Also known as: Semyon V. Tsynkov; S. Tsynkov; S. V. Tsynkov

Numerical analysis, Scientific computing, Applied mathematics, Computational physics, Optics, Electromagnetism, Plasma, Inverse problems, Control, Remote sensing, Radar imaging, Ionosphere, Geophysics, Partial differential equations

Updated: July 8th, 2024 06:09

2024 journal article

Computation of unsteady electromagnetic scattering about 3D complex bodies in free space with high-order difference potentials

*JOURNAL OF COMPUTATIONAL PHYSICS*, *498*.

Sources: Web Of Science, NC State University Libraries

Added: February 12, 2024

2024 journal article

Fourth-Order Accurate Compact Scheme for First-Order Maxwell's Equations

*JOURNAL OF SCIENTIFIC COMPUTING*, *100*(2).

Sources: Web Of Science, NC State University Libraries

Added: July 1, 2024

2024 journal article

Modeling the Earth's Ionosphere by a Phase Screen for the Analysis of Transionospheric SAR Imaging

*IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING*, *62*.

author keywords: Ionosphere; phase correction; phase screen; synthetic aperture radar (SAR)

Sources: Web Of Science, NC State University Libraries

Added: January 16, 2024

2023 journal article

Transionospheric Autofocus for Synthetic Aperture Radar

*SIAM JOURNAL ON IMAGING SCIENCES*, *16*(4), 2144–2174.

author keywords: synthetic aperture radar; ionosphere; autofocus; optimization

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(OpenAlex)

Sources: Web Of Science, NC State University Libraries

Added: February 26, 2024

2023 article

Transionospheric Autofocus for Synthetic Aperture Radar

*2023 INTERNATIONAL CONFERENCE ON ELECTROMAGNETICS IN ADVANCED APPLICATIONS, ICEAA*, pp. 24–24.

Sources: Web Of Science, NC State University Libraries

Added: April 8, 2024

2023 journal article

Vertical autofocus for the phase screen in a turbulent ionosphere

*INVERSE PROBLEMS*, *39*(4).

Sources: Web Of Science, NC State University Libraries

Added: March 27, 2023

2022 journal article

3D time-dependent scattering about complex shapes using high order difference potentials

*JOURNAL OF COMPUTATIONAL PHYSICS*, *471*.

UN Sustainable Development Goal Categories

14. Life Below Water
(OpenAlex)

Sources: Web Of Science, NC State University Libraries

Added: November 7, 2022

2022 article

A MATHEMATICAL PERSPECTIVE ON RADAR INTERFEROMETRY

Gilman, M., & Tsynkov, S. (2021, July). *INVERSE PROBLEMS AND IMAGING*, Vol. 7.

Sources: Web Of Science, NC State University Libraries

Added: November 23, 2021

2022 journal article

A high order compact time/space finite difference scheme for the 2D and 3D wave equation with a damping layer

*JOURNAL OF COMPUTATIONAL PHYSICS*, *460*.

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: May 31, 2022

2022 article

High-order accurate numerical simulation of monochromatic waves in photonic crystal ring resonators with the help of a non-iterative domain decomposition

North, E., Tsynkov, S., & Turkel, E. (2022, November 20). *JOURNAL OF COMPUTATIONAL ELECTRONICS*, Vol. 11.

Sources: Web Of Science, NC State University Libraries

Added: December 5, 2022

2022 journal article

Non-iterative domain decomposition for the Helmholtz equation with strong material discontinuities

*APPLIED NUMERICAL MATHEMATICS*, *173*, 51–78.

Sources: Web Of Science, NC State University Libraries

Added: July 11, 2022

2022 journal article

Polarimetric radar interferometry in the presence of differential Faraday rotation

*INVERSE PROBLEMS*, *38*(4).

Sources: Web Of Science, NC State University Libraries

Added: March 28, 2022

2021 journal article

Divergence Measures and Detection Performance for Dispersive Targets in SAR

*RADIO SCIENCE*, *56*(1).

author keywords: synthetic aperture radar; dispersive target; speckle; misclassification frequency; Hellinger distance

TL;DR:
A linear relation is established between the misclassification rate and the Hellinger distance for a certain class of simple target models and this relation allows us to make predictions of the error rate without performing the Monte Carlo simulations.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: February 22, 2021

2021 article

Numerical Solution of 3D Unsteady Scattering Problems with Sub-linear Complexity

*2021 INTERNATIONAL APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY SYMPOSIUM (ACES)*.

author keywords: method of difference potentials; Huygens' principle; 3D wave equation

TL;DR:
An efficient high order accurate boundary algorithm for the numerical solution of unsteady exterior initial boundary problems for the three-dimensional wave equation using the method of difference potentials combined with the Huygens' principle is presented.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: December 20, 2021

2021 journal article

Solution of three-dimensional multiple scattering problems by the method of difference potentials

*WAVE MOTION*, *107*.

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 31, 2021

2020 journal article

Deep Learning Approach to the Detection of Scattering Delay in Radar Images

*JOURNAL OF STATISTICAL THEORY AND PRACTICE*, *15*(1).

author keywords: Radar imaging; Dispersive targets; Classification; Convolutional neural network

TL;DR:
A convolutional neural network is applied to the problem of discrimination between the instantaneous and delayed targets in synthetic aperture radar images, and a trained neural network demonstrates the discrimination quality commensurate with that of the benchmark maximum likelihood-based classifier.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: January 4, 2021

2020 journal article

Method of Difference Potentials for Evolution Equations with Lacunas

*COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS*, *60*(4), 711–722.

author keywords: method of difference potentials; Huygens principle; lacunas; wave equation

Sources: Web Of Science, NC State University Libraries

Added: June 29, 2020

2020 journal article

STATISTICAL CHARACTERIZATION OF SCATTERING DELAY IN SYNTHETIC APERTURE RADAR IMAGING

*INVERSE PROBLEMS AND IMAGING*, *14*(3), 511–533.

author keywords: SAR imaging; scattering delay; speckle; confidence level; Monte-Carlo

TL;DR:
A maximum likelihood based approach for discriminating between the instantaneous and delayed targets in SAR images that takes into account the difference in thresholds for different target contrasts without making any assumptions about the statistics of those contrasts.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

10. Reduced Inequalities
(OpenAlex)

Sources: Web Of Science, NC State University Libraries

Added: April 14, 2020

2019 conference paper

A high order method of boundary operators for the 3D time-dependent wave equation

*Book of Abstracts, The 14th International Conference on Mathematical
and Numerical Aspects of Wave Propagation, WAVES 2019,
Vienna University of Technology (TU Wien),
Vienna, Austria, August 25-30, 2019*, 363–365. https://stsynkov.math.ncsu.edu/publications/Unsteady_DPM_waves2019_v6.pdf

Source: ORCID

Added: September 6, 2019

2019 conference paper

A method of boundary equations for unsteady hyperbolic problems in 3D

*Mathematics and Its Applications, Book of Abstracts for the International
Conference in honor of the 90th birthday of Sergei K. Godunov,
Novosibirsk, Russia, August 4-10, 2019*, 68. https://stsynkov.math.ncsu.edu/publications/a82e_godunov90.pdf

Source: ORCID

Added: September 6, 2019

2019 journal article

Compact High Order Accurate Schemes for the Three Dimensional Wave Equation

*Journal of Scientific Computing*, *5*, 1–29.

