Point-based surface processing has developed into an attractive alternative to mesh-based processing techniques for a number of geometric modeling applications. By working with point cloud data directly, any processing is based on the given raw data and its underlying geometry rather than any arbitrary intermediate representations and generally artificial connectivity relations. In this paper, ...

This is the first in a series of two papers generated from a study on probabilistic meshless analysis of cracks. In this paper (Part I), a Galerkin-based meshless method is presented for predicting first-order derivatives of stress-intensity factors with respect to the crack size in a linear-elastic structure containing a single crack. The method involves meshless discretization of cracked stru...

Keywords: ADI leapfrog method Meshless methods Smoothed particle electromagnetics a b s t r a c t Grid based methods coupled with an explicit approach for the evolution in time are traditionally adopted in solving PDEs in computational electromagnetics. The discretiza-tion in space with a grid covering the problem domain and a stability step size restriction, must be accepted. Evidence is given...

We consider numerical solutions of second-order elliptic partial di erential equations, such as Laplace's equation, or linear elasticity, in two-dimensional, non-convex domains by the element-free Galerkin method (EFG). This is a meshless method, in which the shape functions are constructed by using weight functions of compact support. For non-convex domains, two approaches to the determination...

While the generation of meshes has always posed challenges for computational scientists, the problem has become more acute in recent years. Increased computational power has enabled scientists to tackle problems of increasing size and complexity. While algorithms have seen great advances, mesh generation has lagged behind, creating a computational bottleneck. For industry and government looking...

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...

We study meshless collocation methods using radial basis functions to approximate regular solutions of systems of equations with linear diier-ential or integral operators. Our method can be interpreted as one of the emerging meshless methods, cf. 1]. Its range of application is not conned to elliptic problems. However, the application to the boundary value problem for an elliptic operator, conn...

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...

This study modifies and discusses the application of a complete meshless method based on Shepard approximation with an emphasis on the detailed description of this computational technique and its numerical implementations. A new weighting function would be suggested. The global shape function and its derivatives are built based only on the discretisation of the domain in nodes. To deal with the...