This work presents a global radial basis collocation combining with the quasiNewton iteration method for solving semilinear elliptic partial differential equations. A convergence analysis for such a meshfree discretization has been established. The main result is that there exists an exponential convergence rate with respect to the number and the shape of the radial basis functions. In addition...

The collocation method with multiquadrics basis functions and a first-order shear deformation theory are used to find natural flexural frequencies of a square plate with various material symmetries and subjected to different boundary conditions. Computed results are found to agree well with the literature values obtained by the solution of the three-dimensional elasticity equations using the fi...

A general framework for proving error bounds and convergence of a large class of unsymmetric meshless numerical methods for solving well-posed linear operator equations is presented. The results provide optimal convergence rates, if the test and trial spaces satisfy a stability condition. Operators need not be elliptic, and the problems can be posed in weak or strong form without changing the t...

Abstract: In this paper, a new solution of solidification problems in continuous casting based on meshless method is presented with multiple strategies to solve the practical problems. An additional term is added to stabilise the computation with Neumann boundary. The enthalpy method is used to calculate the latent heat and the corresponding iterative solution is given. An iteration scheme for ...

a new approach for analyzing cracked problems in 2d orthotropic materials using the well-known element free galerkin method and orthotropic enrichment functions is proposed. the element free galerkin method is a meshfree method which enables discontinuous problems to be modeled efficiently. in this study, element free galerkin is extrinsically enriched by the recently developed crack-tip orthot...

Abstract Background The association of advanced digital image correlation (DIC) and numerical simulation has been widely used for inverse parameter identification. Objective It is attractive to develop an accurate DIC method sharing the common features with simulation, which can lead better synergy between experiments simulations. Methods A new meshfree (MF-DIC) using element free Galerkin (EFG...

We present a family of approximation schemes, which we refer to as second-order maximum-entropy (max-ent) approximation schemes, that extends the first-order local max-ent approximation schemes to second-order consistency. This method retains the fundamental properties of first-order max-ent schemes, namely the shape functions are smooth, non-negative, and satisfy a weak Kronecker-delta propert...

We propose the use of the meshfree radial basis point interpolation (RBPI) to solve the Black–Scholes model for European and American options. The RBPI meshfree method offers several advantages over the more conventional radial basis function approximation, nevertheless it has never been applied to option pricing, at least to the very best of our knowledge. In this paper the RBPI is combined wi...

This paper presents an effective three-dimensional (3D) nonlinear explicit dynamic meshfree algorithm for the simulation of soft tissue mechanical responses. In the algorithm soft tissues are considered to be hyperelastic and nearly incompressible materials. The algorithm is based on the element-free Galerkin (EFG) method using total Lagrangian formulation and moving least square (MLS) approxim...