The Boundary Mapped Collocation Method for Heat Conduction Problems with Heat Generation Spatially Varying Conductivity (Advances in Applied Mathematics and Mechanics, 2024)
In this paper, the boundary mapped collocation (BMC) approach is presented for the analysis of heat conduction problems involving heat generation andnon-homogeneous thermal conductivity. The proposed methodology is introducedto produce the numerical solutions of the temperature field within the framework ofthe BMC method, a novel boundary meshless method, without resorting to requiringany integral calculation, neither in the domain nor at the boundary. In particular, thearrangement 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-dimensionalbasis functions and weight functions for two- and three-dimensional approximationimplementation. In addition, four numerical applications and comparisons with theoutcomes of the finite element approach and another meshfree method are used todemonstrate the correctness, convergence, and stability of the BMC method.