The requirements for interpolation of scattered data are high accuracy and high efficiency. In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed. We firstly construct a triangulation mesh using the given scattered point set. Based on this mesh, the computational point (x, y) is divided into two types: interior point and exterior point. The value of ...

Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...

A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the ...

An algorithm for use with several meshless schemes is presented based on a local extremum diminishing property. The scheme is applied to the Euler equations in two dimensions. The algorithm is suitable for use with many meshless schemes, three of which are detailed here. First, a method based on Taylor series expansion and least squares is highlighted. Next, a similar least squares method is us...

Introduction Moving least squares approximation is one kind of meshless methods in which the approximation is built from nodes only. Comparing to mesh-based methods, meshless methods have advantages on (1) refining is simpler to incorporate, (2) moving discontinuities can be treated easily, (3) large deformation can be handled robustly, (4) higher-order continuous shape functions, (5) non-local...

Casting is considered as a major manufacturing process. Thermal analysis of a solidifying medium is of great importance for appropriate design of casting processes. The conventional governing equation of a solidifying medium is based on the Fourier heat conduction law, which does not account for the phase-lag between the heat flux and the temperature gradient. In this paper, the concept of phas...

The MLPG method is the general basis for several variations of meshless methods presented in recent literature. The interrelation of the various meshless approaches is presented in this paper. Several variations of the meshless interpolation schemes are reviewed also. Recent developments and applications of the MLPG methods are surveyed.

in this paper the meshless local petrov-galerkin (mlpg) method is implemented to study the buckling of isotropic cylindrical shells under axial load. displacement field equations, based on donnell and first order shear deformation theory, are taken into consideration. the set of governing equations of motion are numerically solved by the mlpg method in which according to a semi-inverse method, ...

In this paper, one of the simplest and most regular members of the family of the Meshless Local Petrov-Galerkin (MLPG) methods; namely MLPG5, is applied to analyze the thick-walled isotropic laminated cylinders under elasto-static pressure. A novel simple technique is proposed to eliminate a very important difficulty of the meshless methods to deal with material discontinuities regarding to the...

In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable wit...