Complex variable moving least‐squares method: a meshless approximation technique

Abstract

SUMMARYBased on the moving least-squares (MLS) approximation, we propose a new approximation method-the complex variable moving least-squares (CVMLS) approximation. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of the MLS approximation, and we can thus select fewer nodes in the meshless method that is formed from the CVMLS approximation than are required in the meshless method of the MLS approximation with no loss of precision. The meshless method that is derived from the CVMLS approximation also has a greater computational efficiency. From the CVMLS approximation, we propose a new meshless method for two-dimensional elasticity problems-the complex variable meshless method (CVMM)-and the formulae of the CVMM for two-dimensional elasticity problems are obtained. Compared with the conventional meshless method, the CVMM has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVMM.

A local Petrov-Galerkin approach with moving Kriging interpolation for solving transient heat conduction problems

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“…As an alternative to mesh-based methods, meshless methods [4][5][6][7][8][9][10][11][12][13][14] have attracted much attention in recent years due to: (1) the lack of dependence on mesh and avoiding meshing;…”

Application of direct meshless local Petrov–Galerkin (DMLPG) method for some Turing-type models

“…The moving least squares (MLS) method [11,28,30,31] was proposed for approximating a function u(x) inside a region ⊂ R d using the values u(x j ) at nodes X = {x j } N j=1 . It should be noted that, for the sparsity of the final coefficient matrix, the set X can be replaced by a subset that consists only the nodes that are located on the neighborhood of the point of interest.…”

Analyzing three-dimensional potential problems with the improved element-free Galerkin method

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