Open Access
20 May 2003 Use of the multigrid methods for heat radiation problem
Naji A. Qatanani
J. Appl. Math. 2003(6): 305-317 (20 May 2003). DOI: 10.1155/S1110757X03301160


We consider the integral equation arising as a result of heat radiation exchange in both convex and nonconvex enclosures of diffuse grey surfaces. For nonconvex geometries, the visibility function must be taken into consideration. Therefore, a geometrical algorithm has been developed to provide an efficient detection of the shadow zones. For the numerical realization of the Fredholm integral equation, a boundary element method based on Galerkin-Bubnov discretization scheme is implemented. Consequently, multigrid iteration methods, which are closely related to two-grid methods, are used to solve the system of linear equations. To demonstrate the high efficiency of these iterations, we construct some numerical experiments for different enclosure geometries.


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Naji A. Qatanani. "Use of the multigrid methods for heat radiation problem." J. Appl. Math. 2003 (6) 305 - 317, 20 May 2003.


Published: 20 May 2003
First available in Project Euclid: 26 May 2003

zbMATH: 1024.65117
MathSciNet: MR2036974
Digital Object Identifier: 10.1155/S1110757X03301160

Primary: 65N38 , 65R20
Secondary: 65F10 , 65N55

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 6 • 20 May 2003
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