A fast interpolating meshless method for 3D heat conduction equations

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 dif-ference 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.

Automated summary

A fast interpolating meshless (FIM) method is introduced for solving three-dimensional heat conduction equations. The method employs the dimension splitting method to transform the 3D problem into relevant 2D problems and utilizes the improved interpolating moving least-squares method for obtaining accurate approximation functions. Finite difference method is used for time domain and direction splitting. The FIM method overcomes difficulties caused by singular weight functions and can directly implement Dirichlet boundary conditions. Numerical examples demonstrate that the FIM method effectively improves computation speed and accuracy.