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nu-spline curves for boundary geometry modeling in two-dimensional potential boundary value problems with singular corner points

100%

Zieniuk E.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2002

tom Vol. 6, No 4

641-650

The paper presents a new modeling method of boundary geometry in boundary value-problems by nu-spline curves. To define a smooth boundary geometry both Bezier and B-spline curves are applied. At the segment join points Bezier curves ensure continuity C1, and B-spline curves allow us to maintain continuity C2. However, the curves hinder boundary modeling with corner points. In order to weaken the continuity at segment join points nu-spline curves are proposed. These curves are combined analytically with the Green formula, thus yielding the Parametric Integral Equation System (PIES). To solve the PIES a pseudospectral method is used. The results obtained for the domains with singular corner points are compared with the corresponding non-singular ones as defined by the nu-spline curves.

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

63%

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.