Basic issues of active noise shielding problem

We consider a problem of active noise shielding form street noise inside a room with open window. The problem is considered as an example of more complex problem of real time active shielding of the prescribed domain from an external noise. We consider an active shielding which means that it is performed using additional sound sources (“speakers”) which are situated at the domain boundary. These sound sources are complemented by measurement facilities which follow the acoustic state of the environment. The sound sources accompanied by measurement facilities are called “shielding device”. For solution of this problem in the works of V.S. Riabenkiy it was developed the mathematical model of the acoustic shielding process based on the difference potentials method and real-time acoustic exploration. In this model an external noise can be reduced by the predefined ratio by controlling the output of the “speakers”. However, a practical implementation of the proposed approach is hindered because “shielding device” components are supposed to enclose the shielding domain by a dense ring of measurement facilities and “speakers”. To avoid these difficulties in this paper an approximate model of the shielding device is developed which uses a coarse mesh of “speakers” using special approximation of the original mathematical model.
We describe a mathematical model of the shielding process using simple example. The presentation is carried out in a way that provides wide possibilities in a choice of concrete variants of shielding. Further an approach is presented to derive an efficient numerical approximation of the mathematical model. A number of numerical examples are described which demonstrate its efficiency and, in the case of an accurate implementation, stability.