eXtended FEM, Generalized FEM (XFEM, GFEM) - variants of FEM (finite element method) combining some meshless aspects.Partition of unity methods (PoUM) - provide general approximation formulation used in some meshfree methods.Moving least squares (MLS) - provide general approximation method for arbitrary set of nodes.Moving particle finite element method (MPFEM).Generalized finite difference method (GFDM).Reproducing kernel particle method (RKPM) (1995).Element-free Galerkin method (EFG / EFGM) (1994).Smoothed particle hydrodynamics (SPH) (1977).The following numerical methods are generally considered to fall within the general class of 'meshfree' methods. One of the earlier methods without a mesh is smoothed particle hydrodynamics, presented in 1977. Meshfree (or 'meshless' as this is also used) methods seem attractive as alternative to finite elements (FEM) for the general engineering community, which consider the process of generating finite element meshes as more difficult and expensive than the remainder of analysis process. There is also an additional 'sales' oriented aspect of this name. Meshfree methods eliminate some or all of the traditional mesh-based view of the computational domain and rely on a particle (either Lagrangian or Eulerian) view of the field problem.Ī goal of meshfree methods is to facilitate the simulation of increasingly demanding problems that require the ability to treat large deformations, advanced materials, complex geometry, nonlinear material behavior, discontinuities and singularities.įor example the melting of a solid or the freezing process can be simulated using meshfree methods.

Meshfree particle methods li