In this paper we present a boundary detection algorithm for unorganized point sets and apply it for surface reconstruction using the meshless parameterization method from M. S. Floater and M. Reimers, Meshless parameterization and surface reconstruction, Comp. Aided Geom. Design, 18:77-92, 2001. The algorithm consists of two steps. Under mild assumptions, we can prove that the first step of our...

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...

We propose a new numerical method for modeling motion of open curves in two dimensions and open surfaces in three dimensions. Following the grid based particle method we proposed in [15], we represent the open curve or the open surface by meshless Lagrangian particles sampled according to an underlying fixed Eulerian mesh. The underlying grid is used to provide a quasi-uniform sampling and neig...

The general Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement & traction boundary integral equations are presented, for solids undergoing small deformations. Using the directly derived non-hyper singular integral equations for displacement gradients, simple and straight-forward derivations of weakly singular traction BIE's for solids undergoing small deformations are als...

This paper presents a new approach based on the meshless local Petrov–Galerkin (MLPG) and collocation methods to treat the parabolic partial differential equations with non-classical boundary conditions. In the presented method, the MLPG method is applied to the interior nodes while the meshless collocation method is applied to the nodes on the boundaries, and so the Dirichlet boundary conditio...

A meshless approximation and local integral equation (LIE) formulation are proposed for elastodynamic analysis of a hollow cylinder made of quasicrystal materials with decagonal quasicrystal properties. The cylinder is assumed to be under shock loading. Therefore, the general transient elastodynamic problem is considered for coupled phonon and phason displacements and stresses. The equations of...

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 ...

This paper proposes a method for approximating unorganized points in lR 3 with smooth B-spline surfaces. The method involves: meshless parameteri-zation; triangulation; shape-preserving reparameterization; and least squares spline approximation.