Journal of Applied Mathematics

Use of the multigrid methods for heat radiation problem

Naji A. Qatanani

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2003, Number 6 (2003), 305-317.

Dates
First available in Project Euclid: 26 May 2003

Permanent link to this document
https://projecteuclid.org/euclid.jam/1053975527

Digital Object Identifier
doi:10.1155/S1110757X03301160

Mathematical Reviews number (MathSciNet)
MR2036974

Zentralblatt MATH identifier
1024.65117

Subjects
Primary: 65R20: Integral equations 65N38
Secondary: 65F10 65N55

Citation

Qatanani, Naji A. Use of the multigrid methods for heat radiation problem. J. Appl. Math. 2003 (2003), no. 6, 305--317. doi:10.1155/S1110757X03301160. https://projecteuclid.org/euclid.jam/1053975527


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