Meshless methods have been extensively popularized in literature in recent years, due to their flexibility in solving boundary value problems. The meshless local Petrov-Galerkin(MLPG) method for solving the bending problem of the thin plate is presented and discussed in the present paper. The method uses the moving least-squares approximation to interpolate the solution variables, and employs a...

The present work addresses the need for an efficient, versatile, accurate and open-source numerical tool to be used during design stage of wave energy converters (WECs). device considered here is heaving point-absorber developed tested by Sandia National Laboratories. smoothed particle hydrodynamics (SPH) method, as implemented in DualSPHysics, proposed since its meshless approach presents some...

Motivated by 5] we describe a method related to scattered Hermite interpolation for which the solution of elliptic partial diierential equations by collocation is well-posed. We compare the method of 5] with our method. x1. Introduction In this paper we discuss the numerical solution of elliptic partial diierential equations using a collocation approach based on radial basis functions. To make ...

The need for the processing of surface geometry represents an ubiquitous problem in computer graphics and related disciplines. It arises in numerous important applications such as computer-aided design, reverse engineering, rapid prototyping, medical imaging , cultural heritage acquisition and preservation, video gaming and the movie industry. Existing surface processing techniques predominantl...

The radial basis function (RBF) collocation techniques for the numerical solution of partial differential equation problems are increasingly popular in recent years thanks to their striking merits being inherently meshless, integration-free, and highly accurate. However, the RBF-based methods have markedly been limited to handle isotropic problems due to the use of the isotropic Euclidean dista...

In this paper, three dimensional (3D) static and dynamic analysis of thick plates based on the Meshless Local Petrov-Galerkin (MLPG) is presented. Using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a uni...

in the present work, a meshless method called finite point method (fpm) is developed to simulate the solidification process of a continuously cast steel bloom in both primary and secondary cooling regions. the method is based on the use of a weighted least-square interpolation procedure. a transverse slice of the bloom moving at casting speed is considered as the computational domain and two di...

In this paper, a meshless method for the acoustic eigenfrequencies using radial basis function (RBF) is proposed. The coefficients of influence matrices are easily determined by the two-point functions. In determining the diagonal elements of the influence matrices, two techniques, limiting approach and invariant method, are employed. Based on the RBF in the imaginary-part kernel, the method re...

A meshfree radial point interpolation method (RPIM) is developed for stress analysis of threedimensional (3D) solids, based on the Galerkin weak form formulation using 3D meshfree shape functions constructed using radial basis functions (RBFs). As the RPIM shape functions have the Kronecker delta functions property, essential boundary conditions can be enforced as easily as in the finite elemen...