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

*(English)*Zbl 07031678Summary: 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.

##### MSC:

65M38 | Boundary element methods for initial value and initial-boundary value problems involving PDEs |

45K05 | Integro-partial differential equations |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

47G10 | Integral operators |