Applications of Mathematics

, Volume 64, Issue 1, pp 75–100 | Cite as

Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

  • Yao-Chuang HanEmail author
  • Yu-Feng Nie
  • Zhan-Bin Yuan


This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision algorithm is developed to handle the computation of the integrals containing the visibility factor. An efficient iterative algorithm is proposed to solve the nonlinear discrete system and its convergence is also established. Numerical experiment results are also presented to verify the effectiveness and accuracy of the proposed method and algorithm.


radiative heat transfer existence and uniqueness collocation-boundary element method shadow detection iterative nonlinear solver 

MSC 2010

65M38 45K05 80A20 47G10 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsNorthwestern Polytechnical UniversityXian, ShaanxiChina

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