In addition, since meshless methods use a functional basis and allow arbitrary placement of points, the solution and its derivatives may be found directly where they are needed and with greater accuracy than with FD, FE and BE methods where differences and interpolation are required. Meshless methods originated from the work on finite difference (FD), finite element (FE) and boundary element (BE) methods, but meshless methods can treat an irregular distribution of points and require no costly mesh generation. A number of methods has been proposed so far including the smooth particle hydrodynamics (SPH) method, the diffuse element method (DEM), the element free Galerkin (EFG) method, the reproducing kernel particle method (RKPM), the moving least-squares reproducing kernel (MLSRK) method, the partition of unity finite element method (PUFEM), the hp-clouds method, the finite point method, the meshless local Petrov-Galerkin (MLPG) method, boundary node method (BNM), the local boundary integral equation (LBIE) method, and the method of finite spheres (which is a special case of the MLPG method, when the local sub-domains are chosen to be spheres in 3-D). In spite of the great success of the finite and boundary element methods as the most effective numerical tools for the solution of boundary value problems in complex domains, there has been a growing interest in the so-called meshless methods over the past decade. The boundary element method (BEM) has become an efficient and popular alternative to the FEM, especially for stress concentration problems, or for boundary value problems wherein a part of the boundary extends to infinity. The loss of accuracy is observed when the elements in the mesh become extremely skewed or distorted. It is well-known that the FEM method relies on a mesh discretization, which leads to complications for certain classes of problems. It is a robust and thoroughly developed technique, but it is not without its own shortcomings. The finite element method (FEM), for the modelling of complex problems in applied mechanics and related fields, is well established. Sladek The development of approximate methods for the numerical solutions of boundary value problems has attracted the attention of engineers, physicists and mathematicians for a long time.
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