1. Objective

Over the last twenty years, a major research effort in numerical mechanics has focused on avoiding the mesh construction step in standard simulation procedures, and more particularly for various applications of the finite element method. This is one of the most costly steps in the search for numerical approximations to the solutions of partial differential equations for complex geometries, particularly for models associated with physical phenomena where changes in geometry are frequent and significant (crack propagation, forming processes, free or moving surface flow problems, etc.).

The fact that meshless methods are gaining in importance is evident from the large number of methods that have been developed over a short period of time (see