Michael Medvinsky
Application to the simulation of the biological cell electropermeabilization model, Difference potentials, Helmholtz equation, High-order accuracy, Curvilinear boundaries, Interface problems, Infinite domain problems, OSRC, Artificial boundary conditions, Boundary Projections, Non-confirming boundaries, Non-confirming interfaces, Curvilinear boundaries, Variable coefficients, piecewise-constant coefficients, Non-matching grids, parallel algorithms
Works (21)
Updated: April 4th, 2024 03:49
2021 journal article
Solution of three-dimensional multiple scattering problems by the method of difference potentials
WAVE MOTION, 107.
author keywords: Time-harmonic waves; Unbounded domain; Helmholtz equation; Finite differences; High-order accuracy; Scattering objects; Cartesian grid; Non-conforming boundary; Artificial outer boundary; BGT radiation condition
Sources: ORCID, Web Of Science, NC State University Libraries
Added: August 31, 2021
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, ORCID, NC State University Libraries, Crossref
Added: December 10, 2018
2017 journal article
High-order numerical schemes based on difference potentials for 2D elliptic problems with material interfaces
APPLIED NUMERICAL MATHEMATICS, 111, 64–91.
author keywords: Boundary value problems; Piecewise-constant coefficients; High-order accuracy; Difference potentials; Boundary projections; Interface problems; Non-matching grids; Mixed-order; Parallel algorithms; Application to the simulation of the biological cell electropermeabilization model
TL;DR:
This work considers 2D elliptic models with material interfaces and develops efficient high-order accurate methods based on Difference Potentials for such problems as partial differential equations with varying coefficients and domains with irregular geometry.
(via Semantic Scholar)
manuscript.elsevier.com (publisher PDF)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2016 journal article
Solving the Helmholtz equation for general smooth geometry using simple grids
Wave Motion, 62, 75–97.
author keywords: Difference potentials; Boundary projections; Calderon's operators; Curvilinear boundaries; High order compact differencing; Multiple scattering
Sources: Crossref, ORCID, NC State University Libraries, Web Of Science
Added: August 6, 2018
2015 chapter
On the Solution of the Elliptic Interface Problems by Difference Potentials Method
In Lecture Notes in Computational Science and Engineering (pp. 197–205).
TL;DR:
This work considers Difference Potentials Method (DPM) as an efficient and accurate solver for the variable coefficient elliptic interface problems.
(via Semantic Scholar)
Source: Crossref
Added: July 28, 2019
2013 conference paper
High Order Numerical Simulation of the Transmission and Scattering of Waves Using the Method of Difference Potentials
Proceedings of the International Conference "Difference Schemes and Applications" in honor of the 90-th Birthday of Prof. V. S. Ryaben'kii, 33–34. Moscow. Russia: Keldysh Institute of Applied Mathematics.
Source: NC State University Libraries
Added: December 9, 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: Crossref, ORCID, Web Of Science, NC State University Libraries
Added: August 6, 2018
2013 thesis
High order numerical simulation of waves using regular grids and non-conforming interfaces
(Ph.D Dissertation). Tel Aviv University.
Source: NC State University Libraries
Added: July 10, 2019
2013 thesis
High order numerical simulation of waves using regular grids and non-conforming interfaces
http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA617619
Source: ORCID
Added: December 6, 2019
2013 article
Providing easy access to radio networks
(2013, June 19). http://appft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&co1=AND&d=PG01&s1=%22Providing+easy+access+radio+networks%22.TTL.&OS=TTL/%22Providing+easy+access+to+radio+networks%22&RS=TTL/%22Providing+easy+access+to+radio+networks%22
Source: ORCID
Added: December 6, 2019
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.
author keywords: Difference potentials; Boundary projections; Calderon's operators; Regular grids; Curvilinear boundaries; Variable coefficients; Compact differencing; High order accuracy
Sources: Crossref, ORCID, Web Of Science, NC State University Libraries
Added: August 6, 2018
2010 journal article
On surface radiation conditions for an ellipse
Journal of Computational and Applied Mathematics, 234(6), 1647–1655.
author keywords: Helmholtz equation; OSRC; Mathieu functions
TL;DR:
This work compares several On Surface Radiation Boundary Conditions in two dimensions, for solving the Helmholtz equation exterior to an ellipse, and introduces a new boundary condition for anEllipse based on a modal expansion in Mathieu functions.
(via Semantic Scholar)
Source: Crossref
Added: July 28, 2019
2010 journal article
On surface radiation conditions for an ellipse
http://www.sciencedirect.com/science/article/pii/S0377042709004865
Source: ORCID
Added: December 6, 2019
2008 patent
Expiditing Seamless Roaming in Heterogenous Networking
https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2008073438
Source: ORCID
Added: December 6, 2019
2008 journal article
Local absorbing boundary conditions for elliptical shaped boundaries
Journal of Computational Physics, 227(18), 8254–8267.
author keywords: Helmholtz equation; absorbing boundary conditions; Mathieu functions
TL;DR:
This work compares several local absorbing boundary conditions for solving the Helmholtz equation by a finite difference or finite element method, exterior to a general scatterer, and introduces a new boundary condition for an ellipse based on a modal expansion.
(via Semantic Scholar)
Sources: Crossref, ORCID
Added: July 28, 2019
2008 patent
Masking Changes for Seamless Roaming in Heterogenous Networking
https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2008073492
Source: ORCID
Added: December 6, 2019
2007 article
Providing easy access to radio networks
(2007, May 3). http://appft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&co1=AND&d=PG01&s1=%22Providing+easy+access+radio+networks%22.TTL.&OS=TTL/%22Providing+easy+access+to+radio+networks%22&RS=TTL/%22Providing+easy+access+to+radio+networks%22
Source: ORCID
Added: December 6, 2019
2007 thesis
Comparison of local absorbing radiation conditions for scattering about elliptical body
(Master's thesis). Tel Aviv University.
Source: NC State University Libraries
Added: July 28, 2019
2007 thesis
Comparison of local absorbing radiation conditions for scattering about elliptical body
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.728.1981&rep=rep1&type=pdf
Source: ORCID
Added: December 6, 2019
chapter
On the Solution of the Elliptic Interface Problems by Difference Potentials Method
Source: ORCID
Added: December 6, 2019
Employment
Updated: September 12th, 2016 20:06
2016 - present
North Carolina State University Raleigh, NC, US
Research Assistant Professor
Department of Mathematics
2013 - present
University of Utah Salt Lake City, UT, US
Scott Assistance Professor Lecturer
math
Education
Updated: October 15th, 2019 15:52
Tel Aviv University Tel Aviv, IL
PhD
math
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