Use of the Multigrid Methods for Heat Radiation Problem

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Journal Title, Volume, Page: 
Journal of Applied Mathematics 2003:6 (2003) 305–317
Year of Publication: 
2003
Authors: 
Naji A. Qatanani
Department of Mathematics, Al-Quds University, Jerusalem, Palestine
Current Affiliation: 
Department of Mathematics, An-Najah National University, Nablus, Palestine
Preferred Abstract (Original): 

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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