The Boundary Mapped Collocation Method for Heat Conduction Problems with Heat Generation Spatially Varying Conductivity

In this paper, the boundary mapped collocation (BMC) approach is presented for the analysis of heat conduction problems involving heat generation and non-homogeneous thermal conductivity. The proposed methodology is introduced to produce the numerical solutions of the temperature field within the framework of the BMC method, a novel boundary meshless method, without resorting to requiring any integral calculation, neither in the domain nor at the boundary. In particular, the arrangement of discrete nodes is restricted to the axis, which brings the spatial dimension down by one. The technique also reduced the traditional complex shape functions to succinct one-dimensional boundary shape functions by using one-dimensional basis functions and weight functions for two- and three-dimensional approximation implementation. In addition, four numerical applications and comparisons with the outcomes of the finite element approach and another meshfree method are used to demonstrate the correctness, convergence, and stability of the BMC method.