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Zbl 1079.65117
Qatanani, Naji; Schulz, Monika
The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries. (English)
[J] J. Appl. Math. 2004, No. 4, 311-330 (2004). ISSN 1110-757X; ISSN 1687-0042/e

The paper presents analytical and numerical results concerning the integral operator of the radiosity equation. There are two types of enclosure geometries which are considered: convex and nonconvex, the last one being responsible for the shadow zones. The authors prove with the help of the Banach fixed point theorem the existence and the uniqueness of the solution of the radiosity equation. Then they describe the Bubnov-Galerkin discretization scheme for the solution of the radiosity boundary integral equation and present a numerical example for the calculation of the outgoing flux for a nonconvex enclosure.
[Adrian Carabineanu (Bucureşti)]

MSC 2000:: *65N38 Boundary element methods (BVP of PDE)
80A20 Heat and mass transfer
80M15 Boundary element methods
35J65 (Nonlinear) BVP for (non)linear elliptic equations

Keywords: radiosity equation; boundary integral equation; Bubnov-Galerkin discretization scheme; numerical example

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Zentralblatt MATH Berlin [Germany]