A singularity-avoiding moving least squares scheme for two-dimensional unstructured meshes

In this paper, a new method for deriving the moving least-squares (MLS) approximation is presented, and the interpolating moving least-squares (IMLS) method proposed by Lancaster is improved. Compared with the IMLS method proposed by Lancaster, a simpler formula of the shape function is given in the improved IMLS method in this paper so that the new method has higher computing efficiency. Combining the shape function constructed by the improved IMLS method with Galerkin weak form of the elasticity problems, the interpolating element-free Galerkin (IEFG) method for the two-dimensional elasticity problems is presented, and the corresponding formulae are obtained. In the IEFG method, the boundary conditions can be applied directly which makes the computing efficiency higher than the conventional EFG method. Some numerical examples are presented to demonstrate the validity of the method.

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Modified moving least squares method for two-dimensional linear and nonlinear systems of integral equations

Computational and Applied Mathematics ◽

10.1007/s40314-018-0667-6 ◽

2018 ◽

Vol 37 (5) ◽

pp. 5857-5875 ◽

Cited By ~ 3

Author(s):

M. Matinfar ◽

M. Pourabd

Keyword(s):

Nonlinear Systems ◽

Least Squares ◽

Least Squares Method ◽

Moving Least Squares ◽

Two Dimensional ◽

Moving Least Squares Method ◽

Systems Of Integral Equations ◽

Linear And Nonlinear ◽

Linear And Nonlinear Systems ◽

Modified Moving Least Squares

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A NEW ELEMENT-FREE GALERKIN METHOD BASED ON IMPROVED COMPLEX VARIABLE MOVING LEAST-SQUARES APPROXIMATION FOR ELASTICITY

International Journal of Computational Materials Science and Engineering ◽

10.1142/s204768411250011x ◽

2012 ◽

Vol 01 (01) ◽

pp. 1250011 ◽

Cited By ~ 15

Author(s):

HONGPING REN ◽

YUMIN CHENG

Keyword(s):

Least Squares ◽

Complex Variable ◽

Weak Form ◽

Moving Least Squares ◽

Two Dimensional ◽

Element Free Galerkin Method ◽

Element Free Galerkin ◽

Variable Element ◽

Elasticity Problems ◽

Element Free

In this paper, by constructing a new functional, an improved complex variable moving least-squares (ICVMLS) approximation is presented. Based on element-free Galerkin (EFG) method and the ICVMLS approximation, a new complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems is presented. Galerkin weak form is used to obtain the discretized equations and the essential boundary conditions are applied with Lagrange multiplier. Then the formulae of the new CVEFG method for two-dimensional elasticity problems are obtained. Compared with the conventional EFG method, the new CVEFG method has greater computational precision and efficiency. For the purposes of demonstration, some selected numerical examples are solved using the ICVEFG method.

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Generalized moving least squares approximation for the solution of local and non-local models of cancer cell invasion of tissue under the effect of adhesion in one- and two-dimensional spaces

Computers in Biology and Medicine ◽

10.1016/j.compbiomed.2020.103803 ◽

2020 ◽

Vol 124 ◽

pp. 103803 ◽

Cited By ~ 4

Author(s):

Vahid Mohammadi ◽

Mehdi Dehghan

Keyword(s):

Least Squares ◽

Cancer Cell ◽

Cell Invasion ◽

Moving Least Squares ◽

Two Dimensional ◽

Local Models ◽

Least Squares Approximation ◽

Cancer Cell Invasion ◽

Non Local ◽

Moving Least Squares Approximation

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AN INTERPOLATING BOUNDARY ELEMENT-FREE METHOD WITH NONSINGULAR WEIGHT FUNCTION FOR TWO-DIMENSIONAL POTENTIAL PROBLEMS

International Journal of Computational Methods ◽

10.1142/s0219876213500436 ◽

2013 ◽

Vol 10 (06) ◽

pp. 1350043 ◽

Cited By ~ 41

Author(s):

JUFENG WANG ◽

JIANFEI WANG ◽

FENGXIN SUN ◽

YUMIN CHENG

Keyword(s):

Integral Equation ◽

Weight Function ◽

Least Squares ◽

Boundary Element ◽

Boundary Integral Equation ◽

Boundary Integral ◽

Moving Least Squares ◽

Two Dimensional ◽

Potential Problems ◽

Element Free

In this paper, an improved interpolating moving least-squares (IIMLS) method with nonsingular weight function is presented. The shape function of the IIMLS method satisfies the property of Kronecker δ function. The IIMLS method can overcome the difficulties caused by the singularity of the weight function in the interpolating moving least-squares (IMLS) method presented by Lancaster and Salkauskas. By combining the boundary integral equation (BIE) method with the IIMLS method, an improved interpolating boundary element-free (IIBEF) method is presented for two-dimensional potential problems. The IIBEF method is a direct meshless boundary integral equation method in which the basic unknown quantities are the real solutions to the nodal variables, and the boundary conditions can be applied directly and easily. Thus, it gives greater computational precision. Some numerical examples are presented to demonstrate the IIMLS and IIBEF methods.

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