ABSTRACT
Nowadays, a significant portion of the computational mechanics scientific community is focused on solving partial differential equations (PDEs) using numerical methods, such as “Finite Element Method” (FEM). This popular numerical method consists of dividing the problem in small elements and using shape functions in order to obtain field variables.The influence domain is defined by the elements which can not overlap each other. When an element is manifestly distorted, the shape functions obtained show a poor quality, affecting the results. In the computation of problems with irregular geometries, mesh generation is more time-consuming than the actual solution of the PDEs. Taking in consideration these disadvantages, meshless methods emerge, using nodes random distributed along the domain and field functions approximated within an influence domain rather than an element. In opposition to the FEM, the influence domains may and must overlap each other.
