This contribution concerns the construction of meshless Lagrangian particle methods for the numerical simulation of multiscale phenomena in linear transport problems, where mass conservative discretization methods are essentially required. The proposed discretization scheme works with a finite set of unstructured nodes, each corresponding to one flow particle. In this method, corresponding part...

The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Although the finite element method (FEM) is a well-established method for modeling nonlinear problems, it often encounters difficulties for large deformation analyses due to the mesh distortion issues. Because no mesh is used, the meshless methods show very good potential for the la...

In recent years, there have been extensive efforts to find the numerical methods for solving problems with interface. The main idea of this work is to introduce an efficient truly meshless method based on the weak form for interface problems. The proposed method combines the direct meshless local Petrov–Galerkin method with the visibility criterion technique to solve the interface problems. It ...

This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial boundary conditions. These depend mainly on orthogonal polynomials, which are the method of operational matrix derivative that depends Bernstein polynomials Shifted Legendre polynomials. The basic procedure this is to convert equation a system linear by using, matrices we ...

We show how to provide safe a–posteriori error bounds for numerical solutions of well-posed operator equations using kernel–based meshless trial spaces. The presentation is kept as simple as possible in order to address a larger community working on applications in Science and Engineering. 1 Operator Equations Most contributions within application–oriented conferences only present numerical res...

Meshless approximations based on moving least squares kernels and partitions of unity are examined It is shown that the three methods are in most cases iden tical except for the important fact that partitions of unity enable p adaptivity to be achieved Methods for constructing discontinuous approximations and approx imations with discontinuous derivatives are also described Next several issues ...

For the purpose of surgical simulation, we propose an algorithm based upon the Element Free Galerkin method, Total Lagrangian explicit dynamics and nonlinear material formulation. The proposed algorithm does not require a finite element mesh, so is well suited to simulations with irregular geometry. As an example, a simplified 3D simulation of craniotomy induced brain shift including brain, ven...

In the present work, the numerical solution of two-dimensional variable-order fractional cable (VOFC) equation using meshless collocation methods with thin plate spline radial basis functions is considered. In the proposed methods, we first use two schemes of order O(τ2) for the time derivatives and then meshless approach is applied to the space component. Numerical results obtained ...

In this work we address the problem of numerically simulating the Friction Stir Welding process. Due to the special characteristics of this welding method (i.e., high speed of the rotating pin, very large deformations, etc.) finite element methods encounter several difficulties. Meshless methods somewhat alleviate this problems, allowing for an updated Lagrangian framework in the simulation. Ac...