The root of this study, comes from the lack of regularity where exists in shape function selection in meshless methods. Up to now, shape functions in meshless methods were being established by basis functions. In other words, there was no predictable rule by which the shape functions be predetermined, without any need to basis functions. In presented approach, the authors are going to establish...

The root of this study, comes from the lack of regularity where exists in shape function selection in direct meshless methods. In this work, we are going to establish a technique which is based on both analytical and simulated results; helps select a well-behaved shape function for which the shape parameters have been predetermined. This work has been focused on wave equation as the most import...

(2000) Meshless local Petrov–Galerkin (MLPG) method in combination with finite element and boundary element approaches. Abstract The Meshless Local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using Moving Least Squares (MLS) interpolants. It is, however, computationally expensive for some problems. A coupled MLPG/Finite Element ...

The Meshless Local Petrov–Galerkin method (MLPG) is one of the popular meshless methods that has been used very successfully to solve several types of boundary value problems since the late nineties. In this paper, using a generalized moving least squares (GMLS) approximation, a new direct MLPG technique, called DMLPG, is presented. Following the principle of meshless methods to express everyth...

In this paper, a meshless method for solving the eigenproblems of plate vibration using the radial basis function (RBF) is proposed. By employing the RBF in the imaginary-part fundamental solution, spurious eigenequations in conjunction with the true ones are obtained at the same time. Mathematical analysis for the appearance of spurious eigenequations by using degenerate kernel and circulant i...

During the past few years, the idea of using meshless methods for numerical solution of partial differential equations (PDEs) has received much attention throughout the scientific community, and remarkable progress has been achieved on meshless methods. The meshless local Petrov–Galerkin (MLPG) method is one of the ‘‘truly meshless’’ methods since it does not require any background integration ...

We combine the theory of radial basis functions with the field of Galerkin methods to solve partial differential equations. After a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions.

In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. Kansa’s well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent m...

Keywords: ADI leapfrog method Meshless methods Smoothed particle electromagnetics a b s t r a c t Grid based methods coupled with an explicit approach for the evolution in time are traditionally adopted in solving PDEs in computational electromagnetics. The discretiza-tion in space with a grid covering the problem domain and a stability step size restriction, must be accepted. Evidence is given...