MESHLESS LOCAL PETROV-GALERKIN (MLPG) METHOD FOR CONVECTION DIFFUSION PROBLEMS

By H. Lin, Satya N. Atluri. 2000

205 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/bd43be3e80f751fe1f99a538cbcbd93b436fe487

How researchers see this paper

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

In Computational Mechanics

1. Qingwei Ma
2. S. Shen
3. Satya N. Atluri
4. Gang Li
5. Xiaozhong Jin
6. H. Ching
7. L. Qian
8. N. Aluru

In Electrical and Electronic Engineering

1. Qingwei Ma
2. S. Shen
3. Mategaonkar Meenal
4. T. Eldho
5. H. Ching
6. L. Qian
7. Satya N. Atluri
8. H. Lin

In Mechanics of Materials

1. Qingwei Ma
2. Satya N. Atluri
3. S. Shen
4. Xiaozhong Jin
5. N. Aluru
6. Gang Li
7. Chein-Shan Liu
8. H. Ching

Citations in the corpus

• The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations (2001, methodology): “This kind of upwinding scheme has been extended to solve the nonlinear Burgers' equations successfully in Lin and Atluri (2000b).”
• The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple \& Less-costly Alternative to the Finite Element and Boundary Element Methods (2002, methodology): “Remarkable successes of the MLPG method have been reported in solving the convection-diffusion problems [Lin & Atluri (2000)]; fracture mechanics problems [Kim & Atluri (2000), Ching & Batra (2001)]; Navier-Stokes flows [Lin & Atluri (2001)]; and plate bending problems [Gu & Liu (2001), and Long &…”
• Investigations on the Accuracy and Condition Number for the Method of Fundamental Solutions (2006, background): “Later, Smyrlis and Karageorghis (2004) revisited the same issue by using the least-square MFS, which has more collocation points than source points.”
• Simulation of groundwater flow in unconfined aquifer using meshfree point collocation method (2011, methodology): “Lin and Atluri [10] proposed meshless Petrov–Galerkin (MLPG) method to solve steady convection diffusion problems, in 1D and 2D and found that even for very high Peclet number flows, themodel gives very good results.”
• Meshless local Petrov-Galerkin method for two-dimensional nonlinear water wave problems (2005, methodology): “The success of the MLPG method has been reported in solving fracture mechanics problems [10], beam and plate bending problems [11], three dimensional elasto-static and -dynamic problems [12,13] and some fluid dynamic problems such as steady flow around a cylinder [8], steady convection and diffusion”
• On the Equivalence Between Least-Squares and Kernel Approximations in Meshless Methods (2001, background): “…boundary integral equation (LBIE) [Zhu, Zhang, Atluri (1998)], meshless local PetrovGalerkin (MLPG) [Atluri and Zhu (1998); Kim and Atluri (2000); Lin and Atluri (2000)], finite point method [Onate, et al. (1996); Wordelman et al. (2000)], boundary node method [Mukherjee and Mukherjee (1997)]…”
• Static and dynamic analysis of 2‐D functionally graded elasticity by using meshless local petrov‐galerkin method (2004, methodology): “The recent developments in the MLPG method include the following: Atluri and Zhu (2000) solved elastostatic problems, Lin and Atluri (2000) introduced the upwinding scheme to analyze steady state convectiondiffusion problems, and Liu and Gu (2000) coupled the MLPG method with either the finite…”