https://orbilu.uni.lu/bitstream/10993/13726/1/phu-meshless.pdf

Review: Meshless methods: A review and computer implementation aspects

A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

Many of the computer vision algorithms have been posed in various forms of differential equations, derived from minimization of specific energy functionals, and the finite element representation and computation have become the de facto numerical strategies for solving these problems. However, for cases where domain mappings between numerical iterations or image frames involve large geometrical shape changes, such as deformable models for object segmentation and nonrigid motion tracking, these strategies may exhibit considerable loss of accuracy when the mesh elements become extremely skewed or compressed. We present a new computational paradigm, the meshfree particle method, where the object representation and the numerical calculation are purely based on the nodal points and do not require the meshing of the analysis domain. This meshfree strategy can naturally handle large deformation and domain discontinuity issues and achieve desired numerical accuracy through adaptive node and polynomial shape function refinement. We discuss in detail the element-free Galerkin method, including the shape function construction using the moving least square approximation and the Galerkin weak form formulation, and we demonstrate its applications to deformable model based segmentation and mechanically motivated left ventricular motion analysis.

/pdf/meshfree-particle-method-nlso0afl37.pdf

Meshfree particle method

A review of meshless methods for laminated and functionally graded plates and shells

This paper gives an overview over Meshfree Methods Starting point is an extended and modified classification of Meshfree Methods due to three aspects: The construction of a partition of unity, the choice of an approximation either with or without using an extrinsic basis and the choice of test functions, resulting into a collocation, Bubnov-Galerkin or Petrov-Galerkin Meshfree Method Most of the relevant Meshfree Methods are described taking into account their different origins and viewpoints as well as their advantages and disadvantages Typical problems arising in meshfree methods like integration, treatment of essential boundary conditions, coupling with mesh-based methods etc~are discussed Some valuing comments about the most important aspects can be found at the end of each section This text was revised in 2004

Luis Gavete

Papers

Influence of several factors in the generalized finite difference method

Solving parabolic and hyperbolic equations by the generalized finite difference method

Improvements of generalized finite difference method and comparison with other meshless method

An h-adaptive method in the generalized finite differences

Solving second order non-linear elliptic partial differential equations using generalized finite difference method