author keywords: Unsteady wave propagation; Fourth order accurate approximation; Small stencil; Cartesian grid; Implicit scheme; Multigrid methods

TL;DR:
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 with inversion at the upper time level is constructed.
(via Semantic Scholar)

Sources: Crossref, NC State University Libraries, ORCID

Added: June 21, 2019

2019 journal article

Detection of delayed target response in SAR

*Inverse Problems*, *4*, 085005 (38pp).

author keywords: delayed scattering; dispersive targets; synthetic aperture radar; speckle; range-delay ambiguity

TL;DR:
A simple model of a delayed scatterer is developed by modifying the random function that describes a homogeneous extended scatterers to obtain a relation between the deterministic parameters of the target model and statistical moments of the SAR image.
(via Semantic Scholar)

Sources: Crossref, NC State University Libraries, ORCID

Added: June 21, 2019

2019 journal article

Direct implementation of high order BGT artificial boundary conditions

*Journal of Computational Physics*, *376*, 98–128.

author keywords: Propagation of waves over unbounded regions; Helmholtz equation; Spherical artificial boundary; Expansion with respect to continuous basis; Method of difference potentials (MDP); Beltrami operator

TL;DR:
This paper implements high order Bayliss–Turkel ABCs directly — with no auxiliary variables yet no discrete approximation of the constituent high order derivatives either and represents the solution at the boundary as an expansion with respect to a continuous basis.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: December 10, 2018

2019 journal article

Preface to the Special Issue in Memory of Professor Saul Abarbanel

*Journal of Scientific Computing*.

Source: ORCID

Added: December 4, 2019

2019 conference paper

Stochastic Models in Coordinate-Delay Synthetic Aperture Radar Imaging

*Book of Abstracts, The 14th International Conference on Mathematical
and Numerical Aspects of Wave Propagation, WAVES 2019,
Vienna University of Technology (TU Wien),
Vienna, Austria, August 25-30, 2019*, 330–331. https://stsynkov.math.ncsu.edu/publications/Dispersive_targets_Waves2019_v3_final.pdf

Source: ORCID

Added: September 6, 2019

2018 journal article

A High Order Compact Time/Space Finite Difference Scheme for the Wave Equation with Variable Speed of Sound

*Journal of Scientific Computing*, *76*(2), 777–811.

author keywords: Compact finite differences; Wave equation; Variable coefficients; High order accuracy

TL;DR:
This work considers fourth order accurate compact schemes, in both space and time, for the second order wave equation with a variable speed of sound, and demonstrates that usually this is much more efficient than lower order schemes despite being implicit and only conditionally stable.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2018 journal article

A method of boundary equations for unsteady hyperbolic problems in 3D

*Journal of Computational Physics*, *365*, 294–323.

author keywords: Time-dependent wave equation; Calderon's boundary equation; The Huygens' principle; Method of difference potentials (MDP); Sub-linear complexity; Parallelization in time

TL;DR:
The Huygens' principle is used to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time, and the resulting boundary equation is solved efficiently by the method of difference potentials (MDP).
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(OpenAlex)

Sources: Crossref, NC State University Libraries, ORCID, Web Of Science

Added: August 6, 2018

2018 conference paper

Cross-Channel Contamination of PolSAR Images due to Frequency Dependence of Faraday Rotation Angle

*2018 IEEE Conference on Antenna Measurements & Applications (CAMA)*, 1–4.

Event: 2018 IEEE Conference on Antenna Measurements & Applications (CAMA)

Sources: ORCID, Crossref, NC State University Libraries

Added: September 6, 2019

2018 journal article

Differential Faraday Rotation and Polarimetric SAR

*SIAM Journal on Applied Mathematics*, *78*(3), 1422–1449.

author keywords: inverse scattering; scattering matrix; gyrotropy; electromagnetic waves; polarization; rotation of polarization plane; radar signal bandwidth; radar ambiguity theory; polarimetric matched filter; Earth's ionosphere; magnetic field of the Earth

TL;DR:
The propagation of linearly polarized electromagnetic waves through the Earth's ionosphere is accompanied by Faraday rotation (FR), which is due to gyrotropy of the ionospheric plasma in the magnet.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2018 journal article

Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials

*Journal of Computational Physics*, *354*, 26–42.

author keywords: Method of difference potentials (MDP); Compact finite difference scheme; Implicit scheme; Regular structured grid; Nonconforming boundary; High-order accuracy; High-order MDP

TL;DR:
This work solves the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time using an implicit finite difference scheme and solving an elliptic equation at each time step by the method of difference potentials (MDP).
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2017 conference paper

An efficient numerical algorithm for the 3D wave equation in domains of complex shape

*Mathematical
and Numerical Aspects of Wave Propagation WAVES 2017,
The 13th International Conference, Minneapolis, MN, USA, May 15--19, 2017.
Book of Abstracts*, 365–366. https://stsynkov.math.ncsu.edu/publications/wavesPetropTsynkov_v3.pdf

Source: ORCID

Added: September 6, 2019

2017 conference paper

Computational complexity of artificial boundary conditions for Maxwell's equations in the FDTD method

*Mathematical
and Numerical Aspects of Wave Propagation WAVES 2017,
The 13th International Conference, Minneapolis, MN, USA, May 15--19, 2017.
Book of Abstracts*, 275–276. https://stsynkov.math.ncsu.edu/publications/OsTsy_4.pdf

Source: ORCID

Added: September 6, 2019

2017 article

Conventional SAR imaging

*TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING*, pp. 19–57.

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2017 conference paper

High order accurate solution of the wave equation by compact finite differences and difference potentials

*Mathematical
and Numerical Aspects of Wave Propagation WAVES 2017,
The 13th International Conference, Minneapolis, MN, USA, May 15--19, 2017.
Book of Abstracts*, 63–64. https://stsynkov.math.ncsu.edu/publications/waves2017_Steven_v4.pdf

Source: ORCID

Added: September 6, 2019

2017 conference paper

High order numerical solution of the Helmholtz equation for domains with reentrant corners

Source: ORCID

Added: September 6, 2019

2017 journal article

High-order numerical solution of the Helmholtz equation for domains with reentrant corners

*Applied Numerical Mathematics*, *118*, 87–116.

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2017 journal article

Inverse scattering off anisotropic targets

*Transionospheric Synthetic Aperture Imaging*, 373–415.

Source: NC State University Libraries

Added: August 6, 2018

2017 conference paper

Mathematical analysis of SAR imaging through a turbulent ionosphere

(M. D. Todorov, Ed.).

Ed(s): M. Todorov

Event: APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’17

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2017 article

Modeling radar targets beyond the first Born approximation

*TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING*, pp. 311–371.

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2017 journal article

Non-deteriorating time domain numerical algorithms for Maxwell's electrodynamics

*Journal of Computational Physics*, *336*, 1–35.

author keywords: Unsteady electromagnetic waves; Maxwell's equations; Unbounded regions; Grid truncation; Artificial outer boundaries; Artificial boundary conditions (ABCs); Non-reflecting boundaries; Perfectly matched layer (PML); Long time deterioration; Loss of accuracy, loss of stability, error build-up; The Huygens' principle; Aft fronts of the waves; Lacunae of the solutions; Quasi-lacunae; Accumulation of charge; Guaranteed accuracy; Temporally uniform error bounds

TL;DR:
The main contribution of the current paper is to remove this limitation and modify the algorithm in such a way that one can rather avoid the accumulation of charge all together, which facilitates obtaining the temporally uniform error estimates as in the case of classical lacunae.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2017 article

SAR imaging through the Earth's ionosphere

*TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING*, pp. 59–161.

