Gutachter: Prof. Dr.-Ing. M. Möser

Gutachter: Prof. Dr.-Ing. habil. W. Ahnert

Tag der wissenschaftlichen Aussprache: 10 July 2008

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First of all, I would like to thank my advisor Professor Möser for giving me the opportunity of

conducting this reseach. His helpful suggestions were always beneficial for the accomplishment

of this work.

I am really thankful to Stefan Feistel from SDA for guiding me all through this research. I have

learned a lot from him. From technical part to philosophical part, he was always there to guide

me. He always tried to find time for me from his busy schedule.This whole work has been

completed only because of his deep involvement, constant encouragement, and above all, his

faith in me.

I am deeply thankful to Dr. Wolfgang Ahnert from ADA for advising me in every aspect of life.

language at volkshochschule to watching world cup football matches at “fanmeile” in Berlin, I

enjoyed everything here. I enjoyed the company of several friends especially Jatin, Anand,

Umesh, Vinay and Manohar who made my stay in berlin a wonderful experience.

Lastly, I thank ADA Foundation gGmbH for supporting this work financially.

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extend the existing sound particle models like ray tracing and image source methods. Chapter 1

starts with the introduction of approaches being used for auralization purpose in room acoustics.

Detailed methodology behind particle approaches are discussed. However, such particle or ray

based approaches are not sufficient in small and complex shaped rooms to take proper account of

the wave nature of the sound field. These methods fail to obtain room acoustic characteristics of

higher quality in the low frequency bands. In order to effectively simulate the sound field at low

frequencies, where the dimensions of the walls are comparable to the wavelength, one needs to

clearly know the reflection and diffraction properties of walls. This thesis presents the use of

numerical techniques like finite element method (FEM) and boundary element method (BEM) to

solve the Helmholtz wave equation in order to obtain a better or more realistic impulse response.

thesis in Chapter 2, introduces a new approach “cutting plane algorithm” to generate an all-

hexahedral mesh. The cutting plane algorithm is based upon cutting the polyhedron as proposed

by Chazelle [24] into simpler shaped elements and the main emphasis in this work is to

investigate it’s practical applicability in architectural designs. It is shown that after applying a

sequence of cuts on the given arbitrary polyhedron, one can obtain convex and trivalent

polyhedrons. These polyhedrons can then be converted into a hexahedral mesh using Mid-Point

subdivision scheme. Special cutting schemes are suggested using examples for typical

architectural designs. Special considerations are given to mesh quality in acoustical models

where balconies, domes (for mosques), stairs, pillers etc. are very common. Furthermore, for

curved surfaces a new projection algorithm is introduced. It is shown that with proper

complex shapes and general impedance boundary condition is considered. This work is mainly

concerned with the attempt of showing the practical feasibility of FEM in room acoustics and to

combine it with particle models in order to obtain the broad band response of the room. Also,

fundamental points regarding the finite element method, iterative methods and required mesh

quality are discussed.

In Chapter 4, the thesis tries to investigate the scattering behavior of incident plane waves at

arbitrarily shaped wall surfaces using BEM. For comparison purposes, a simple point-source

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based model to calculate scattered wave fronts is also introduced. The incident plane waves are

considered at various angles and scattering coefficients computed in both models are then

compared with the measured data. It is found that while the point-source model can give