When to Use BEM
Solving acoustics problems using the boundary element method (BEM) can be very advantageous compared to the finite element method (FEM) for some types of problems. For others problems, FEM has its advantages. The recommended approach is to use the BEM and FEM methods where they apply best and also to combine them. Since the BEM interface is fully enabled with multiphysics capabilities, it can be coupled seamlessly with the physics interfaces that are based on FEM. This functionality includes coupling to vibrating structures with the
Acoustic-Structure Boundary
multiphysics coupling and to other acoustic domains with the
Acoustic FEM-BEM Boundary
multiphysics coupling. This approach enables modeling in a FEM-BEM framework, using the strength of each formulation adequately. The BEM-based interface is especially well suited for radiation and scattering problems.
The advantage of the boundary element method is that only boundaries need to be meshed and the DOFs solved for are restricted to the boundaries. This introduces some clear ease-of-use for handling complex geometries. However, the BEM technique results in fully populated or dense matrices that need dedicated numerical methods. Assembling and solving these matrices can be very demanding. This means that when solving acoustic models of small and medium size,
The Pressure Acoustics, Frequency Domain Interface
will often be faster than solving the same problem with the BEM interface.
The challenge with using the FEM interface is to set up open boundaries in an efficient way, for example, by using PMLs. When PMLs cannot easily be placed snugly around radiating structures or two structures are far apart, large air domains need to be meshed. This costs a lot on the computational side, as the frequency is increased. These problems are well suited for the BEM interface, as only the boundary of the radiating structure needs to be meshed.
Interior problems can be solved with the BEM interface, but typically it is much more efficient to solve these problems using the FEM-based interfaces. Remember also that an iterative solver will struggle to solve interior problems, with no or little damping, when resonances appear. If you are close to an eigenfrequency with a high Q, the solution will also be very mesh sensitive.
Note also that at very low frequencies, the BEM method may “break down” for interior problems and give inaccurate results. This is in practice not an issue, as this kind of problem should be solved with
The Pressure Acoustics, Frequency Domain Interface
.