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2017 conference paper

The Doppler Effect for SAR

Source: ORCID

Added: September 6, 2019

2017 article

The effect of ionospheric anisotropy

*TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING*, pp. 217–264.

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2017 article

The effect of ionospheric turbulence

*TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING*, pp. 163–215.

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2017 article

The start-stop approximation

*TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING*, pp. 265–309.

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2017 book

Transionospheric Synthetic Aperture Imaging

In *Applied and Numerical Harmonic Analysis* (pp. 1–1).

Event: at Cham, Switzerland

UN Sustainable Development Goal Categories

13. Climate Action
(OpenAlex)

Sources: Web Of Science, Crossref, NC State University Libraries, ORCID

Added: August 6, 2018

2017 journal article

Transionospheric Synthetic Aperture Imaging Discussion and outstanding questions

*Transionospheric Synthetic Aperture Imaging*, 417–431.

Source: NC State University Libraries

Added: August 6, 2018

2017 journal article

Transionospheric synthetic aperture imaging Introduction

*Transionospheric Synthetic Aperture Imaging*, 1–17.

Source: NC State University Libraries

Added: August 6, 2018

2016 conference paper

A universal framework for non-deteriorating time-domain numerical algorithms in Maxwell’s electrodynamics

(M. D. Todorov, Ed.).

Ed(s): M. Todorov

Event: APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’16

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2016 chapter

Difference Potentials Methods for Hyperbolic Problems Using High Order Finite Difference Schemes

In *Book of Abstracts, International Conference on Spectral and High Order Methods, ICOSAHOM 2016,
Rio De Janeiro, Brazil, June 2016*. https://stsynkov.math.ncsu.edu/publications/icosahomAbstract2016.pdf

Source: ORCID

Added: September 6, 2019

2015 journal article

A Mathematical Model for SAR Imaging beyond the First Born Approximation

*SIAM Journal on Imaging Sciences*, *8*(1), 186–225.

author keywords: synthetic aperture imaging; SAR ambiguity theory; linearized scattering; linearized inverse problem; backscattering; Bragg resonance; weak scattering; strong scattering

TL;DR:
The foundations of the SAR ambiguity theory are revisited in order to address this and other existing inconsistencies, such as the absence of the Bragg scale in scattering, and a new model for radar targets that allows to compute the scattered field from first principles.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2015 journal article

Computation of singular solutions to the Helmholtz equation with high order accuracy

*Applied Numerical Mathematics*, *93*, 215–241.

author keywords: Difference potentials; Boundary projections; Calderon's operators; Regular grids; Curvilinear boundaries; Non-conforming boundaries; Solutions with singularities; Singularity subtraction; Discontinuous boundary data; Asymptotic expansion near singularity; Compact differencing; High order accuracy

TL;DR:
A broad spectrum of problems involving different boundary conditions and/or data on "smooth" segments of the boundary can be solved economically since the discrete counterparts of Calderon's projections need to be calculated only once and then can be applied to each individual formulation at very little additional cost.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2015 journal article

Professor V.S. Ryaben'kii. On the occasion of the 90-th birthday

*Applied Numerical Mathematics*, *93*, 1–2.

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

2015 journal article

Solving the Helmholtz equation for general smooth geometry using simple grids

*Wave Motion*, *62*, 75–97.

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2015 chapter

Transmission and Scattering of Waves by General Shapes with High Order Accuracy Using the Difference Potentials Method

In *Book of Abstracts, The 12th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, WAVES 2015,
Karlsruhe, Germany, July 20--24, 2015* (pp. 256–257). https://stsynkov.math.ncsu.edu/publications/Waves2015-book-of-abstracts.pdf

Source: ORCID

Added: September 6, 2019

2015 journal article

Viktor Solomonovich Ryaben'kii and his school (on his 90th birthday)

*Russian Mathematical Surveys*, *70*(6), 1183–1210.

Sources: Crossref, NC State University Libraries

Added: September 4, 2020

2015 journal article

Виктор Соломонович Рябенький и его школа (к девяностолетию со дня рождения)

*Uspekhi Matematicheskikh Nauk*, *70*(6(426), 213–236.

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

2014 conference paper

Detection of Material Dispersion Using SAR

*Proceedings of the 10th European Conference on Synthetic Aperture Radar (EUSAR 2014)*, 1013–1016. https://stsynkov.math.ncsu.edu/publications/eusar-2014.pdf

Event: at Berlin-Offenbach, Germany

Source: ORCID

Added: September 6, 2019

2014 journal article

Single-polarization SAR imaging in the presence of Faraday rotation

*Inverse Problems*, *30*(7), 075002.

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2013 journal article

A High-Order Numerical Method for the Helmholtz Equation with Nonstandard Boundary Conditions

*SIAM Journal on Scientific Computing*, *35*(5), A2255–A2292.

author keywords: difference potentials; boundary projections; Calderon's operators; regular grids; curvilinear boundaries; boundary value problems; variable coefficients; Robin boundary conditions; mixed/piecewise boundary conditions; compact differencing; high-order accuracy

TL;DR:
The approach combines compact finite difference schemes that provide an inexpensive venue toward high-order accuracy with the method of difference potentials developed by Ryaben'kii, introducing a universal framework for treating boundary conditions of any type.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2013 journal article

Discrete Calderon’s projections on parallelepipeds and their application to computing exterior magnetic fields for FRC plasmas

*Journal of Computational Physics*, *234*, 172–198.

author keywords: Field reversed configuration (FRC); Single fluid magnetohydrodynamics (MHD); Quasi-static magnetic field; Artificial boundary condition (ABC); The method of difference potentials; Calderon's potentials and projections; Boundary equations with projections

TL;DR:
A quasi-static ABC for the magnetic field is obtained in the form of a discrete Calderon boundary equation with projection on the artificial boundary shaped as a parallelepiped, computed by convolution with the discrete fundamental solution on the three-dimensional Cartesian grid.
(via Semantic Scholar)

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

2013 chapter

High Order Numerical Simulation of the Transmission and Scattering of Waves Using the Method of Difference Potentials

In *Proceedings of the International Conference Difference Schemes and Applications
in honor of the 90-th Birthday of Prof. V. S. Ryaben'kii, Moscow, Russia, May 27--31, 2013* (pp. 33–34). https://stsynkov.math.ncsu.edu/publications/Tsynkov_abstract_for_Ryabenkii-90.pdf

Event: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Source: ORCID

Added: September 6, 2019

2013 journal article

High order numerical simulation of the transmission and scattering of waves using the method of difference potentials

*Journal of Computational Physics*, *243*, 305–322.

author keywords: Difference potentials; Boundary projections; Calderon's operators; Regular grids; Curvilinear boundaries; Non-conforming boundaries/interfaces; Variable coefficients; Compact differencing; High order accuracy; Exterior problems; Artificial boundary conditions

TL;DR:
The method of difference potentials generalizes the method of Calderon’s operators from PDEs to arbitrary difference equations and systems and solves the scattering of time-harmonic waves about smooth shapes, subject to various boundary conditions.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2013 journal article

Reduction of ionospheric distortions for spaceborne synthetic aperture radar with the help of image registration

*Inverse Problems*, *29*(5), 054005.

