TY - EJOU
AU - Liu, Cheinshan
AU - Kuo, Chunglun
TI - The Progress of Energy Meshless Methods by Using Trial Functions as the Bases of Solution
T2 - The International Conference on Computational \& Experimental Engineering and Sciences
PY - 2019
VL - 22
IS - 4
SN - 1933-2815
AB - 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.
KW - Linear differential operator equation
KW - energy regularization technique
KW - energetic bases
KW - energy gap functional
KW - optimal parameters
DO - 10.32604/icces.2019.05074