An-Najah Staff

In this paper a rigorous convergence and error analysis of the Galerkin boundary element method for the heat radiation integral equation in convex and non-convex enclosure geometries is presented. The convergence of the approximation is shown and quasi-optimal error estimates are presented. Numerical results have shown to be consistent with available theoretical results.

The radiation exchange in both convex and non-convex enclosures of diffuse gray surfaces is given in the form of a Fredholm boundary integral equation of the second kind. A boundary element method which is based on the Galerkin discretization schem is implemented for this integral equation. Four iterative methods are used to solve the linear system of equations resulted from the Galerkin discretization scheme. A comparison is drawn between these methods. Theoretical error estimates for the Galerkin method has shown to be in a good agreement with numerical experiments.

This article deals with the mathematical and the numerical aspects of the Fredholm integral equation of the second kind arising as a result of the heat energy exchange inside a convex and non-convex enclosure geometries. Some mathematical results concerning the integral operator are presented. The Banach fixed point theorem is used to guarantee the existence and the uniqueness of the solution of the integral equation. For the non-convex geometries the visibility function has to be taken into consideration, then a geometrical algorithm is developed to provide an efficient detection of the shadow zones. For the numerical simulation of the integral equation we use the boundary element method based on the Galerkin discretization scheme. Some iterative methods for the discrete radiosity equation are implemented. Several two- and three-dimensional numerical test cases for convex and non-convex geometries are included. This give concrete hints which iterative scheme might be more useful for such practical applications.