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2012 journal article

A linearized inverse scattering problem for the polarized waves and anisotropic targets

*Inverse Problems*, *28*(8), 085009.

UN Sustainable Development Goal Categories

16. Peace, Justice and Strong Institutions
(OpenAlex)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2012 journal article

Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number

*Journal of Computational Physics*, *232*(1), 272–287.

author keywords: Helmholtz equation; Compact high order schemes; Variable wave number; High frequency; Large wave number; Parallel computing; CARP-CG

TL;DR:
This paper extends compact fourth order accurate finite difference approximation for the Helmholtz equation to variable k in both two and three dimensions and demonstrates that for large wave numbers, the second order scheme cannot produce comparable results with reasonable grid sizes.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2012 journal article

Erratum to: The Method of Difference Potentials for the Helmholtz Equation Using Compact High Order Schemes

*Journal of Scientific Computing*, *53*(2), 482–482.

Sources: Crossref, NC State University Libraries

Added: September 8, 2020

2012 journal article

The Method of Difference Potentials for the Helmholtz Equation Using Compact High Order Schemes

*Journal of Scientific Computing*, *53*(1), 150–193.

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2011 journal article

A non-deteriorating algorithm for computational electromagnetism based on quasi-lacunae of Maxwell’s equations

*Journal of Computational Physics*, *231*(2), 558–585.

author keywords: Propagation of unsteady electromagnetic waves; The Huygens' principle; Aft fronts; Accumulation of charge; Electrostatic field; Numerical solution; Long-time computations; Artificial boundary conditions (ABCs); Perfectly matched layers (PMLs); Uniform error bound

TL;DR:
This work proposes a universal algorithm that relies on the Huygens' principle in the generalized form, when a non-zero electrostatic solution can be present behind aft fronts of the propagating waves, i.e., inside the lacunae of Maxwell's equations.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2011 journal article

Dual Carrier Probing for Spaceborne SAR Imaging

*SIAM Journal on Imaging Sciences*, *4*(2), 501–542.

author keywords: synthetic aperture radar; Earth's ionosphere; dispersion of radio waves; image distortions; cold plasma; matched filter; multicarrier probing; correction of the filter; range and azimuthal resolution; image sharpness

TL;DR:
This work concludes that the deterioration of SAR images was due to the mismatch between certain parameters of the actual received signal, which is slowed down by the temporal dispersion in the ionosphere, and the corresponding parameter of the matched filter, which was taken as if the propagation were unobstructed.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2011 chapter

Interfaces for the Helmholtz Equation with High Order Accuracy

In *Proceedings of the 10th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, WAVES 2011,
Vancouver, Canada, July 25--29, 2011* (pp. 659–662). https://stsynkov.math.ncsu.edu/publications/a66e_waves11.pdf

Event: Pacific Institute for the Mathematical Sciences

Source: ORCID

Added: September 6, 2019

2011 journal article

Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes

*Communications in Computational Physics*, *9*(3), 520–541.

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2011 journal article

Quasi-Lacunae of Maxwell's Equations

*SIAM Journal on Applied Mathematics*, *71*(4), 1109–1122.

author keywords: waves propagation; unsteadiness; Huygens' principle; odd-dimension spaces; aft fronts; accumulation of charge; electrostatic solution

TL;DR:
It is shown that the notion of classical lacunae can be generalized, and that even when the steady-state charges are present, the waves still have sharp aft fronts, and there is a nonzero electrostatic solution rather than one identically zero.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2010 journal article

A Compact Fourth Order Scheme for the Helmholtz Equation in Polar Coordinates

*Journal of Scientific Computing*, *45*(1-3), 26–47.

author keywords: Helmholtz equation; Variable coefficients; Polar coordinates; High order accuracy; Compact finite differences; Exact artificial boundary condition (ABC)

TL;DR:
This work develops a new compact scheme that is provably fourth order accurate even for scattering problems and presents numerical results that corroborate the fourth order convergence rate for several scattering problems.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2009 journal article

A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media

*Journal of Computational Physics*, *228*(10), 3789–3815.

author keywords: Nonlinear optics; Kerr nonlinearity; Inhomogeneous medium; Material discontinuities; Discontinuous coefficients; Layered medium; Nonparaxiality; Forward scattering; Backscattering; (Narrow) solitons; Paraxial approximation; Nonlinear Schrodinger equation; Arrest of collapse; Finite-difference approximation; Compact scheme; High-order method; Artificial boundary conditions (ABCs); Two-way ABCs; Traveling waves; Complex valued solutions; Frechet differentiability; Newton's method

TL;DR:
The first ever evidence that the singularity of the solution indeed disappears in the scalar NLH model that includes the nonparaxial effects is provided, which enables simulation of the wavelength-width spatialsolitons, as well as of the counter-propagating solitons.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2009 journal article

Active control of sound with variable degree of cancellation

*Applied Mathematics Letters*, *22*(12), 1846–1851.

author keywords: Inverse source problem; Active shielding; Calderon's projections; Difference potentials

TL;DR:
A general solution for controls in the continuous and discrete setting is presented by adding special control sources defined only at the interface between the subdomains of a linear PDE or system on a composite domain.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2009 journal article

Difference Problem of Noise Suppression and Other Problems of Active Control for Time-Harmonic Sound over Composite Regions

*Doklady Rossiiskoi Akademii Nauk, Matematika (Transactions of the Russian Academy of Sciences, Mathematics)*, *425*(4), 456–458.

Source: NC State University Libraries

Added: July 28, 2019

2009 journal article

Difference problem of noise suppression and other problems of active control of single-frequency sound on a composite domain

*Doklady Mathematics*, *79*(2), 240–242.

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2009 journal article

Experimental Validation of the Active Noise Control Methodology Based on Difference Potentials

*AIAA Journal*, *47*(4), 874–884.

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2009 journal article

Fourth order schemes for time-harmonic wave equations with discontinuous coefficients

*Commun. Comput. Phys.*, *5*(2-4), 442–455. http://global-sci.org/intro/article_detail/cicp/7742.html

Source: ORCID

Added: September 6, 2019

2009 conference paper

Fourth order schemes for time-harmonic wave equations with discontinuous coefficients

*Communications in Computational Physics*, *5*(2-4), 442–455.

Source: NC State University Libraries

Added: August 6, 2018

2009 journal article

Long-Time Performance of Unsplit PMLs with Explicit Second Order Schemes

*Journal of Scientific Computing*, *41*(1), 1–12.

author keywords: Perfectly matched layer (PML); Long-time growth; Wave propagation; Maxwell's equations; Numerical solution; Second order approximation; Yee scheme; Leap-frog scheme; Lax-Wendroff scheme; Central difference/Runge-Kutta scheme; Yee/Runge-Kutta scheme

TL;DR:
Analysis of the temporal behavior of unsplit PMLs for some commonly used second order explicit finite-difference schemes that approximate the Maxwell’s equations finds that the type of the layer and the choice of the scheme play a major role in how rapidly this growth may manifest itself and whether or not it manifests itself at all.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2009 chapter

Numerical Simulation of Focusing Nonlinear Waves in the Nonparaxial Regime

In H. Barucq, A.-S. Bonnet-Bendhia, G. Cohen, J. Diaz, A. Ezziana, & P. Joly (Eds.), *Proceedings of the 9th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, WAVES 2009,
Pau, France, June 15--19, 2009* (pp. 325–327). https://stsynkov.math.ncsu.edu/publications/a54e_waves09-abstract.pdf

