An improved meshless method with almost interpolation property for isotropic heat conduction problems

作者：Zhang, Xiaohua^*; Zhang, Ping; Zhang, Lin

来源：Engineering Analysis with Boundary Elements, 2013, 37(5): 850-859.

DOI：10.1016/j.enganabound.2013.03.004

• Meshless method
• Heat conduction
• Spatial varying conductivity
• Computational efficiency
• Interpolation property

In the paper an improved element free Galerkin method is presented for heat conduction problems with heat generation and spatially varying conductivity. In order to improve computational efficiency of meshless method based on Galerkin weak form, the nodal influence domain of meshless method is extended to have arbitrary polygon shape. When the dimensionless size of the nodal influence domain approaches 1, the Gauss quadrature point only contributes to those nodes in whose background cell the Gauss quadrature point is located. Thus, the bandwidth of global stiff matrix decreases obviously and the node search procedure is also avoided. Moreover, the shape functions almost possess the Kronecker delta function property, and essential boundary conditions can be implemented without any difficulties. Numerical results show that arbitrary polygon shape nodal influence domain not only has high computational accuracy, but also enhances computational efficiency of meshless method greatly.

• 出版日期2013-5
• 单位多相复杂系统国家重点实验室; 中国科学院