A MESHLESS METHOD BASED ON LEAST-SQUARES APPROACH FOR STEADY- AND UNSTEADY-STATE HEAT CONDUCTION PROBLEMS
A MESHLESS METHOD BASED ON LEAST-SQUARES APPROACH FOR STEADY- AND UNSTEADY-STATE HEAT CONDUCTION PROBLEMS
复制标题
DOI：
10.1080/10407790590901648
复制
发表时间：
2005-02
期刊：
影响因子：
--
通讯作者：
Y. Liu;X. Zhang;M. Lu
中科院分区：
文献类型：
--
作者：
Y. Liu;X. Zhang;M. Lu
摘要将基于最小二乘法的无网格方法--无网格加权最小二乘法（MWLS）推广到求解导热问题。MWLS公式首先建立了稳态问题，然后扩展到非稳态问题的时间步进计划。理论分析和数值算例表明，与基于Galerkin方法的无网格方法相比，本方法可以采用更大的时间步长。数值研究表明，该方法是一种精度高、收敛速度快、计算效率高的真正无网格方法。
ABSTRACT The meshless method based on the least-squares approach, the meshless weighted least-squares (MWLS) method, is extended to solve conduction heat transfer problems. The MWLS formulation is first established for steady-state problems and then extended to unsteady-state problems with time-stepping schemes. Theoretical analysis and numerical examples indicate that larger time steps can be used in the present method than in meshless methods based on the Galerkin approach. Numerical studies show that the proposed method is a truly meshless method with good accuracy, high convergence rate, and high efficiency.