Ed(s): H. Barucq, A. Bonnet-Bendhia, G. Cohen, J. Diaz, A. Ezziana & P. Joly

Event: Institut National De Recherche en Informatique et en Automatique

Source: ORCID

Added: September 6, 2019

2009 chapter

Numerical solution of the nonlinear Helmholtz equation

In *Mathematics in Applications, Proceedings of the conference in honor of the 80th birthday
of Academician S. K. Godunov, Novosibirsk, Russia, July 20--24, 2009* (pp. 37–38). https://stsynkov.math.ncsu.edu/publications/a54e_godunov80.pdf

Source: ORCID

Added: September 6, 2019

2009 journal article

On SAR Imaging through the Earth's Ionosphere

*SIAM Journal on Imaging Sciences*, *2*(1), 140–182.

author keywords: synthetic aperture radar (SAR); spaceborne radar; ionosphere; dispersion of electromagnetic waves; cold plasma; ionospheric distortions; turbulent fluctuations; geometrical optics; refraction index; range and azimuthal resolution; scattering

TL;DR:
The ionospheric phenomena, both deterministic and random, are shown to affect the azimuthal resolution of a SAR sensor stronger than the range resolution; also, the effect of randomness appears weaker than that of the baseline dispersion.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2009 chapter

On SAR Imaging through the Earth's Ionosphere

In H. Barucq, A.-S. Bonnet-Bendhia, G. Cohen, J. Diaz, A. Ezziana, & P. Joly (Eds.), *Proceedings of the 9th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, WAVES 2009,
Pau, France, June 15--19, 2009* (pp. 312–313). https://stsynkov.math.ncsu.edu/publications/a52e_waves09-abstract.pdf

Ed(s): H. Barucq, A. Bonnet-Bendhia, G. Cohen, J. Diaz, A. Ezziana & P. Joly

Event: Institut National De Recherche en Informatique et en Automatique

Source: ORCID

Added: September 6, 2019

2009 journal article

On the Use of Start-Stop Approximation for Spaceborne SAR Imaging

*SIAM Journal on Imaging Sciences*, *2*(2), 646–669.

author keywords: synthetic aperture radar (SAR); spaceborne SAR imaging; high-speed motion; start-stop approximation; Doppler effect; Lorentz transform; displacement of the antenna; range and azimuthal resolution; image sharpness (contrast)

TL;DR:
For the image to stay largely unaffected by Doppler, the frequency shift must be included in the definition of a matched filter, otherwise, there will be a geometric shift (translation) of the entire imaged scene from its true position, and there may also be a slight deterioration of the image sharpness (contrast).
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2008 journal article

Lacunae based stabilization of PMLs

*Journal of Computational Physics*, *227*(15), 7322–7345.

author keywords: perfectly matched layer (PML); long-time stability; weak well-posedness; wave propagation; hyperbolicity; the Huygens' principle; Lacunae; Maxwell's equations; artificial boundary conditions (ABCs); numerical solution

TL;DR:
This work proposes a modification that stabilizes any PML applied to a hyperbolic partial differential equation/system that satisfies the Huygens' principle and allows us to establish a temporally uniform error bound for arbitrarily long-time intervals.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2008 chapter

Numerical Solution of the Nonlinear Helmholtz Equation

In *Effective Computational Methods for Wave Propagation* (Vol. 5, pp. 37–62).

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

2008 journal article

Simulations of the nonlinear Helmholtz equation: arrest of beam collapse, nonparaxial solitons and counter-propagating beams

*Optics Express*, *16*(17), 13323.

MeSH headings : Light; Lighting / methods; Models, Theoretical; Nonlinear Dynamics; Scattering, Radiation

TL;DR:
The (2+1)D nonlinear Helmholtz equation (NLH) for input beams that collapse in the simpler NLS model is solved, providing the first ever numerical evidence that nonparaxiality and backscattering can arrest the collapse.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2007 journal article

Active Control of Sound for Composite Regions

*SIAM Journal on Applied Mathematics*, *67*(6), 1582–1609.

author keywords: active shielding; noise control; inverse source problem; time-harmonic acoustic fields; composite domain; communication pattern; the Helmholtz equation; generalized Calderon's potentials; exact volumetric cancellation; general solution; incoming and outgoing waves; wave split

TL;DR:
A methodology for the active control of time-harmonic wave fields, e.g., acoustic disturbances, in composite regions, which extends the previous approach developed for the case of arcwise connected regions.
(via Semantic Scholar)

Sources: Web Of Science, ORCID, Crossref, NC State University Libraries

Added: August 6, 2018

2007 chapter

High-Order Numerical Method for the Nonlinear Helmholtz Equation with Material Discontinuities

In N. Biggs, A.-S. Bonnet-Bendhia, P. Chamberlain, S. Chandler-Wildea, G. Cohen, H. Haddar, … R. Potthast (Eds.), *Proceedings of the 8th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, WAVES 2007,
University of Reading, UK, July 23 -- 27, 2007* (pp. 455–457). https://stsynkov.math.ncsu.edu/publications/Waves_2007_proceedings.pdf

Ed(s): N. Biggs, A. Bonnet-Bendhia, P. Chamberlain, S. Chandler-Wildea, G. Cohen, H. Haddar, P. Joly, S. Langdon

Source: ORCID

Added: September 6, 2019

2007 journal article

High-order numerical method for the nonlinear Helmholtz equation with material discontinuities in one space dimension

*Journal of Computational Physics*, *227*(1), 820–850.

author keywords: Kerr nonlinearity; nonlinear optics; inhomogeneous medium; discontinuous coefficients; finite volume discretization; C mpact scheme; high-order method; artificial boundary conditions (ABCs); two-way ABCs; traveling waves; complex valued solutior; Frechet differentiability; Newton's method

TL;DR:
This study numerically solve the one-dimensional NLH using a Newton-type nonlinear solver and introduces a novel compact finite-volume fourth order discretization for the NLH with material discontinuities that corroborate the design fourth order convergence of the method.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2007 chapter

Lacuna-based stabilization of PMLs

In N. Biggs, A.-S. Bonnet-Bendhia, P. Chamberlain, S. Chandler-Wildea, G. Cohen, H. Haddar, … R. Potthast (Eds.), *Proceedings of the 8th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, WAVES 2007,
University of Reading, UK, July 23 -- 27, 2007* (pp. 298–300). https://stsynkov.math.ncsu.edu/publications/Waves_2007_proceedings.pdf

Source: ORCID

Added: September 6, 2019

2007 report

On Spectral Accuracy of Quadrature Formulae Based on Piecewise Polynomial Interpolation

(No. CRSC-TR07-11). https://stsynkov.math.ncsu.edu/publications/a43e5.crsc.pdf

Event: at Raleigh, NC

Source: ORCID

Added: September 6, 2019

2007 journal article

Weak Lacunae of Electromagnetic Waves in Dilute Plasma

*SIAM Journal on Applied Mathematics*, *67*(6), 1548–1581.

author keywords: Huygens' principle; wave diffusion; aftereffects; aft fronts; lacunae; ionospheric propagation; isotropic plasma; Langmuir frequency; cold plasma; transverse waves; Maxwell equations; Klein-Gordon equation; weak dispersion; short waves; external magnetic field; cyclotron frequency; gyrotropy; Faraday rotation

TL;DR:
Lacunae can be efficiently exploited for the numerical simulation of unsteady waves, and considerable progress has been made toward the development of lacunae-based methods for computational electromagnetism.
(via Semantic Scholar)

Sources: Web Of Science, ORCID, Crossref, NC State University Libraries

Added: August 6, 2018

2006 book

A Theoretical Introduction to Numerical Analysis

(p. xiv+537).

