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

by Qatanani, N., Schulz, M..

Series: 2003-17, Preprints

45B05 Fredholm integral equations
65R20 Integral equations
65F10 Iterative methods for linear systems
65N38 Boundary element methods

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.

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