and elasticity problems by the boundary elements method. The power-type asymptoties for the density at edges of the boundary are accounted for explicitly.