### 2003-25

by Qatanani, N., Schulz, M..

**Series:** 2003-25, Preprints

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

**Abstract:**

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.

**Keywords:**

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