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Preconditioned conjugate gradient method for three-dimensional non-convex enclosure geometries with diffuse and grey surfaces

by Qatanani, N., Schulz, M..

Series: 2003-25, Preprints

45B05 Fredholm integral equations
65R20 Integral equations
65N38 Boundary element methods
65N22 Solution of discretized equations

Our main concern in this paper is the numerical simulation of the heat radiation
exchange in a three-dimensional non-convex enclosure geometry with a diffuse
and grey surface. This physical phenomena is governed by a boundary integral
equation of the second kind. Due to the non-convexity of the enclosure the
presence of the shadow zones must be taken into account in the heat radiation
analysis. For that purpose we have developed a geometrical algorithm to provide
an efficient detection of these shadow zones that are needed to calculate the
visibility function. For the discretization of the boundary integral equation we have
used the boundary element method based on the Galerkin-Bubnov scheme. The
system of linear equations which subsequently arise has been solved by the con-
jugate gradient method with preconditioning. To demonstrate the high efficiency
of this method a numerical experiment has been constructed for non-convex
geometry; the heat radiation in an aperture has been considered.

heat radiation, non-convex geometries, Fredholm integral equations, Galerkin scheme, conjugate gradient method, boundary element method.