Enforcement of boundary conditions in meshfree methods using interpolating moving least squares

An element-free Galerkin forward solver for the complete-electrode model in electrical impedance tomography

“…In data preparation stage, the following are determined (a) geometry and material physical properties of the subregions, (b) a nodal distribution for discretizing the full domain, (c) the domain of influence for each node, (d) the number and size of the integration cells, and the number of integration points inside each integration cell, (e) support domain for each integration point, (f) weights, shape functions, and shape function derivatives, for each node in the entire region, (g) nodes and integration points along electrodes, and (h) computation of the second term on the right hand side of Eq. (22) and the terms on the right hand side of Eqs. (23) and (24) for each electrode.…”

“…A number of meshfree methods have been recently developed [20][21][22][23][24][25][26][27][28][29][30][31]. Since the meshfree methods require only nodal data and no element connectivity is needed, there are more flexible than the FEM in EIT problems with moving objects inside the imaging region [24].…”

Steady heat conduction analyses using an interpolating element-free Galerkin scaled boundary method

“…The radial coordinate ξ is defined to be zero at the scaling center, unity value at the boundary, and infinity for far field. The conversion between the scaled boundary and Cartesian coordinate system can be written as follows [10][11][12][13][14] ) ( (29) with the Jacobian at the boundary being defined as…”

“…However, the use of IMLS method still has great difficulty in numerical computation because the singularity involved in the weight function complicates the computation of the inverse of the singular matrix and thus increases the computational cost. To overcome this shortcoming, a perturbation technique was introduced by Netuzhylov [29] into the IMLS method.…”

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

“…Kaljevic and Saigal presented an improved formulation of the EFG method based on the IMLS method [33]. Netuzhylov used the meshfree collocation method based on the IMLS method to solve boundary value problems [49]. Ren et al presented the interpolating boundary element-free (IBEF) method and interpolating element-free Galerkin (IEFG) method for two-dimensional potential and elasticity problems [57][58][59][60].…”