Being different from mesh-based methods, e.g. Finite Element Method, the meshfree methods only used nodes to represent the problem domain. For discretization, nodes are generated on the boundaries in inside the domain. Due to the absence of elements, information on the nodal connectivity is not required. Thus, meshfree methods offer better flexibility in terms of refinement and modelling moving boundaries.
The meshfree methods can be classified into both strong-form based, e.g. the collocation method, and weak-form based, e.g. the Element Free Galerkin method, the Reproducing Kernel Particle method, the Radial Point Interpolation method, etc. In meshfree analysis, the value at an arbitrary point x is approximated by the values of nodes surrounding it, namely the support domain of x. Figure 1 illustrates meshfree analysis of a cracked domain.
