Finite element methods are commonly used to model melting problems where the problem domain is defined using a mesh support. When the domain evolves the mesh becomes very distorted, and remeshing as well as field projection between successive meshes are then required [5]. Moreover, to represent the thermal transmission conditions through the interface (melting or solidification fronts) the inte...

In Meshless natura1 neighbour Petrov-Galerkin method, The natural neighbour interpolation is used as trial function and a weak form over the local polygonal sub-domains constructed by Delaunay triangular is used to obtain the discretized system of equilibrium equations, and it’s a new truly meshless method. This method simplified the formation of the equilibrium equations, facilitates the impos...

Partial differential equations for domains with moving boundaries and moving interfaces are solved numerically using meshless finite difference schemes. The advantage of the approach is that it is easy to add nodes where there is a requirement of higher precision and delete nodes where the precision requirements are less stringent. TVD and ENO schemes are considered in this context and some num...

This paper proves convergence of variations of the unsymmetric kernel-based collocation method introduced by E. Kansa in 1986. Since then, this method has been very successfully used in many applications, though it may theoretically fail in special situations, and though it had no error bound or convergence proof up to now. Thus it is necessary to add assumptions or to make modifications. Our m...

We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions. New meshless stencil selection and adaptive refinement algorithms are proposed in 2D. Numerical experiments show that the accuracy of the solution is comparable with, and often better than that achieved by the me...

Numerical solution of the generalized Burger?s-Huxley equation is established utilizing two effective meshless methods namely: local differential quadrature method and global line. Both proposed used radial basis functions to discretize space derivatives which convert given model system ODE then we have utilized Euler get required numerical solution. experiments are carried out check efficiency...

In this paper, we employ the regularized meshless method to solve antiplane shear problems with multiple inclusions. The solution is represented by a distribution of double-layer potentials. The singularities of kernels are regularized by using a subtracting and adding-back technique. Therefore, the troublesome singularity in the method of fundamental solutions (MFS) is avoided and the diagonal...

Abstract. This paper presents a meshless implementation for the dual analysis of 2D linear elasticity problems. The derivation of the governing system of equations for the discretized equilibrated model is detailed. Crucial implementation issues of the equilibrated algorithm are described. It presents the inf-sup condition for particular cases of essential boundary conditions approximations whe...

A central problem of numerical analysis is the approximate evaluation of integrals or derivatives of functions. In more generality, this is the approximate evaluation of a linear functional defined on a space of functions. Users often just have values of a function u at scattered points x1, . . . ,xN in the domain Ω of u, and then the value λ (u) of a linear functional λ must be approximated vi...

This work concerns the development of a highly accurate and efficient meshless flow solver for inviscid flow in two dimensions. Novel aspects of this work include the application of mesh-based reconstruction, diffusion, and convergence acceleration schemes within an edge-based meshless framework. Most notably, “multicloud,” a meshless counterpart to multigrid, has been implemented. Multicloud d...