Event: at Boca Raton, FL

Sources: ORCID, Crossref, NC State University Libraries

Added: July 10, 2019

2006 journal article

High-order numerical solution of the nonlinear Helmholtz equation with axial symmetry

*Journal of Computational and Applied Mathematics*, *204*(2), 477–492.

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2006 journal article

Inverse source problem and active shielding for composite domains

*Applied Mathematics Letters*, *20*(5), 511–515.

author keywords: multiply connected domain; inverse source; active shielding; control of sound; Calderon's projection; difference potentials method

TL;DR:
In the paper, general solution for a discretized composite AS problem is obtained and it is shown that it reduces to solving a collection of auxiliary problems for simply connected domains.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2006 journal article

The Problem of Active Shielding for Composite Regions

*Dokl. Akad. Nauk*, *411*(2), 164–166. https://stsynkov.math.ncsu.edu/publications/a45r.pdf

Source: ORCID

Added: September 6, 2019

2006 journal article

The Problem of Active Shielding for Multiply Connected Regions

*Doklady Rossiiskoi Akademii Nauk Matematika (Transactions of the Russian Academy of Sciences, Mathematics)*, *411*(2), 164–166.

Source: NC State University Libraries

Added: July 28, 2019

2006 journal article

The problem of active noise shielding in composite domains

*Doklady. Mathematics*, *74*(3), 812–814.

Sources: NC State University Libraries, NC State University Libraries

Added: August 6, 2018

2005 conference paper

Numerical Solution of the Nonlinear Helmholtz Equation Using Nonorthogonal Expansions

*Proceedings of the 7th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, WAVES 2005,
Brown University, Providence, RI, June 20 -- 24, 2005*, 379–381.

Source: ORCID

Added: September 6, 2019

2005 journal article

Numerical solution of the nonlinear Helmholtz equation using nonorthogonal expansions

*Journal of Computational Physics*, *210*(1), 183–224.

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2004 journal article

On the application of lacunae-based methods to Maxwell's equations

*Journal of Computational Physics*, *199*(1), 126–149.

Sources: NC State University Libraries, NC State University Libraries

Added: August 6, 2018

2004 journal article

On the application of lacunae-based methods to Maxwell's equations

*Journal of Computational Physics*, *199*(1), 126–149.

Sources: ORCID, Crossref, NC State University Libraries

Added: September 6, 2019

2004 journal article

Optimization of power in the problems of active control of sound

*Mathematics and Computers in Simulation*, *65*(4-5), 323–335.

author keywords: noise cancellation; active control sources; volumetric and surface controls; general solution; monopoles and dipoles; radiation of waves; complex-valued quantities; load on the sources by the field; net power gain

TL;DR:
It turns out that the corresponding analysis necessarily involves interaction between the sources of sound and the surrounding acoustic field, which was not the case for either L1 or L2.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(OpenAlex)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2004 journal article

Quadratic optimization in the problems of active control of sound

*Applied Numerical Mathematics*, *52*(4), 381–400.

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2003 journal article

*Journal of Scientific Computing*, *18*(2), 155–189.

author keywords: linear differential operator; discontinuous solution; distribution; monopole; dipole; fundamental solution; convolution; boundary integral; single- and double-layer potentials; surface density of the potential; linear difference operator; multi-layer grid boundary; discontinuous grid function; discrete monopole and dipole layers; Calderon's potential; difference potential

TL;DR:
The motivation for introducing and analyzing the discrete surface potentials was provided by the problems of active shielding and control of sound, in which the source terms that drive the potentials are interpreted as the acoustic control sources that cancel out the unwanted noise on a predetermined region of interest.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2003 report

Artificial Boundary Conditions for the Numerical Simulation of Unsteady Electromagnetic Waves

(No. CRSC–TR03–19). https://stsynkov.math.ncsu.edu/publications/a34p.ncsu.pdf

Event: at Raleigh, NC

Source: ORCID

Added: September 6, 2019

2003 journal article

Artificial boundary conditions for the numerical simulation of unsteady acoustic waves

*Journal of Computational Physics*, *189*(2), 626–650.

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(OpenAlex)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2003 journal article

Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves

*SIAM Journal on Applied Mathematics*, *63*(5), 1718–1736.

author keywords: Kerr medium; nonlinear wave propagation; self-focusing; singularity formation; linear damping; limiting absorption; two-way ABCs

TL;DR:
This paper develops new local discontinuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions and presents new results on a post-processing technique, originally designed for methods with good negative-order error estimates, that works as well for the new higher derivative cases.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2003 chapter

Lacunae-Based Artificial Boundary Conditions for the Numerical Simulation of Unsteady Waves Governed by Vector Models

In G. C. Cohen, E. Heikkola, P. Joly, & P. Neittaanmäki (Eds.), *Mathematical
and Numerical Aspects of Wave Propagation --- WAVES 2003,
The Sixth International Conference, Jyväskylä, Finland, June 30 -- July 4, 2003.
Proceedings* (pp. 103–108). https://stsynkov.math.ncsu.edu/publications/waves2003p.pdf

Ed(s): G. Cohen, E. Heikkola, P. Joly & P. Neittaanmäki

Event: at Berlin

Source: ORCID

Added: September 6, 2019

2003 chapter

Optimization in the Context of Active Control of Sound

In *Computational Science and Its Applications — ICCSA 2003* (Vol. 2668, pp. 801–810).

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(OpenAlex)

Sources: NC State University Libraries, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2003 journal article

Optimization of Acoustic Source Strength in the Problems of Active Noise Control

*SIAM Journal on Applied Mathematics*, *63*(4), 1141–1183.

author keywords: noise cancellation; control sources; minimization of amplitude; volume velocity; surface monopoles

TL;DR:
A rigorous proof of global L1 minimality for both continuous and discrete optimization problems in the one-dimensional case and a conjecture that the same result holds in the general case, i.e., for multidimensional settings and domains of arbitrary shape.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2002 report

A Future Role of Numerical and Applied Mathematics in Material Sciences

(No. 40, NASA/CR–2002–211453). https://apps.dtic.mil/dtic/tr/fulltext/u2/a402142.pdf

Event: at Hampton, VA

Source: ORCID

Added: September 6, 2019

2002 journal article

Computation of Nonlinear Backscattering Using a High-Order Numerical Method

*Journal of Scientific Computing*, *17*(1-4), 351–364.

author keywords: Kerr medium; wave propagation; self focusing; fourth-order method; two-way ABCs

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(Web of Science)

Sources: Crossref, NC State University Libraries, ORCID

Added: July 10, 2019

2002 chapter

On the Results of the Application of the Method of Difference Potentials to the Construction of Artificial Boundary Conditions for External Flow Computations

In *Method of Difference Potentials and Its Applications* (Vol. 30, pp. 403–441).

Event: at Berlin

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

2002 journal article

On the combined performance of nonlocal artificial boundary conditions with the new generation of advanced multigrid flow solvers

*Computers & Fluids*, *31*(3), 269–308.

Source: ORCID

Added: September 6, 2019

2002 journal article

On the combined performance of nonlocal artificial boundary conditions with the new generation of advanced multigrid flow solvers

*Computers & Fluids*, *31*(3), 269–308.

