Open Access

ABSTRACT

The Progress of Energy Meshless Methods by Using Trial Functions as the Bases of Solution

Cheinshan Liu^1,2,3, Chunglun Kuo²

1 College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, China.
2 Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung 202-24, Taiwan.
3 Center of Excellence for the Oceans, National Taiwan Ocean University, Keelung 202-24, Taiwan.

*Corresponding Author: Cheinshan Liu. Email:

The International Conference on Computational & Experimental Engineering and Sciences 2019, 22(4), 189-191. https://doi.org/10.32604/icces.2019.05074

Abstract

For the linear differential operator equation equipped with boundary conditions we derive an energy identity. Then we propose an energy regularization technique to choose the energetic bases in the numerical solution of linear differential operator equation. In many meshless methods with some trial functions as the bases of numerical solution, there exist certain parameters in the numerical method. We derive a very simple energy gap functional and minimize it to determine the optimal parameters. The new methodology upon adopting optimal parameters by minimizing the energy gap functional can improve the accuracy of the meshless methods in the numerical solutions.

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Keywords

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