A three dimensional adaptive nodes technique applied to meshless-type methods

We present a new three dimensional adaptive nodes technique based on equi-distribution principles and dimension reduction. The idea is to first produce a uniform mesh in a three dimensional domain and then equi-distribute the mesh in the three coordinate directions using an iterative method. The final mesh forms hexahedrons whose edges equi-distribute the grid curves in the three coordinate directions. The performance of the mesh points produced is examined by the collocation meshless method using the arc-length monitor and employing two well known radial basis functions, namely a generalized thin plate spline and a polynomial function. The generated mesh points are suitable for meshless-type methods which only need some scattered points rather than a mesh with some smoothness properties. Some experimental results will be presented to illustrate the effectiveness of the proposed method.