Qatanani, Naji; Schulz, Monika The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries. (English) Zbl 1079.65117 J. Appl. Math. 2004, No. 4, 311-330 (2004). 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. Reviewer: Adrian Carabineanu (Bucureşti) Cited in 2 Documents MSC: 65N38 Boundary element methods for boundary value problems involving PDEs 80A20 Heat and mass transfer, heat flow (MSC2010) 80M15 Boundary element methods applied to problems in thermodynamics and heat transfer 35J65 Nonlinear boundary value problems for linear elliptic equations Keywords:radiosity equation; boundary integral equation; Bubnov-Galerkin discretization scheme; numerical example PDFBibTeX XMLCite \textit{N. Qatanani} and \textit{M. Schulz}, J. Appl. Math. 2004, No. 4, 311--330 (2004; Zbl 1079.65117) Full Text: DOI EuDML