Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.

Numerical simulation of bulk metal forming by meshless method

Abstract: Conventional finite element (FE) analysis of bulk metal forming processes often breaks down due to severe mesh distortion. In recent years, meshless methods have been considerably developed for structural applications. The main feature of these methods is that the problem domain is represented by a set of nodes, and a finite element mesh is unnecessary. This new generation of computational methods can avoid time-consuming meshing and remeshing. A meshless method based on reproducing kernel particle method (RKPM) is applied to bulk metal forming analysis. The displacement shape functions are developed from a reproducing kernel (RK) approximation that satisfies consistency conditions. The shape function is modified to impose essential boundary conditions accurately and expediently. A material kernel function that deforms with the material is introduced to assure the stability of the RKPM shape function during large deformations. A program based on RKPM is developed to simulate two examples of bulk metal for...

On the a-priori error analysis and convergence of meshless BEM

Abstract: This paper deals with the a-priori error analysis and convergence of meshless boundary element methods. The paper investigates the convergence of the particular solution method (PSM) in conjunction with the boundary element method (BEM) as well as the method of fundamental solutions (MFS) and the radial basis functions (RBF)—type techniques. A-priori error estimates for meshless BEMs are also provided, and several illustrating numerical experiments are derived.

The collocation and meshless methods for differential equations in R(2)

Abstract: The Collocation and Meshless Methods for Differential Equations in by Thamira Abid Jaijees Dr. Xin Li, Examination Committee Chair Associate Professor of Mathematics University of Nevada, Las Vegas In recent years, meshless methods have become popular ones to solve differential equations. In this thesis, we aim at solving differential equations by using Radial Basis Functions, collocation methods and fundamental solutions (MFS). These methods are meshless, easy to understand, and even easier to implement.