Adapting nodes in three dimensional irregular regions for meshless‐type methods

In this paper, a new adaptive nodes technique based on equi‐distribution principles and dimension reduction is presented for irregular regions in three dimensional cases. The mesh generation is performed by first producing some adaptive nodes in a cube based on equi‐distribution along the coordinate axes and then transforming the generated nodes to the physical domain followed by a refinement process. The mesh points produced are appropriate for meshless‐type methods which need only some scattered points rather than a mesh with some smoothness properties. The effectiveness of the generated mesh points is examined by a collocation meshless method using a well known radial basis function, namely ϕ(r) = r ⁵ which is sufficiently smooth for our purpose. Some experimental results will be presented to illustrate the effectiveness of the proposed method.