Journal of Applied Mathematics
Volume 2003 (2003), Issue 6, Pages 305-317
doi:10.1155/S1110757X03301160
Use of the multigrid methods for heat radiation problem
Department of Mathematics, Al-Quds University, East Jerusalem, Palestinian Authority
Received 29 January 2003
Copyright © 2003 Naji A. Qatanani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.