Many applications require that nodes be scattered locally quasi-uniformly within 2-D regions or on curved surfaces in 3-D space, while obeying some prescribed spatially varying density function. This study focuses on creating variable density node layouts that are suitable for meshfree discretizations of PDEs. Another application is ‘dithering’ to simulate half-tone images. The method is an ’ad...

Recent engineering applications successfully introduced unsymmetric meshless local Petrov-Galerkin (MLPG) schemes. As a step towards their mathematical analysis, this paper investigates nonstationary unsymmetric Petrov-Galerkin-type meshless kernel-based methods for the recovery of L2 functions from finitely many weak data. The results cover solvability conditions and error bounds in negative S...

This paper solves the Laplace equation ∆u = 0 on domains Ω ⊂ R by meshless collocation on scattered points of the boundary ∂Ω. In contrast to the Method of Fundamental Solutions, there are no singularities and no artificial boundaries, since we use new singularity–free positive definite kernels which are harmonic in both arguments. In contrast to many other techniques, e.g. the Boundary Point M...

Though the technique introduced by E. Kansa [7, 8] is very successful in engineering applications, there were no proven results so far on the unsymmetric meshless collocation method for solving PDE boundary value problems in strong form. While the original method cannot be proven to be fail–safe in general, we prove asymptotic feasibility for a generalized variant using separated trial and test...

We combine the theory of radial basis functions with the field of Galerkin methods to solve partial differential equations. After a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions.

In this paper, attempt is made to solve a few problems using the Polynomial Point Collocation Method (PPCM), the Radial Point Collocation Method (RPCM), Smoothed Particle Hydrodynamics (SPH), and the Finite Point Method (FPM). A few observations on the accuracy of these methods are recorded. All the simulations in this paper are three dimensional linear elastostatic simulations, without account...

A meshfree computational method is proposed in this paper to solve Kirchhoff plate problems of various geometries. The deflection of the thin plate is approximated by using a Hermite-type radial basis function approximation technique. The standard Galerkin method is adopted to discretize the governing partial differential equations which were derived from using the Kirchhoff’s plate theory. The...