We construct a family of compact fourth order accurate finite difference schemes for the three
dimensional scalar wave (d'Alembert) equation with constant or variable propagation speed …

In many problems, one wishes to solve the Helmholtz equation in cylindrical or spherical
coordinates which introduces variable coefficients within the differentiated terms. Fourth …

For a class of linear constant-coefficient finite-difference operators of the second order, we
introduce the concepts similar to those of conventional single-and double-layer potentials for …

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 …

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 …

We present a methodology for the active control of time-harmonic wave fields, eg, acoustic
disturbances, in composite regions. This methodology extends our previous approach …

We analyze the problem of suppressing the unwanted component of a time-harmonic
acoustic field (noise) on a predetermined region of interest. The suppression is rendered by …

This paper extends a potential-based approach to active noise shielding with preservation of
wanted sound in three-dimensional settings. The approach, which was described in a …