Meshless Finite Element Methods, namely elementfree Galerkin and point-interpolation method were implemented and tested concerning their applicability to typical engineering problems like electrical fields and structural mechanics. A class-structure was developed which allows a consistent implementation of these methods together with classical FEM in a common framework. Strengths and weaknesses...

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H(Ω) (k ≥ 1). With a special kind of radial basis function, we construct a basis in H(Ω) and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density. Mathematics subject classification: 41...

In this paper, we propose a brief and general process to compute the eigenvalue of arbitrary waveguides using meshless method based on radial basis functions (MLM-RBF) interpolation. The main idea is that RBF basis functions are used in a point matching method to solve the Helmholtz equation only in Cartesian system. Two kinds of boundary conditions of waveguide problems are also analyzed. To v...

A new meshless Local Boundary Integral Equation (LBIE) method for solving two-dimensional elastostatic problems is proposed. Randomly distributed points without any connectivity requirement cover the analyzed domain and Local Radial Basis Functions (LRBFs) are employed for the meshless interpolation of displacements. For each point a circular support domain is centered and a local integral repr...

In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radial basis functions (RBFs) constructed on a set of disordered data. The method is a meshless method, because it ...

In this paper, the conventional moving least squares interpolation scheme is generalized, to incorporate the information concerning the derivative of the ®eld variable into the interpolation scheme. By using this generalized moving least squares interpolation, along with the MLPG (Meshless Local Petrov±Galerkin) paradigm, a new numerical approach is proposed to deal with 4th order problems of t...

An improvement to the traditional Finite Volume Method (FVM) for the solution of boundary value problems is presented. The new method applies the local Hermitian interpolation with Radial Basis Functions (RBF) as an interpolation scheme to the FVM discretization. This approach, called the Control Volume-Radial Basis Function (CV-RBF) method, uses an interpolation scheme based on the meshless Sy...

This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. In this method, an element free Galerkin (EFG) formulation, an enriched basic function and some special shape functions that contain discontinuous derivatives are employed. Based on the moving least squares (MLS) interpolation approach, the EFG method i...

in the recent paper, one of the numerical methods without element, for static analysis of thin plates displacement based on classical plates theory (cpt), has been presented. in this method, the domain of problem solving is shown only by the means of a set of nodes, and there is no need to any mesh scheme or element. one of the kinds of element free methods used here is the radial point interpo...