03-17

On the Fredholm ontegral equation for the two-and three-dimensional heat radiation problem.

by Qatanani, N.; Schulz, M.

 

Preprint series: 03-17, Preprints

MSC:
45B05 Fredholm integral equations
65R20 Integral equations
65F10 Iterative methods for linear systems, See also {65N22}
65N38 Boundary element methods

 

Abstract: 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 also 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 implementes. 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.

Keywords: heat radiation, Fredholm integral equation, boundary element method, iterative methods, Galerkin scheme.


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