Numerical sound field calculations by coupling the finite and boundary element methods

For numerical calculation of sound fields at low and medium frequencies two numerical methods presently hold a dominating position: the finite element method (FEM) and the boundary element method (BEM). The finite element method is characterised by the division of the solution space into a finite number of elements. However, many applications in acoustics involve an infinite domain, for example radiation into free space, which is difficult to handle with the FEM. Such problems may be handled efficiently with the BEM.
A number of acoustic design and noise problems involve a finite domain that is coupled to free space by an opening. A promising stategy to treat such problems seems to be a coupling of a FEM calculation for the interior problem with a BEM calculation for the exterior problem. Since a direct coupling of the two methods destroys the desired symmetric and bandlimited structure of the FEM matrices, an iterative approach has been investigated. The iterative approach appears to be an efficient method of coupling the two methods, but it was found that for some problems the iteration does not converge to a solution. Further investigations into the convergence and accuracy of the BEM revealed that discontinuities in a geometry cause the particle velocity to tend to infinity near the discontinuity. In the iterative approach the particle velocity on the surface separating the two domains is one of the free variables that must be iterated to a solution, and hence this surface must be choosen far from any geometric discontinuities.
Another problem was the eigenfrequencies of the interior problem, which appear in all closed domains. It was found that introducing losses in the interior model was important to ensure convergence at all frequencies.