A New High-Precision Boundary-Type Meshless Method for Calculation of Multidomain Steady-State Heat Conduction Problems

Abstract

This article presents the idea for calculating 2-D steady-state heat conduction problems with multidomain combination by employing the virtual boundary meshless least-square method. Being different from the conventional virtual boundary-element method (VBEM), this method incorporates the point interpolation method (PIM) with the compactly supported radial basis function (CSRBF) to approximately construct the virtual source function of the VBEM. Thus, the proposed method has the advantages of both the boundary-type meshless method and the virtual boundary element method. Since the configuration of the virtual boundary requires a certain preparation, the integration along the virtual boundary can be carried out over the smooth simple curve that can be structured beforehand (for 2-D problems) to reduce the complexity and difficulty of calculus without loss of accuracy, while the “vertex question” existing in the BEM can be avoided. Numerical examples show that the proposed method is more precise than several other numerical methods while selecting fewer degrees of freedom. In addition, its numerical stability is also verified by computing several cases.