What are Particle and Meshless Methods?

There are still some problems that FE methods do not solve efficiently or accurately. In particular, FE methods are not ideally suited for solution of dynamic problems involving a large amount of deformation because an accurate solution requires regularly-shaped elements and the movement of the nodes can lead to mesh distortion and badly-shaped elements. One approach to avoiding the problems associated with mesh deformation is remeshing, where anew mesh of regularly shaped elements is created during the solution process. This approach is computationally expensive and has potential loss of accuracy as it requires the mapping of the solution from one mesh to the next which is why meshless or particle methods may be a useful numerical method to explore.