TY - JOUR
T1 - The Boundary Mapped Collocation Method for Heat Conduction Problems with Heat Generation Spatially Varying Conductivity
AU - Huang , Zhentian
AU - Lei , Dong
AU - Han , Zi
AU - Xie , Heping
AU - Zhu , Jianbo
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 240
EP - 262
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2022-0250
UR - https://global-sci.org/intro/article_detail/aamm/23601.html
KW - Boundary mapped collocation method, heat conduction, heat generation, spatially varying conductivity, meshless method.
AB - <p style="text-align: justify;">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.</p>