Boundary Element calculations at high frequencies

The purpose of this project has been to investigate the possibilities of extending boundary element calculations to higher frequencies. One feature of the boundary element method is the division of the object(s) in question into small surfaces — boundary elements. For an accurate calculation these elements must be small compared with the wavelength — two to five elements per wavelength are often used. Since the computational effort in terms of calculation time and storage required increases dramatically with the number of elements, boundary element calculations are often limited to relatively low frequencies.
An approximate boundary element formulation for the solution of high frequency problems, the plane wave approximation, has been examined; it was found that the accuracy of this formulation was dependent of the problem.
For the standard boundary element approach, which is accurate for any problem, the possibility of using iterative methods for solving the resulting system of equations has been investigated. It was found that the quasi-minimal-residual method is very well suited for acoustic boundary element computations, and leads to far less calculation time. With regard to the storage required it was found that for some problems a substantial number of terms could be neglected in the boundary element matrices without significant loss of accuracy.
The project has been financed by the Danish Technical Research Council.