A spatio-temporal radial basis function collocation method based on Hausdorff fractal distance for Hausdorff derivative heat conduction equations in three-dimensional anisotropic materials

Abstract

In this paper, the spatio-temporal radial basis function (RBF) collocation method based on Hausdorff fractal distance is developed and used to simulate the transient heat transfer problems in anisotropic materials governed by Hausdorff derivative heat conduction equations. We introduce Hausdorff fractal distance into the conventional RBFs, and based on this incorporation, establish a meshless method to address Hausdorff derivative heat conduction problems, in which the anisotropy of the thermal conductivity of the material and spatio-temporal fractal characteristics are taken into account. We set the source points of the collocation method outside the spatial computational domain instead of distributing them within the original domain to further improve the accuracy of the method. Numerical experiments carried out in this study demonstrate the superior performance of the proposed approach compared to the finite element method and traditional RBF collocation method, showing that the developed method can be considered as a competitive tool for simulating Hausdorff derivative transient heat conduction problems in complex geometries.