The method of difference potentials was originally proposed by Ryaben'kii and can be
interpreted as a generalized discrete version of the method of Calderon's operators in the …

In many problems, one wishes to solve the Helmholtz equation with variable coefficients
within the Laplacian-like term and use a high order accurate method (eg, fourth order …

We describe a high-order accurate methodology for the numerical simulation of time-
harmonic waves governed by the Helmholtz equation. Our approach combines compact …

In the present paper, we consider active control of noise propagating from a long cylinder.
For that purpose control sources are distributed on the external surface of the cylinder. They …

The method of difference potentials generalizes the method of Calderon's operators from
PDEs to arbitrary difference equations and systems. It offers several key advantages, such …

Calderón–Ryaben'kii potentials provide the foundation for the difference potential method,
which is an efficient way for solving boundary-value problems (BVPs) in arbitrary domains …

The problem of active shielding (AS) for a multiply connected domain consists of
constructing additional sources of the field (eg, acoustic) so that all individual subdomains …

ACTIVE control of sound is a rich and lively research area in acoustics. A typical problem
formulation in this area involves a given region of space (bounded or unbounded) to be …

We consider a problem of eliminating the unwanted time-harmonic noise on a
predetermined region of interest. The desired objective is achieved by active means, ie, by …

This paper describes an active sound control methodology based on difference potentials.
The main feature of this methodology is its ability to automatically preserve “wanted” sound …