The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple \& Less-costly Alternative to the Finite Element and Boundary Element Methods

By Satya N. Atluri, S. Shen. 2002

527 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/786463576620d55b11f58d0ee5d83a70effa00ce

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

The MLPG Mixed Collocation Method for Material Orientation and Topology Optimization of Anisotropic Solids and Structures (2008, methodology): “With the potential benefits of the meshless methods, especially research in [Atluri and Zhu(1998), Atluri and Shen(2002a, 2002b), and Atluri(2004)] shows that the MLPG method is becoming the most effective numerical-analytical method for optimizing structures.”
A highly accurate collocation Trefftz method for solving the Laplace equation in the doubly connected domains (2008, methodology): “Recently, the meshless local boundary integral equation (LBIE) method [1], and the meshless local Petrov–Galerkin (MLPG) method [2] are proposed.”
On Approximation in Meshless Methods (2005, background): “The simplest such approach is to collocate the boundary condition in a (finite) set of points Y ⊂ ∂Ω as was proposed, for example, in [2,54,111].”
Corrected First-Order Derivative ISPH in Water Wave Simulations (2017, methodology): “Thirdly, the Moving Least Square (MLS) principle was adopted for this purpose (Atluri and Shen, 2002; Ma, 2005).”
A new meshless interpolation scheme for MLPG_R method (2008, methodology): “A meshless method, called Meshless Local Petrove-Galerkin (MLPG) method, has been invented by Atluri and Zhu (1998) and Atluri and Shen (2002) and has been developed into many forms as summarised in Atluri, Liu and Han (2006).”
GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE (2004, methodology): “…method using test functions with small supports (instead of Dirac functions as mentioned in the last paragraph), have also been reported in the engineering literature, but without rigorous mathematical analysis [Atluri and Shen (2002); Liu (2002); Onate et al. (2001); Xiao and McCarthy (2003)].”
REDUCED-ORDER MODELS FOR MICROELECTROMECHANICAL RECTANGULAR AND CIRCULAR PLATES INCORPORATING THE CASIMIR FORCE (2008, methodology): “and n ¼ 1. They match very well with those obtained by Batra et al. (2007a), Batra et al. (2006a) by solving the two-dimensional governing equation with the meshless local Petrov-Galerkin method ( Atluri and Shen, 2002 ).”