Local Boundary Integral Equation Method Based on Radial Basis Functions

Dai, Baodong

doi:10.3901/jme.2006.11.150

Cited by 9 publications

(10 citation statements)

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“…Besides the EFG method, many researchers presented various meshless methods, such as radial basis functions (RBF) method [28,70], finite point method (FPM) [14,15,50,66], meshless local Petrov-Galerkin (MLPG) method [4,11], complex variable element-free Galerkin method [5, 19-21, 24-26, 38, 39, 43, 47, 53, 54, 64, 65], complex variable reproducing kernel particle method (CVRKPM) [8-10, 12, 71], meshless manifold method [30,40,41], meshfree reproducing kernel particle Ritz method [17], boundary element-free method (BEFM) [22,23,34,[44][45][46]51], local boundary integral equation (LBIE) method [3,29], and boundary node method [35].…”

Section: Introductionmentioning

confidence: 99%

Error estimates for the interpolating moving least-squares method in n -dimensional space

Sun

Wang

Cheng

et al. 2015

Applied Numerical Mathematics

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Section: Introductionmentioning

confidence: 99%

Error estimates for the interpolating moving least-squares method in n -dimensional space

Sun

Wang

Cheng

et al. 2015

Applied Numerical Mathematics

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“…At present, some meshless methods such as the element-free Galerkin (EFG) method [10], the reproducing kernel particle method (RKPM) [11], Hp-clouds meshless method [12], the finite point method [13,14], the meshless local Petrov-Galerkin (MLPG) method [15], the meshless point collocation method (PCM) [16], the wavelet particle method (WPM) [17], the meshless finite element method (MFEM) [18], the complex variable meshless method [19][20][21], the meshless manifold method [22,23], the meshless boundary integral equation methods [24][25][26][27][28][29], etc., have been developed. The RKPM is developed on the basis of the smoothed particle hydrodynamics (SPH) method.…”

Section: Introductionmentioning

confidence: 99%

The complex variable reproducing kernel particle method for elasto-plasticity problems

Chen

Cheng

2010

Sci. China Phys. Mech. Astron.

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On the basis of reproducing kernel particle method (RKPM), using complex variable theory, the complex variable reproducing kernel particle method (CVRKPM) is discussed in this paper. The advantage of the CVRKPM is that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is formed. Then the CVRKPM is applied to solve two-dimensional elasto-plasticity problems. The Galerkin weak form is employed to obtain the discretized system equation, the penalty method is used to apply the essential boundary conditions. And then, the CVRKPM for two-dimensional elasto-plasticity problems is formed, the corresponding formulae are obtained, and the Newton-Raphson method is used in the numerical implementation. Three numerical examples are given to show that this method in this paper is effective for elasto-plasticity analysis. meshless method, reproducing kernel particle method (RKPM), complex variable reproducing kernel particle method (CVRKPM), correction function, elasto-plasticity PACS: 02.60. Cb, 02.90.+p,

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“…The meshless method based on the MLS approximation can generate a solution possessing great precision. The meshless boundary integral equation methods are developed by combining the MLS approximation with boundary integral equation methods [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The boundary node method (BNM) is one of the meshless boundary integral equation methods, and Mukherjee et al [3][4][5] used it to solve potential problems and linear elasticity problems.…”

mentioning

confidence: 99%

“…The boundary node method (BNM) is one of the meshless boundary integral equation methods, and Mukherjee et al [3][4][5] used it to solve potential problems and linear elasticity problems. Another equally important method of the meshless boundary integral equation methods is the local boundary integral equation (LBIE) method, which Atluri et al [6][7][8] present to solve linear and nonlinear boundary value problems. In the BNM, the basic unknown quantities are approximations of the nodal variables.…”

mentioning

confidence: 99%

“…Combining different approximation functions in the meshless method with the boundary integral equation method, researchers have developed meshless boundary integral equation methods, such as the boundary node method (BNM) [3][4][5], the local boundary integral equation (LBIE) method [6][7][8], and the boundary element-free method (BEFM) [9][10][11][12][13][14][15][16][17][18][19].…”

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confidence: 99%

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An interpolating boundary element-free method (IBEFM) for elasticity problems

Ren

Cheng

2010

Sci. China Phys. Mech. Astron.

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The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method. moving least-squares (MLS) approximation, interpolating moving least-squares (IMLS) method, boundary integral equation, meshless method, boundary element-free method (BEFM), interpolating boundary element-free method (IBEFM), elasticity problem PACS: 02.60.Ed, 02.70.-c, 02.70.Pt, 46.15.-x In recent years, more and more attention has been paid to research on the meshless (or meshfree) method [1,2]. The meshless method has some advantages over the traditional computational methods, such as finite element method (FEM) and boundary element method (BEM). The meshless boundary integral equation method points to one of the important research directions of the meshless method. Combining different approximation functions in the meshless method with the boundary integral equation method, researchers have developed meshless boundary integral equation methods, such as the boundary node method (BNM) [3-5], the local boundary integral equation (LBIE) method [6-8], and the boundary element-free method (BEFM) [9-19]. The moving least-squares (MLS) approximation is one of the bases of the meshless method [1,2,20]. The meshless method based on the MLS approximation can generate a solution possessing great precision. The meshless boundary integral equation methods are developed by combining the MLS approximation with boundary integral equation methods [3-19]. The boundary node method (BNM) is one of the meshless boundary integral equation methods, and Mukherjee et al. [3-5] used it to solve potential problems and linear elasticity problems. Another equally important method of the meshless boundary integral equation methods is the local boundary integral equation (LBIE) method, which Atluri et al. [6-8] present to solve linear and nonlinear boundary value problems.In the BNM, the basic unknown quantities are approximations of the nodal variables. However, as they are not the real nodal variables, the boundary conditions cannot be directly applied. In the LBIE method, the traction term is not included in the local boundary integral equations.

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Local Boundary Integral Equation Method Based on Radial Basis Functions

Cited by 9 publications

References 0 publications

Error estimates for the interpolating moving least-squares method in n -dimensional space

Error estimates for the interpolating moving least-squares method in n -dimensional space

The complex variable reproducing kernel particle method for elasto-plasticity problems

An interpolating boundary element-free method (IBEFM) for elasticity problems

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