BEM Acoustics

In direct BEM, boundary unknowns are physical quantities (pressure, velocity); the integral equation relates these directly. In indirect BEM, fictitious sources (monopoles, dipoles) on the boundary are the unknowns, and physical quantities are derived from them. Direct BEM is more common and physically intuitive; indirect BEM can be more computationally efficient for certain problems.

A common rule of thumb is to use element size ≤ λ/6, where λ is the acoustic wavelength at the highest frequency. For example, at 1 kHz in air (c = 343 m/s), λ = 0.343 m, so element size should be ≤ 5.7 cm. Coarser meshes are adequate for lower frequencies; local refinement near sources and complex geometry is often beneficial.

Yes, but it requires additional effort. Material absorption is represented as surface impedance, which varies with frequency. BEM solvers can incorporate frequency-dependent impedance, but the computation must be repeated at each frequency of interest, increasing cost. FEM with frequency-independent properties may be simpler for weakly frequency-dependent materials.

BEM requires meshing only boundaries, reducing degrees of freedom (typically 5–10× fewer than FEM for the same problem). For exterior or radiation problems, BEM naturally handles infinite domains without artificial boundaries. However, BEM produces dense, non-sparse matrices, while FEM produces sparse systems; for very large problems, FEM with iterative solvers may be competitive.

Compare simulations against analytical solutions (plane wave propagation, spherical radiation) for simple geometries, then validate against measurements in real spaces or scale models. Perform mesh sensitivity studies (coarsen and refine the mesh to ensure results are mesh-independent). Use frequency resolution analysis to verify accuracy across the frequency band of interest.