Intervention-point principle of meshless method

Simulation of Electroosmosis Using a Meshless Finite Point Method

A Finite Point Method (FPM) based on a weighted least squares interpolation is presented for the simulation of electroosmotic transport in capillaries. This method requires no mesh and involves no Galerkin-type integration, making it more computationally efficient than the traditional finite element method. The FPM has been employed to solve the non-linear Poisson-Boltzmann equation for charge ...

Three-dimensional Crack Propagation Analysis Using Meshless Point Collocation Method

This paper presents a meshless point collocation method for three-dimensional crack propagation. The meshless point collocation method is based on direct discretization of strong-form governing equations to achieve a truly meshless scheme that does not require mesh structures or a numerical integration procedure. These characteristics of the point collocation method enable the direction of an a...

Hp-meshless Cloud Method

Nonlinear Cable equation, Fractional differential equation, Radial point interpolation method, Meshless local Petrov – Galerkin, Stability analysis

The cable equation is one the most fundamental mathematical models in the neuroscience, which describes the electro-diffusion of ions in denderits. New findings indicate that the standard cable equation is inadequate for describing the process of electro-diffusion of ions. So, recently, the cable model has been modified based on the theory of fractional calculus. In this paper, the two dimensio...

The meshless finite element method

A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. Furthermore, the method proposed also shares several of the advantages of the Finite Element Method such as: (a) the simplicity of the shape functi...