The use of the finite element method (FEM) for making predictions for acoustic fields in the time domain is investigated. First, an introduction to FEM for acoustics is given. This includes a description of important present day algorithms and a derivation of FEM. The overall performance of these algorithms is then examined with particular emphasis on accuracy and computational costs. It is shown that the most important error is one that takes the form of a falsely predicted dispersion. The dispersion error can be reduced by using smaller elements and time steps, but this is very costly. Attempts were therefore made to find more economical means of reducing this error. Direct attempts at reducing the error were not very successful, but it was possible to find techniques to reduce the computational cost of a calculation. In the course of the project, a good understanding of the origin and consequences of the dispersion error has been obtained. This led to a new method for determining the optimum element and time step size. The method is valuable because the present way of doing this is not theoretically well-founded.
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Department of Acoustic Technology, Technical University of Denmark, 1996