A fast interpolating meshless method for 3D heat conduction equations. (December 2022) - Meng, Zhijuan; Ma, Yuye; Ma, Lidong
Abstract: A fast interpolating meshless (FIM) method for three-dimensional (3D) heat conduction equations is presented. Transforming a 3D problem into the relevant two-dimensional (2D) problems using the dimension splitting method (DSM) is the main idea of FIM method. The improved interpolating moving least-squares (IIMLS) method is applied in 2D problems to obtain required approximation function with interpolation property. Finite difference method (FDM) is utilized in time domain and the direction of splitting. Take the improved element-free Galerkin (IEFG) method as a comparison, difficulties created by the singularity of weight functions, such as truncation error and calculation inconvenience, are overcome by the FIM method. And it can directly implement the Dirichlet boundary conditions. To prove the advantages of the new method, three examples are selected and solved by the FIM method. Comparing and analyzing the calculation results, it can be shown that the FIM method effectively improves computation speed and precision.