In this paper we investigate the application of radial basis functions to solve variational problems as they appear in the weak formulation of elliptic partial diierential equations. Two algorithms based on a multilevel scheme are introduced. Their numerical advantages and disadvantages are discussed and demonstrated on an example. x1. Introduction The classical Galerkin approach for the soluti...

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...

In this paper, natural heat convection inside square and equilateral triangular cavities was studied using a meshless method based on collocation local radial basis function (RBF). The nanofluids used were Cu-water or -water mixture with nanoparticle volume fractions range of . A system continuity, momentum, energy partial differential equations in modeling the flow temperature behavior fluids....

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

A meshless local Petrov-Galerkin (MLPG) method is applied to solve problems of Reissner-Mindlin shells under thermal loading. Both stationary and thermal shock loads are analyzed here. Functionally graded materials with a continuous variation of properties in the shell thickness direction are considered here. A weak formulation for the set of governing equations in the Reissner-Mindlin theory i...

Based on the radial basis function (RBF), non-singular general solution and dual reciprocity method (DRM), this paper presents an inherently meshless, exponential convergence, integration-free, boundary-only collocation techniques for numerical solution of general partial differential equation systems. The basic ideas behind this methodology are very mathematically simple and generally effectiv...

A very effective method for some kind of problems is the Method of Fundamental Solutions (MFS). It is a boundary meshless method which does not need any mesh and in linear problems only nodes (collocation points) on the domain boundaries and a set of source functions (fundamental solutions, i.e. Kelvin functions) in points outside the domain are necessary to satisfy the boundary conditions. Ano...

In this paper we present a more accurate method for solving a frequency-dependent inductance of 3-D structures that contains permeable materials. The extracted inductance using the new method is much more accurate than when using the traditional collocation method for no increased cost. Computational results are presented and compared with data to demonstrate the accuracy improvement of the app...

We introduce a radial basis collocation method to solve axially moving beam problems