The meshless local Petrov-Galerkin method for the analysis of heat conduction due to a moving heat source, in welding

Shibahara, Masakazu; Atluri, Satya N.

doi:10.1016/j.ijthermalsci.2010.12.012

Cited by 45 publications

(28 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…If the solution is sought for long time instant, it will cost our large computing sources and computational time particularly as the dimension of Eq. (14) increases. In order to overcome this deficiency, POD which can build a low-dimension matrix to approximate a high-dimension matrix is introduced to reduce the computational time of meshless method.…”

Section: Figmentioning

confidence: 92%

“…That is, using the optimal POD basis matrix U to Eq. (14) or Eq. (13), the following reduced form of Eq.…”

Section: Fundamentals Of Pod and Coupled With Efgmentioning

confidence: 99%

“…From the above algorithm, it can be found that the EFG-POD only solves k Â k system equations at each time loop, while EFG (Eq. (14)) needs to solve m Â m system equations (usually m ) k) at each time loop. This means that EFG-POD requires less computational time than that of EFG, although the determination of the optimal POD basis needs some additional computational time.…”

Section: Fundamentals Of Pod and Coupled With Efgmentioning

confidence: 99%

“…Based on the moving Kriging interpolation, Chen and Liew [13] developed meshless local Petrov-Galerkin approach to solve transient heat conduction problems in 2-D and 3-D spaces. Shibahara and Atluri [14] applied MLPG to transient heat conduction involving in a moving heat source. Khosravifard et al [15] presented an improved meshless RPIM for nonlinear transient heat conduction problems and implemented the method to analyze the functionally graded materials with non-homogenous and temperature-dependent heat sources.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A fast meshless method based on proper orthogonal decomposition for the transient heat conduction problems

Zhang

Xiang

2015

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

Section: Figmentioning

confidence: 92%

“…That is, using the optimal POD basis matrix U to Eq. (14) or Eq. (13), the following reduced form of Eq.…”

Section: Fundamentals Of Pod and Coupled With Efgmentioning

confidence: 99%

Section: Fundamentals Of Pod and Coupled With Efgmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A fast meshless method based on proper orthogonal decomposition for the transient heat conduction problems

Zhang

Xiang

2015

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

“…See Nguyen, 2008 [7] for a review. Methods such as the Element-Free Galerkin (EFG) method [8] , the Meshless Local Petrov-Galerkin (MPLG) method [9] and the Edge-based Smoothed Point Interpolation…”

Section: Introductionmentioning

confidence: 99%

The virtual node polygonal element method for nonlinear thermal analysis with application to hybrid laser welding

Peng

et al. 2013

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

The nonlinear heat transfer process occurring during hybrid laser welding was simulated using the Virtual-node Polygonal Element (VPE) method within the framework of the Finite Element Method (FEM). To achieve robustness in large-scale welding simulations, a dynamic mesh refinement with quadtree and octree data structures was used in the welding region. Accuracy, convergence and efficiency were verified by solving two and three dimensional problems. It is found that the present VPE can successfully simulate the hybrid laser welding process with good accuracy and convergence. The adaptive refined mesh box can synchronously move with the welding heat source, which dramatically reduces the number of field nodes. Compared with the standard FEM,the VPEM requires only approximately 42% of the total degrees of freedom used in standard FEM for the same accuracy. Furthermore, we compare the computational cost and accuracy of the method to that of the finite element method, the edge based virtual node polygonal element/virtual node method, the edge-based Smoothed Point Interpolation Meshless Method (ES-PIM), the edge-based Element (ES-PIM), the Element Free Galerkin (EFG) method and the Meshless Local Petrove-Galerkin (MLPG) method. Compared to all those methods, the proposed scheme is found competitive in terms of computational cost versus accuracy, and benefit from a simple implementation.

show abstract

A moving Kriging‐based MLPG method for nonlinear Klein–Gordon equation

Shokri

Habibirad

2016

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, the meshless local Petrov–Galerkin approximation is proposed to solve the 2‐D nonlinear Klein–Gordon equation. We used the moving Kriging interpolation instead of the MLS approximation to construct the meshless local Petrov–Galerkin shape functions. These shape functions possess the Kronecker delta function property. The Heaviside step function is used as a test function over the local sub‐domains. Here, no mesh is needed neither for integration of the local weak form nor for construction of the shape functions. So the present method is a truly meshless method. We employ a time‐stepping method to deal with the time derivative and a predictor–corrector scheme to eliminate the nonlinearity. Several examples are performed and compared with analytical solutions and with the results reported in the extant literature to illustrate the accuracy and efficiency of the presented method. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

The meshless local Petrov-Galerkin method for the analysis of heat conduction due to a moving heat source, in welding

Cited by 45 publications

References 9 publications

A fast meshless method based on proper orthogonal decomposition for the transient heat conduction problems

A fast meshless method based on proper orthogonal decomposition for the transient heat conduction problems

The virtual node polygonal element method for nonlinear thermal analysis with application to hybrid laser welding

A moving Kriging‐based MLPG method for nonlinear Klein–Gordon equation

Contact Info

Product

Resources

About