The traditional radial basis function collocation method (RBFCM) has poor stability when solving two-dimensional elastic problems, and the numerical results are very sensitive to shape parameters, especially in problems. In this paper, a novel using fictitious centre nodes is applied problem. proposed RBFCM employs interpolate unknown coefficients, much less parameter compared with RBFCM. detai...

Purpose – To present a new collocation method for numerically solving partial differential equations (PDEs) in rectangular domains. Design/methodology/approach – The proposed method is based on a Cartesian grid and a one-dimensional integrated-radial-basis-function (1D-IRBF) scheme. The employment of integration to construct the RBF approximations representing the field variables facilitates a ...

The main objective of the current work is to determine meshless methods using radial basis function (rbf) approach estimate elastic strain field from energy-resolved neutron imaging. To this end, we first discretize longitudinal ray transformation with rbf give us an unconstrained optimization problem. This discretization then transformed into a constrained problem by adding equilibrium conditi...

In this article, a novel infinitely smooth polyharmonic radial basis function (PRBF) collocation method for solving elliptic partial differential equations (PDEs) is presented. The PRBF with natural logarithm piecewise in the conventional governing equations. We converted into an using source points collocated outside domain to ensure that distance was always greater than zero avoid singularity...

We present a multilevel algorithm based on nonsymmetric collocation with compactly supported radial basis functions for the solution of nonlinear partial diierential equations. At the operator level this algorithm can be viewed as a Newton method. Details of the algorithm as well as numerical experiments are discussed. x1. Introduction Radial basis function (RBF) methods have been studied by va...

In order to assess the performance of some meshless methods based on Radial Basis Function (RBF) Collocation, it is presented a comprehensive comparison between global and multi-domain formulations for solving convection-diffusion equations. Global formulations included are the symmetric or Fasshauer’s method and the overlapping two-domain decomposition method (the classical additive Schwarz te...

Gaussian Radial Basis Function (RBF) interpolation methods are theoretically spectrally accurate. However, in applications this accuracy is seldom realized due to the necessity of solving a very poorly conditioned linear system in order to evaluate the methods. Recently, by using approximate cardinal functions and restricting the method to a uniformly spaced grid (or a smooth mapping thereof), ...

We employ a Kansa-radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains. This discretization leads, with an appropriate selection of collocation points and for any choice of RBF, to linear systems in which the matrices possess block circulant structures. These linear systems can be solved efficiently using matrix decomposition algor...

Many radial basis function (RBF) methods contain a free shape parameter that plays an important role for the accuracy of the method. In most papers the authors end up choosing this shape parameter by trial and error or some other ad hoc means. In this paper, we propose applying the genetic algorithm to determine a good shape parameter of radial basis functions for the solution of partial differ...