In room acoustics the reverberation time, as a parameter, plays a great role, as the sound fields can be graded by it. The reverberation is caused by the fade-out of the energy. If it can be simulated with high precision, we are able to compute the reverberation time from only the model of a room.
The reverberation time was first described by Sabine, who gave formula to calculate. However, in enclosures with diffusely reflecting boundaries or special-shaped enclosures this formula not give a sufficiently accurate estimate. The energy decay can be described by an integral equation, which contains the reflection coefficient between two patch of the wall and the sound flux on the patches. The problem is, that the integral equation contains the intensity (flux) as an unknown.
The purpose of the thesis was an implementation of a solution for the integral equation. With that, the steady state energy distribution on the surface of a rectangular enclosure with diffusely reflecting boundaries can be calculated. From this solution, the decay of the sound field can be derived for the calculation of the reverberation time.
With this modell, I studied the analytic and the half-analytic (with Gaussian-quadratures) method of the calculation of the reflection coefficients. A second objective was to set the optimal resolution for the boundaries, in which we get a precise value for the intensity.
In my thesis, I give a Matlab implementation to solve the integral equation in a stationary case.