On the degrees of freedom in the interaction between sets of elementary scatterers

A series of numerical experiments has been executed to investigate the number of degrees of freedom in the interaction between large scattering bodies. The relation between degrees of freedom and operating frequency establishes the computational complexity for integral equation methods fast solvers based on matrix block compression. In 2D the theoretical asymptotic relation for large frequency soon becomes clear. On the other hand, in 3D even a tendency towards the asymptotic value fails to appear for bodies of hundreds of wavelengths in diameter.