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Meshfree Particle Methods Shaofan Li, Wing Kam Liu
Publisher: Springer

The Material Point Method (MPM), is an extension of the Particle-in-cell (PIC) Method in computational fluid dynamics to computational solid dynamics, and is a Finite element method (FEM)-based particle method. The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Meshfree Particle Methods is a comprehensive and systematic exposition of particle methods, meshfree Galerkin and partition of unity methods, molecular dynamics methods, and multiscale methods. The papers cover a broad range of topics such as meshfree particle methods, Generalized FE and Extended FE methods, inverse analysis and optimization methods. Liu 2003 World Scientific Publishing Company ISBN13:9789812384560;ISBN10:981-238-456-1. Dan's suggestion is an important topic about the methods. But how to evaluate all of the meshfree methods maybe a more difficult problem. If you're a developer and looking for a development code for meshfree Tahoe(Sandia National Lab research code that includes finite element, particle and meshfree methods) is one of the available codes. Springer-Verlag Berlin and Heidelberg, 2004). Belytschko, "Convergence and stabilization of stress-point integration in mesh-free and particle methods," International Journal for Numerical Methods in Engineering, 74:1067-1087 (2008). The smoothed particle hydrodynamics (SPH) is a widelyused messless method. Smoothed particle hydrodynamics: a meshfree particle method G. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Introduction to Meshless MethodsLS-DYNA Seminar3 What is the Meshfree/Meshless/ Particle Method? The Vortex Particle Method (VPM) and Smoothed Particle Hydrodynamics (SPH) are both fluid simulation techniques that use particles to represent the fluid. The reliable material properties are essential to computational modeling of materials and structures with numerical methods such as Finite Element Method (FEM), Meshfree Particle Method (MPM), etc. Physical domain is discretized with particles.