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

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 …

Numerical approximations and computational modeling of problems from Biology and
Materials Science often deal with partial differential equations with varying coefficients and …

Modeling near-wall high-Reynolds-number turbulent flows is a time-consuming problem. A
domain decomposition approach is developed to overcome the problem. The original …

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 …

Near-wall turbulence modeling is a very computationally expensive problem. A new
approach suggested here allows us to avoid calculations of the region with high gradients in …

In near-wall turbulence modeling it is necessary to resolve a thin boundary layer containing
high gradients of the solution. An accurate enough resolution of such a layer can take most …

We formulate and solve a control problem for the field (eg, time-harmonic sound) governed
by a linear PDE or system on a composite domain in Rn. Namely, we require that …

In near-wall turbulence modeling it is required to resolve a thin layer nearby the solid
boundary, which is characterized by high gradients of the solution. An accurate enough …

We consider the problem of active sound control, in which some domain is protected from
the field generated outside. The active shielding is realized via the implementation of …