The Galerkin boundary element solution for thermal radiation problems.

*(English)*Zbl 1066.80008Summary: A Galerkin boundary element method is presented for the computation of thermal radiation exchange in a diffuse, gray enclosure. The method is enhanced with advanced concept of sorting and searching and suitable data structure used for computer graphics to detect the blockage of radiation rays by surface elements or other third party elements and with adaptive integration to account for the strong discontinuity of the kernel functions. In contrast with the traditional boundary element method, the Galerkin method permits a full detection of any geometric obstruction in any complex geometric configuration, especially when it is used together with adaptive integration algorithm. Although the efficiency has been improved substantially through the implementation of sorting and searching algorithms, the blockage determination still accounts for a major portion of the CPU times required to form the matrices A and B. This suggests that a more efficient searching algorithm should be further developed if an increase in computational speed is to be gained. Experience with numerical experiments indicates that an iterative coupling of the boundary element and finite element methods offers a convenient and efficient solution to mixed mode heat transfer problems involving convection, conduction and surface radiation.

##### MSC:

80M15 | Boundary element methods applied to problems in thermodynamics and heat transfer |

80M10 | Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer |

##### Keywords:

Galerkin boundary element method; Thermal radiation exchange; Mixed heat transfer; Finite element method
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\textit{B. Q. Li} et al., Eng. Anal. Bound. Elem. 28, No. 7, 881--892 (2004; Zbl 1066.80008)

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