Meshfree methods

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

The Analysis of Particle Flow using the Parallelised Smoothed Particle Hydrodynamics Method

Abstract: In smoothed particle hydrodynamics (SPH), an adaptive and meshfree particle method, the particle positions and velocities related to particle interactions must be updated at each time step. Thus, parallel computing is necessary to improve the numerical efficiency for the problems involving large computational domains. For the parallelization of the SPH method, the simulation domain is decomposed into subdomains with a group of particles using the new proposed parallel method. In this case, the boundary conditions are composed of the interface particles instead of the ghost zone at the other side of the subdomain. Then, the performance of the parallel computing is evaluated with the simulation of a fluid flow.

How to Choose Basis Functions in Meshless Methods

Abstract: Technical progress in construction of computers, their higher speed, and larger memory gave possibility to develop new numerical methods for solution of boundary value problems. A lot of meshless methods have been developed in last years. Some of them are in a way identical with the Galerkin method, where the trial space is formed by especially constructed functions. The choice of the proper trial space is important, because the error in the Galerkin method is determined by the fact how well the exact solution can be approximated by the elements from this finite dimensional space. In this contribution different trial spaces are considered. We will construct spaces generated by means of B-splines and shape functions received by means of the RKP technique. Examples of using trial spaces mentioned for solution of some boundary value problems will be given. We focus our attention on error estimates in these cases too.

Meshfree methods: An efficient advanced computing approach for Bio-medical problems

Abstract: This paper demonstrates the power of one of the recent but strong computing method for solving ordinary partial differential equations (ODE) & partial differential equations (PDE). Many mathematical models are governed by differential equations and hence due to large data involved, the only possible solution is numerical solution. The basic features of the meshfree methods with special reference to Element free Galerkin method (EFGM) has been presented here. To show its efficiency, one problem as a case study on heat transfer has been solved using this technique. In this problem, unsteady, laminar boundary layer flow of an incompressible, viscous and electrically conducing fluid over a horizontal stretching sheet is considered and governing non-linear partial differential equations are solved with element free galerkin method. The impact of various parameters used in element free galerkin method like penalty parameter, scaling parameter and different weigh functions on obtained velocity and temperature profiles is discussed in detail.

A new meshless “fragile points method (fpm)” based on a galerkin weak-form for 2d flexoelectric analysis

Abstract: A meshless Fragile Points Method (FPM) is presented for analyzing 2D flexoelectric problems. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless differential quadrature approximation of the first three derivatives. Interior Penalty Numerical Fluxes are employed to ensure the consistency of the method. Based on a Galerkin weak-form formulation, the present FPM leads to symmetric and sparse matrices, and avoids the difficulties of numerical integration in the previous meshfree methods. Numerical examples including isotropic and anisotropic materials with flexoelectric and piezoelectric effects are provided as validations. The present method is much simpler than the Finite Element Method, or the Element-Free Galerkin (EFG) and Meshless Local Petrov-Galerkin (MLPG) methods, and the numerical integration of the weak form is trivially simple.