In Meshless natura1 neighbour Petrov-Galerkin method, The natural neighbour interpolation is used as trial function and a weak form over the local polygonal sub-domains constructed by Delaunay triangular is used to obtain the discretized system of equilibrium equations, and it’s a new truly meshless method. This method simplified the formation of the equilibrium equations, facilitates the impos...

For simulation of numerical problems, meshless methods have emerged as an alternative to mesh based methods and become popular due to several reasons. Primarily, mesh generation is a difficult problem, Also these methods have generated promising results in the accuracy of the simulations. Similar to mesh generation problems, meshless methods also induce challenging geometric problems. Partition...

We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions. New meshless stencil selection and adaptive refinement algorithms are proposed in 2D. Numerical experiments show that the accuracy of the solution is comparable with, and often better than that achieved by the me...

In this study, a cellular automaton (CA) is developed o combine the advantages of finite element method (FEM) and meshless method to analyze two-dimensional elastic problems. By the CA, a two-dimensional domain is discretized into a grid of nodes which are distributed randomly in the domain. For convenience, the nodes are classified into the FEM group and the meshless group. In the FEM zone tha...

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 method plays an important role in solving problems in computational mechanics where conventional computational methods are not well suited. In this paper, we examine the property of the kernel matrix and investigate the convergence and timing performance of some well-known Krylov subspace methods on solving linear systems from meshless discretizations.

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...

A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...

Title of dissertation: MESHLESS COLLOCATION METHODS FOR THE NUMERICAL SOLUTION OF ELLIPTIC BOUNDARY VALUED PROBLEMS AND THE ROTATIONAL SHALLOW WATER EQUATIONS ON THE SPHERE Christopher D. Blakely, Doctor of Philosophy, 2009 Dissertation directed by: Professor John Osborn Department of Mathematics Professor Ferdinand Baer Department of Atmospheric and Oceanic Science This dissertation thesis has...

Since meshless methods have been introduced to alleviate the difficulties arising in conventional finite element method, many papers on applications of meshless methods to boundary element method have been published. However, most of these papers use moving least squares approximation functions that have difficulties in prescribing essential boundary conditions. Recently, in order to strengthen...