This project utilizes the integral equation method to formulate and solve several types of multi-domain and thin-body problems in acoustics. For the multi-domain problem, the acoustic domain of interest is interior to a closed surface of arbitrary shape, exterior to a closed body, or coupled to another domain. For the thin body problem, the acoustic domain is exterior to a body whose smallest dimension is of the same order or less than some numerical parameter such as element length. By using integral equation methods, all numerical approximations are confined to the boundaries of the domains. There is no need to discretize the interior of the domain, and therefore a reduction in the computational dimension of the problem by one (three dimensional problems are solved on the two dimensional boundary of the domain), and there is none of the difficulty associated with finite element methods, for example, of deciding where in the acoustic medium to stop the elements. It is thereby potentially simpler and more accurate to solve multi-domain problems using integral equations than alternative techniques requiring solution throughout the domains. The development of methods for the solution of multi-domain and thin-body acoustic problems will be beneficial to a wide range of specific engineering problems. These include the prediction of sound pressure and power radiated by industrial products such as engines, pumps and compressors when partially shrouded by an enclosure for noise control; design of quiet interiors of vehicles and aircraft; understanding how multiple sources may be used in active vibration/active noise control; and the design and optimization of complex networks of acoustic passageways such as those that occur in the interior of mufflers, induction systems of engines and silencers for fans.