Sources: Crossref, NC State University Libraries, NC State University Libraries

Added: August 6, 2018

2001 chapter

A Cartesian Perfectly Matched Layer for the ̆ppercaseHelmholtz Equation

In Tourrette Loı̈c & L. Halpern (Eds.), *Absorbing Boundaries and Layers, Domain Decomposition Methods.
̆ppercaseApplications to Large Scale Computations* (pp. 279–309). https://stsynkov.math.ncsu.edu/publications/a24e7.pdf

Ed(s): L. Tourrette & L. Halpern

Event: at Huntington, NY

Source: ORCID

Added: September 6, 2019

2001 chapter

A Cartesian Perfectly Matched Layer for the Helmholtz Equation

In Tourrette Loı̈c & L. Halpern (Eds.), *Absorbing Boundaries and Layers, Domain Decomposition Methods. Applications to Large Scale Computations* (pp. 279–309). New York: Nova Science Publishers.

Ed(s): L. Tourrette & L. Halpern

Source: NC State University Libraries

Added: July 28, 2019

2001 journal article

Active Shielding and Control of Noise

*SIAM Journal on Applied Mathematics*, *62*(2), 563–596.

author keywords: active shielding; noise control; time-harmonic acoustic fields; the Helmholtz equation; generalized Calderon's potentials; exact volumetric cancellation; general solution; incoming and outgoing waves; near surface control sources; spatial anisotropies; material discontinuities; optimization; Bessel functions

TL;DR:
The key finding is that for eliminating the unwanted component of the acoustic field in a given area, one needs to know relatively little; in particular, neither the locations nor structure nor strength of the exterior noise sources need to be known.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(OpenAlex)

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

2001 journal article

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

*Journal of Computational Physics*, *174*(2), 712–758.

author keywords: artificial boundary conditions; wave propagation; lacunae; nondeteriorating method

TL;DR:
The construction of the global lacunae-based ABCs are delineated in the framework of a discretized wave equation and systematic numerical results that corroborate the theoretical design properties of the ABCs'' algorithm are presented.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2001 journal article

High-Order Two-Way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering

*Journal of Computational Physics*, *171*(2), 632–677.

author keywords: artificial boundary conditions (ABCs); two-way ABCs; radiation; Helmholtz equation; nonlinearity; nonparaxiality; fourth-order schemes; self-focusing; backscattering

TL;DR:
The two-way ABCs are constructed for the nonlinear Helmholtz equation, which models a continuous-wave (CW) laser beam propagation in amedium with nonlinear index of refraction, i.e., generation of waves in the opposite direction to that of the incoming signal.
(via Semantic Scholar)

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

2001 journal article

Long-time numerical computation of wave-type solutions driven by moving sources

*Applied Numerical Mathematics*, *38*(1-2), 187–222.

Sources: Web Of Science, NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2000 journal article

Global Artificial Boundary Conditions for Computation of External Flows with Jets

*AIAA Journal*, *38*(11), 2014–2022.

Sources: ORCID, Crossref, NC State University Libraries

Added: September 6, 2019

2000 journal article

Global artificial boundary conditions for computation of external flows with jets

*AIAA Journal*, *38*, 2014–2022.

Sources: Crossref, NC State University Libraries

Added: June 30, 2019

2000 journal article

Non-Reflecting Artificial Boundary Conditions for the Replacement of Truncated Equations with Lacunae

*Mathematical Modeling*, *12*(12), 108–127.

Source: NC State University Libraries

Added: July 10, 2019

2000 journal article

Nonreflecting artificial boundary conditions for the replacement of rejected equations with gaps

*Mat. Model.*, *12*(12), 108–127. https://mathscinet.ams.org/mathscinet-getitem?mr=1833776

Source: ORCID

Added: September 6, 2019

1999 journal article

External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics

*SIAM Journal on Scientific Computing*, *21*(1), 166–206.

author keywords: external flows; infinite-domain problems; artificial boundary conditions; far-field linearization; boundary projections; generalized potentials; difference potentials method; auxiliary problem; separation of variables

TL;DR:
An innovative approach to constructing highly accurate ABCs for three-dimensional flow computations employing the finite-difference counterparts to Calderon's pseudodifferential boundary projections calculated in the framework of the difference potentials method (DPM) of Ryaben'kii.
(via Semantic Scholar)

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

1999 conference paper

Global artificial boundary conditions for computation of external flow problems with propulsive jets

*14th Computational Fluid Dynamics Conference*, *2*, 836–846.

Event: 14th Computational Fluid Dynamics Conference

Sources: ORCID, Crossref, NC State University Libraries

Added: September 6, 2019

1999 report

Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving Source

(No. 99–23, NASA/CR–1999–209350). https://ntrs.nasa.gov/search.jsp?R=19990062251

Event: at Hampton, VA

Source: ORCID

Added: September 6, 2019

1999 journal article

On Lacunae-Based Algorithm for Numerical Solution of 3D Wave Equation for Arbitrarily Large Time

*Mathematical Modeling*, *11*(12), 113–127.

Source: NC State University Libraries

Added: July 28, 2019

1999 journal article

The use of lacunae of the 3D-wave equation for computing a solution at large time values

*Mat. Model.*, *11*(12), 113–126. https://mathscinet.ams.org/mathscinet-getitem?mr=1761052

Source: ORCID

Added: September 6, 2019

1998 chapter

AN APPLICATION OF THE DIFFERENCE POTENTIALS METHOD TO SOLVING EXTERNAL PROBLEMS IN CFD

In M. Hafez & K. Oshima (Eds.), *Computational Fluid Dynamics Review 1998* (Vol. 1, pp. 169–205).

Ed(s): M. Hafez & K. Oshima

Event: at Singapore

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

1998 chapter

Artificial Boundary Conditions for Infinite-Domain Problems

In *ICASE/LaRC Interdisciplinary Series in Science and Engineering* (Vol. 6, pp. 119–137).

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

1998 journal article

Improved Treatment of External Boundary Conditions for Three-Dimensional Flow Computations

*AIAA Journal*, *36*(11), 1998–2004.

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

1998 journal article

Numerical solution of problems on unbounded domains. A review

*Applied Numerical Mathematics*, *27*(4), 465–532.

author keywords: infinite-domain problems; artificial boundary conditions; pseudodifferential equations; difference potentials method; auxiliary problem; boundary equations with projections

TL;DR:
An extensive survey and comparative assessment of different existing methods for constructing the ABCs are presented and a new ABCs technique proposed in recent work is described, which allows one to obtain highly accurate ABCs in the form of certain (nonlocal) boundary operator equations.
(via Semantic Scholar)

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

1998 chapter

On the Combined Implementation of Global Boundary Conditions with Central Difference Multigrid Flow Solvers

In T. L. Geers (Ed.), *Fluid Mechanics and Its Applications* (Vol. 49, pp. 285–294).

