Development of a new meshless technique is described, called the meshless volume scheme. The method is completely meshless, yet retains the low storage and simple flux distribution technique characteristic of finite volume methods. The new method is based on the well-known Taylor series expansion method with least squares. A least squares weighting scheme is introduced that significantly reduce...

This paper describes a new topology optimization (TO) technique based on meshless method to evolve two-dimensional truss structures. The meshless method has been considered as a very attractive computational technique since it does not need any mesh generation process during the analysis. It has been gradually and widely used in many engineering disciplines and a particular weak point such as t...

Many existing computer-aided design systems for microelectromechanical systems require the generation of a three-dimensional mesh for computational analysis of the microdevice. Mesh generation requirements for microdevices are very complicated because of the presence of mixed-energy domains. Point methods or meshless methods do not require the generation of a mesh, and computational analysis ca...

Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of i...

The numerical implementation of the truly Meshless Local Petrov-Galerkin (MLPG) type weakforms of the displacement and traction boundary integral equations is presented, for solids undergoing small deformations. In the accompanying part I of this paper, the general MLPG/BIE weak-forms were presented [Atluri, Han and Shen (2003)]. The MLPG weak forms provide the most general basis for the numeri...

Spatial–temporal calcium dynamics due to calcium release, buffering and re-uptaking plays a central role in studying excitation–contraction (E–C) coupling in both normal and diseased cardiac myocytes. In this paper, we employ a meshless method, namely, the local radial basis function collocation method (LRBFCM), to model such calcium behaviors by solving a nonlinear system of reaction–diffusion...

A non-overlapping domain decomposition algorithm combining boundary element method with meshless local Petrov-Galerkin method is presented for solving the boundary value problem with discontinuous coefficient in this paper. The static relaxation parameter is employed to speed up the convergence rate. The convergence range and the optimal value of static relaxation parameter are studied, but the...

A truly Meshless Local Petrov-Galerkin (MLPG) method is developed for solving 3D elasto-static problems. Using the general MLPG concept, this method is derived through the local weak forms of the equilibrium equations, by using a test function, namely, the Heaviside step function. The Moving Least Squares (MLS) are chosen to construct the shape functions. The penalty approach is used to impose ...