Meshfree Methods - List of Methods and Acronyms

List of Methods and Acronyms

The following numerical methods are generally considered to fall within the general class of "meshfree" methods. Acronyms are provided in parentheses.

  • Smoothed particle hydrodynamics (SPH) (1977)
  • Diffuse element method (DEM) (1992)
  • Dissipative particle dynamics (DPD) (1992)
  • Element-free Galerkin method (EFG / EFGM) (1994)
  • Reproducing kernel particle method (RKPM) (1995)
  • Finite pointset method (FPM) (1998)
  • hp-clouds
  • Natural element method (NEM)
  • Material Point Method (MPM)
  • Meshless local Petrov Galerkin (MLPG)
  • Moving particle semi-implicit (MPS)
  • Generalized finite difference method (GFDM)
  • Particle-in-cell (PIC)
  • Moving particle finite element method (MPFEM)
  • Finite cloud method (FCM)
  • Boundary node method (BNM)
  • Meshfree moving Kriging interpolation method (MK)
  • Boundary cloud method (BCM)
  • Method of fundamental solution(MFS)
  • Method of particular solution (MPS)
  • Method of Finite Spheres (MFS)
  • Discrete Vortex Method (DVM)
  • Smoothed point interpolation method (S-PIM) (2005).
  • Meshfree local radial point interpolation method (RPIM).
  • Local Radial Basis Function Collocation Method (LRBFCM)
  • Viscous vortex domains method (VVD)
  • Discrete Least Squares Meshless method (DLSM) (2006)

Related methods:

  • Moving least squares (MLS) – provide general approximation method for arbitrary set of nodes
  • Partition of unity methods (PoUM) – provide general approximation formulation used in some meshfree methods
  • Continuous blending method (enrichment and coupling of finite elements and meshless methods) – see Huerta & Fernández-Méndez (2000)
  • eXtended FEM, Generalized FEM (XFEM, GFEM) – variants of FEM (finite element method) combining some meshless aspects
  • Smoothed finite element method (S-FEM) (2007)
  • Gradient smoothing method (GSM) (2008)
  • Local maximum-entropy (LME) – see Arroyo & Ortiz (2006)
  • Space-Time Meshfree Collocation Method (STMCM) – see Netuzhylov (2008), Netuzhylov & Zilian (2009)

Read more about this topic:  Meshfree Methods

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