Nodally Integrated Local Maximum-Entropy Approximation-Based Element-Free Galerkin Method for the Analysis of Steady Heat Conduction

2021 ◽  
Author(s):  
Sreehari Peddavarapu ◽  
S. Raghuraman
Keyword(s):  
Heat Conduction ◽  
Galerkin Method ◽  
Maximum Entropy ◽  
Local Maximum ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Steady Heat Conduction ◽  
Steady Heat

An Improved Element Free Galerkin Method and Precise Time-Step Integration Method for Solving Transient Heat Conduction Problems

2013 ◽  
Vol 444-445 ◽  
pp. 1517-1521
Author(s):  
Xiao Hua Zhang ◽  
Hui Xiang
Keyword(s):  
Heat Conduction ◽  
Galerkin Method ◽  
Integration Method ◽  
Transient Heat Conduction ◽  
Element Free Galerkin Method ◽  
Time Step ◽  
Element Free Galerkin ◽  
Transient Heat Conduction Problem ◽  
Element Free ◽  
Precise Time

An improved element free Galerkin method coupled the precise time-step integration method in the time domain is proposed for solving transient heat conduction problem with spatially varying conductivity in the paper. Firstly the nodal influence domain of element free Galerkin methods is extended to arbitrary convex polygon rather than rectangle and circle. When the dimensionless size of the nodal influence domain is 1.01, the shape function almost possesses interpolation property, thus essential boundary conditions can be implemented without any difficulties for the meshless method. Secondly, the precise time-step integration method is selected for the time discretization in order to improve the computational efficiency. Lastly, one numerical example is given to illustrate the highly accurate and efficient algorithm.

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