Advances in Meshless Methods

Some of the above mentioned meshless methods, namely the RKPM, SPH method, DEM and EFG method, are not truly meshless. All these pseudo meshless methods use integration cells. Only finite point method, the MLPG (and its special variation, the so-called method of finite spheres), and LBIE are truly meshless. However, although considerable efforts have been made in the development of meshless methods, the currently available techniques are still computationally much less efficient than the well established conventional discretization procedures. The primary reason is that non-polynomial shape functions are employed and the required numerical integration is very difficult to perform accurately. Meshless methods belong to one of the most progressively developed part of the computational mechanics. These methods are increasingly applied to many fields of engineering and sciences. Therefore, the number of new results in this field is growing significantly during the past few years. It is a natural need to organize a conference in this subject to discuss about further developments of meshless methods. The first ICCES meshless symposium held in High Tatras, Slovakia brought together both mathematicians and engineers interested in developing new progressive computational methods. The best selected lectures from the symposium are collected in this book in their extended form.