While numerically solving a problem initially formulated on an unbounded domain, one
typically truncates this domain, which necessitates setting the artificial boundary conditions …

2. Governing equations 9 2.1. The transport theorem 9 2.2. Conservation of mass 10 2.3.
Balance of linear momentum 11 2.4. Balance of angular momentum 13 2.5. Mechanical …

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

This work presents the state of the art in the theory of potentials for the solutions of systems
of linear difference equations, which was proposed by the author in 1969. The role played …

In [J. Comput. Phys. 171 (2001) 632–677] we developed a fourth-order numerical method for
solving the nonlinear Helmholtz equation which governs the propagation of time-harmonic …

We construct non-local artificial boundary conditions (ABCs) for the numerical simulation of
genuinely time-dependent acoustic waves that propagate from a compact source in an …

A straightforward application of the previously designed lacunae-based numerical methods
to unsteady electromagnetic problems would encounter certain difficulties, as it may violate …

Numerical solution of infinite-domain boundary-value problems requires some special
techniques that would make the problem available for treatment on the computer. Indeed …

Non-reflective boundary conditions for prediction of acoustic tones in non-uniform mean flow
for ducted flows New Non-Reflective Boundary Conditions (NRBC) are developed and …

Potentials Method and Its Applications,” Mathematische Nachrichten, Vol. 177, Feb. 1996,
pp. 251–264]; it extends the previous technique developed for the two-dimensional case …