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

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

Year:    2025

Author:    Zhentian Huang, Dong Lei, Zi Han, Heping Xie, Jianbo Zhu

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 240–262

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2022-0250

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 240–262

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Boundary mapped collocation method heat conduction heat generation spatially varying conductivity meshless method.

Author Details

Zhentian Huang

Dong Lei

Zi Han

Heping Xie

Jianbo Zhu