The meshless local Petrov-Galerkin (MLPG) method

By Satya N. Atluri, S. Shen. 2002

608 citations recorded by the source corpus.

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Citations in the corpus

A meshless method for some inverse problems associated with the Helmholtz equation (2006, unknown): “Amongst meshless methods, there are element free-Galerkin method (EFGM) [11], H–p cloud [12], reproducing kernel particle method (RKPM) [13], meshless local Petrov–Galerkin (MLPG) method [14], Kansa s method [15], the method of fundamental solutions [16,17] etc.”
A local radial basis functions—Finite differences technique for the analysis of composite plates (2011, methodology): “Weak-form methods include for example the element-free Galerkin [4,5] or the Petrov–Galerkin [6,7] methods where a weight-residual approach is commonly used.”
A meshless method for two-dimensional diffusion equation with an integral condition (2010, methodology): “The meshless local Petrov–Galerkin method (MLPG) was first proposed by Atluri and Zhu [21,22] in 1998 has been applied widely and very successfully in recent years, and it led already to various surveys and two books [14,15].”
Material Point Method Calculations with Explicit Cracks (2003, methodology): “…Kober (2003)] presents it as a Petrov-Galerkin method that has similarities with meshless methods such as Element-Free Galerkin (EFG) methods [Belytschko, Lu, and Gu (1994)] and MeshlessLocal Petrov-Galerkin (MLPG) methods [Atluri and Shen (2002a), Atluri and Shen (2002b), Atluri and Zhu (1998)].”
Second‐order accurate derivatives and integration schemes for meshfree methods (2012, methodology): “Another class of methods that should be mentioned is the support integration method that employs integration (evaluation) points over the nodal supports, as proposed by Atluri and Zhu [14] in the meshless local Petrov–Galerkin method and by De and Bathe [15] in the finite sphere method.”
A Meshless Local Petrov-Galerkin Method for Solving the Bending Problem of a Thin Plate (2002, methodology): “The generality of the MLPG approach, based on either symmetric or unsymmetric weak-forms, and using 5 different types of meshless interpolations of trial functions, as well as 6 different types of meshless interpolation test functions, has been comprehensively discussed by Atluri and Shen (2002a, b)”
Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method (2006, methodology): “…and Toader (2004)], the geometry projection method [Norato, Haber, Tortorelli, and Bendsøe (2004)], the true meshless local Petrov-Galerkin method [Atluri and Shen (2002)], or some extended finite element methods [Belytschko and Black (1999); Strouboulis, Copps, and Babuska (2001); Wang and…”
The Generalized Interpolation Material Point Method (2004, methodology): “…are particle methods derived using a Petrov–Galerkin discretization scheme, of all the various meshless methods, they have the most in common with the Meshless Local Petrov–Galerkin (MLPG) Method introduced in [Atluri and Zhu (1998)] and described in more detail in [Atluri and Shen (2002b)].”
TRANSIENT THERMOELASTIC DEFORMATIONS OF A THICK FUNCTIONALLY GRADED PLATE (2004, methodology): “Two recent books [ 26 , 27 ] summarize developments in meshless methods that include the element-free Galerkin [ 28 ], the hp-clouds [ 29 ], the reproducing kernel particle [ 30 ], the smoothed particle hydrodynamics [ 31 , 32 ], the diffuse element [ 33 ], the partition of unity FE [ 34 ], the na”
Numerical Cubature on Scattered Data by Radial Basis Functions (2005, background): “[ 2 ]) and the \volume integral formulation" of the time dependent conservation equations proposed in [19].”
Meshless methods: A review and computer implementation aspects (2008, background): “Atluri [1] introduced the notion " truly " meshless since no construction of a background 52 mesh is needed for integration purposes.”
Topology-optimization of Structures Based on the MLPG Mixed Collocation Method (2008, methodology): “In recent years, substantial efforts have been made in the development of the meshless meth- 62 Copyright c© 2008 Tech Science Press CMES, vol.26, no.1, pp.61-74, 2008 ods, especially the MLPG method [Atluri and Zhu(1998), Atluri and Shen(2002a, 2002b), and Atluri(2004)].”
The MLPG Mixed Collocation Method for Material Orientation and Topology Optimization of Anisotropic Solids and Structures (2008, methodology): “The conventional topology optimization of a structure proceeds in a sequential manner, and it simultaneously solves the equilibrium equations and optimizes the structure subjected to certain objectives and constraints [Norato, Bendsøe, Haber and Tortorelli (2007), Vemaganti and Lawrence (2005), Cisi”
Meshless method based on the local weak-forms for steady-state heat conduction problems (2008, methodology): “Various numerical techniques have been proposed to enforce the essential boundary conditions, such as the Lagrange multiplier method [29], the penalty approach [30], the transformation method [11,31], the direct interpolation method [32], etc.”