Ed(s): T. Geers

Event: at Dordrecht

Sources: ORCID, Crossref, NC State University Libraries

Added: September 6, 2019

1997 journal article

Artificial Boundary Conditions for Computation of Oscillating External Flows

*SIAM Journal on Scientific Computing*, *18*(6), 1612–1656.

author keywords: oscillating flows; artificial boundary conditions; boundary equations with projections; auxiliary problem; difference potentials method

TL;DR:
This paper contains a general theoretical description of the algorithm for setting the DPM-based ABCs for time-periodic external flows, and expects that these boundary conditions will become an effective tool for constructing robust numerical methods to calculate oscillatory flows.
(via Semantic Scholar)

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

1996 report

Artificial Boundary Conditions Based on the Difference Potentials Method

(No. NASA-TM-110265, NAS 1.15:110265). https://ntrs.nasa.gov/search.jsp?R=19960045440

Event: at Hampton, VA

Source: ORCID

Added: September 6, 2019

1996 journal article

Construction of Artificial Boundary Conditions Using Difference Potentials Method

*Mathematical Modeling*, *8*(9), 118–128. https://mathscinet.ams.org/mathscinet-getitem?mr=1444877

Sources: NC State University Libraries, ORCID

Added: July 9, 2019

1996 journal article

External flow computations using global boundary conditions

*AIAA Journal*, *34*(4), 700–706.

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

1996 conference paper

Nonlocal Artificial Boundary Conditions for Computation of External Viscous Flows

In J.-A. Desideri, C. Hirsch, P. Le Tallec, M. Pandolfi, & J. Périaux (Eds.), *Computational Fluid Dynamics'96.
Proceedings of the Third ECCOMAS CFD Conference,
September 9--13, 1996, Paris, France* (pp. 512–518). https://www.tib.eu/en/search/id/BLCP%3ACN017470620/Nonlocal-Artificial-Boundary-Conditions-for-Computation/

Ed(s): J. Desideri, C. Hirsch, P. Le Tallec, M. Pandolfi & J. Périaux

Event: at Chichester

Source: ORCID

Added: September 6, 2019

1995 journal article

An Application of Nonlocal External Conditions to Viscous Flow Computations

*Journal of Computational Physics*, *116*(2), 212–225.

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

1995 journal article

An effective numerical technique for solving a special class of ordinary difference equations

*Applied Numerical Mathematics*, *18*(4), 489–501.

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

1995 journal article

Artificial Boundary Conditions for the Numerical Solution of External Viscous Flow Problems

*SIAM Journal on Numerical Analysis*, *32*(5), 1355–1389.

Sources: Crossref, NC State University Libraries, ORCID

Added: June 30, 2019

1995 conference paper

Nonlocal Artificial Boundary Conditions Based on the Difference Potentials Method

In M. Hafez (Ed.), *Sixth International Symposium on
Computational Fluid Dynamics. Collection of Technical Papers*: *Vol.* *IV* (pp. 114–119). https://www.tib.eu/en/search/id/TIBKAT%3A228255147/A-collection-of-technical-papers-Sixth-International/

Ed(s): M. Hafez

Event: at Lake Tahoe, Nevada

Source: ORCID

Added: September 6, 2019

1995 chapter

Nonlocal Artificial Boundary Conditions for Computation of External Viscous Flows

In S. N. Atluri, G. Yagawa, & T. A. Cruse (Eds.), *Computational Mechanics ’95* (pp. 1065–1070).

Ed(s): S. Atluri, G. Yagawa & T. Cruse

Event: at Berlin

Sources: ORCID, Crossref, NC State University Libraries

Added: September 6, 2019

1993 journal article

Artificial Boundary Conditions for the Numerical Solution of External Viscous Flow Problems. I

*Rossijskaya Akad. Nauk Inst. Prikl. Mat. Preprint*, (45).

Source: ORCID

Added: September 6, 2019

1993 journal article

Artificial Boundary Conditions for the Numerical Solution of External Viscous Flow Problems. II

*Rossijskaya Akad. Nauk Inst. Prikl. Mat. Preprint*, (46).

Source: ORCID

Added: September 6, 2019

1991 journal article

Application of a model of potential flow to the formulation of conditions on the outer boundary for Euler equations. I

*Akad. Nauk SSSR Inst. Prikl. Mat. Preprint*, (40), 25. https://mathscinet.ams.org/mathscinet-getitem?mr=1156343

Source: ORCID

Added: September 6, 2019

1991 journal article

Application of a model of potential flow to the formulation of conditions on the outer boundary for Euler equations. II

*Akad. Nauk SSSR Inst. Prikl. Mat. Preprint*, (41), 27. https://mathscinet.ams.org/mathscinet-getitem?mr=1156344

Source: ORCID

Added: September 6, 2019

1991 journal article

Boundary equations with projectors in composite domains

*Akad. Nauk SSSR Inst. Prikl. Mat. Preprint*, (112), 20. https://mathscinet.ams.org/mathscinet-getitem?mr=1278545

Source: ORCID

Added: September 6, 2019

1991 journal article

Decomposition algorithms based on boundary equations with projectors

*Akad. Nauk SSSR Inst. Prikl. Mat. Preprint*, (113), 23. https://mathscinet.ams.org/mathscinet-getitem?mr=1278546

Source: ORCID

Added: September 6, 2019

1991 conference paper

Exact Transfer of Boundary Conditions in Subsonic Problems of Computational Gas Dynamics

In A. V. Zabrodin & G. P. Voskresensky (Eds.), *Construction of Algorithms and Solution of Mathematical Physics Problems* (pp. 194–198). Moscow.

Ed(s): A. Zabrodin & G. Voskresensky

Event: Keldysh Institute of Applied Mathematics, USSR Academy of Sciences at Moscow

Source: ORCID

Added: September 6, 2019

1991 journal article

Kinetic-Consistent Finite-Difference Schemes in Curvilinear Coordinate Systems

*Differential Equations*, *27*(7), 1161–1169.

Source: NC State University Libraries

Added: July 28, 2019

1991 journal article

Kinetically consistent difference schemes in curvilinear coordinate systems

*Differentsiaļprime Nye Uravneniya*, *27*(7), 1161–1169, 1285. https://mathscinet.ams.org/mathscinet-getitem?mr=1127501

Source: ORCID

Added: September 6, 2019

1990 journal article

Conditions on the exterior boundary of a computational domain in subsonic problems of computational gas dynamics

*Akad. Nauk SSSR Inst. Prikl. Mat. Preprint*, (108), 26. https://mathscinet.ams.org/mathscinet-getitem?mr=1120837

Source: ORCID

Added: September 6, 2019

1990 journal article

Derivation of Invariant Quasihydrodynamic Equations on the Basis of Kinetic Models

*Akad. Nauk SSSR Inst. Prikl. Mat. Preprint*, (7).

Source: ORCID

Added: September 6, 2019

1990 journal article

Numerical generation of conformal grids in the exterior of a bounded simply connected domain based on the method of difference potentials

*Akad. Nauk SSSR Inst. Prikl. Mat. Preprint*, (61), 21. https://mathscinet.ams.org/mathscinet-getitem?mr=1086442

Source: ORCID

Added: September 6, 2019

1990 journal article

On the construction of images of simply connected domains realized by solutions of a system of Beltrami equations

*Akad. Nauk SSSR Inst. Prikl. Mat. Preprint*, (155), 18. https://mathscinet.ams.org/mathscinet-getitem?mr=1157869

Source: ORCID

Added: September 6, 2019

1989 journal article

Construction of kinetically consistent difference schemes on curvilinear grids

*Akad. Nauk SSSR Inst. Prikl. Mat. Preprint*, (8), 24. https://mathscinet.ams.org/mathscinet-getitem?mr=1019147

Source: ORCID

Added: September 6, 2019

Updated: September 3rd, 2019 12:47

Updated: December 10th, 2019 21:13

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