Analytical comparison between Meshfree Particle methods (MPMs) andgrid-based methods

Numerical simulating using computers has been increasingly become a very important approach for solving problems in engineering and science. Grid or mesh based numerical m difference methods (FDM) and the finite element methods (FEM) are currently the dominate methods in numerical simulations for solving problems in engineering and science. The use of grid/mesh can lead to difficulties in dealing wi for (FDM), and extremely large deformation for (FEM). This paper focused on the development of the next generation of computational Meshfree methods. The key idea of the meshfree methods provide accurate and stable numerical solutions for integral equations. The invention, development, applications and extension of the Meshfree particle methods (MPMs) which are expected to be superior to the conventional grid grid-based FDM and FEM for ma Engineering problems, Meshfree methods, grid-based FDM and FEM for many applications are briefly discussed.