A particular meshless method, named meshless local Petrov–Galerkin is investigated. To treat the essential boundary condition problem, an alternative approach is proposed. The basic idea is to merge the best features of two different methods of shape function generation: the moving least squares (MLS) and the radial basis functions with polynomial terms (RBFp). Whereas the MLS has lower computa...

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...

This paper is aimed at presenting a partition of unity method for the simulation of three-dimensional dynamic crack propagation. The method is a variation of the partition of unity ®nite element method and hp-cloud method. In the context of crack simulation, this method allows for modeling of arbitrary dynamic crack propagation without any remeshing of the domain. In the proposed method, the ap...

In this paper, meshless methods and partition of unity based finite element methods are reviewed. In meshless methods, the approximation is built without the explicit connectivity information between the nodes; moving-least squares approximants and natural neighbor-based interpolants are discussed. The enrichment of the finite element approximation through the partition of unity framework is de...

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...

The aim of the present paper is the development of an efficient numerical algorithm for the solution of magnetohydrodynamics flow problems for regular and irregular geometries subject to Dirichlet, Neumann and Robin boundary conditions. Toward this, the meshless point collocation method (MPCM) is used for MHD flow problems in channels with fully insulating or partially insulating and partially ...

This paper addresses the problem of removing the noise from noisy points clouds in the context of surface reconstruction. We introduce a new smoothing operator Q inspired by the moving least-squares method and robust statistics theory. Our method can be seen as an improvement of the moving least-squares method to preserve sharp features. We also present effective numerical optimization algorith...

We present an algorithm to approximate a set of unorganized points with a simple curve without self-intersections. The moving least-squares method has a good ability to reduce a point cloud to a thin curve-like shape which is a near-best approximation of the point set. In this paper, an improved moving least-squares technique is suggested using Euclidean minimum spanning tree, region expansion ...

An analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented. In particular, theorems are proved concerning the smoothness of interpolants and the description of m.l.s. processes as projection methods. Some properties of compositions of the m.l.s. projector, with projectors associated with finiteelement schemes, are also considered. The analys...

The radial basis function interpolant is known to be the best approximation to a set of scattered data when the error is measured in the native space norm. The approximate moving least squares method, on the other hand, was recently proposed as an efficient approximation method that avoids the solution of the system of linear equations associated with the radial basis function interpolant. In t...