A two dimensional adaptive nodes technique in irregular regions applied to meshless-type methods

TL;DR

This paper introduces a 2D adaptive node placement technique for irregular regions, enhancing meshless methods by improving point distribution based on equi-distribution and dimension reduction, with demonstrated effectiveness through experiments.

Contribution

The paper presents a novel 2D adaptive node generation method for irregular regions, tailored for meshless methods, using equi-distribution and transformation from rectangular grids.

Findings

Improved node distribution in irregular regions.

Enhanced accuracy in meshless collocation methods.

Effective adaptation demonstrated through experiments.

Abstract

We propose a two dimensional (2D) adaptive nodes technique for irregular regions. The method is based on equi-distribution principal and dimension reduction. The mesh generation is carried out by first producing some adaptive nodes in a rectangle based on equi-distribution along the coordinate axes and then transforming the generated nodes to the physical domain. Since the produced mesh is applied to the meshless-type methods, the connectivity of the points is not used and only the grid points are important, though the grid lines are utilized in the adapting process. The performance of the adaptive points is examined by considering a collocation meshless method which is based on interpolation in terms of a set of radial basis functions. A generalized thin plate spline with sufficient smoothness is used as a basis function and the arc-length is employed as a monitor in the equi-distribution process. Some experimental results will be presented to illustrate the effectiveness of the proposed method.