Nonlocal active sound control for composite regions with common boundaries

In active sound control, noise attenuation is achieved via implementation of additional (control) acoustic sources which are usually situated at the perimeter of the domain to be shielded. The control sources are supposed to generate ``anti-noise" inside the protected region. If desired sound exists inside the shielded domain, the problem of sound control becomes much more complicated because it is required to realize noise attenuation while preserving desired sound in the same domain. To solve this inverse source problem, the nonlocal active sound control method has recently been proposed. It only requires the total acoustic field from the primary and secondary sources at the boundary of the shielded domain. In this paper, the nonlocal active sound control algorithm is optimized for composite regions with a common boundary. In this case, desired sound generated on one side of the boundary becomes noise on the opposite side and vice versa. We prove that at the common boundary it is sufficient to have only one layer of the control sources. Thus, they can be effectively shared between both sides from the boundary. This result allows us to reduce the number of control sources for composite domains and significantly simplifies the control algorithm. To support this key finding, numerical experiments are conducted in both frequency and time domains.