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Matem. Mod., 2015, Volume 27, Number 11, Pages 47–55 (Mi mm3667)  

This article is cited in 2 scientific papers (total in 2 papers)

Numerical simulations of boundary layer problems

A. A. Belovab, N. N. Kalitkinb

a Lomonosov Moscow State University, Faculty of Physics, Moscow
b Keldysh Institute of Applied Mathematics of RAS, Moscow

Abstract: At the interface between two media there often appear boundary layers. Singularly perturbed Helmholz equation is typical example. Up-to-date finite difference methods are shown to be capable of effective solving of such problems. Convergence verification procedure is proposed that does not require a priori estimations construction. A superfast algorithm that provides a posteriori asymptotically precise error estimation is described and semi-uniform rectangular grid that resolves all parts of solution is proposed. The algorithm proposed makes it possible to achieve good precisions on moderate grids with number of points $N\sim 200$ in each direction. This algorithm is realized as a program in Matlab environment.

Keywords: singularly perturbed problems, Helmholz equation, error estimation, Richardson method.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00161


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English version:
Mathematical Models and Computer Simulations, 2016, 8:4, 341–347

Bibliographic databases:

Received: 05.11.2014

Citation: A. A. Belov, N. N. Kalitkin, “Numerical simulations of boundary layer problems”, Matem. Mod., 27:11 (2015), 47–55; Math. Models Comput. Simul., 8:4 (2016), 341–347

Citation in format AMSBIB
\Bibitem{BelKal15}
\by A.~A.~Belov, N.~N.~Kalitkin
\paper Numerical simulations of boundary layer problems
\jour Matem. Mod.
\yr 2015
\vol 27
\issue 11
\pages 47--55
\mathnet{http://mi.mathnet.ru/mm3667}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3547136}
\elib{http://elibrary.ru/item.asp?id=25707569}
\transl
\jour Math. Models Comput. Simul.
\yr 2016
\vol 8
\issue 4
\pages 341--347
\crossref{https://doi.org/10.1134/S2070048216040037}


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    2. Zh. O. Dombrovskaya, A. N. Bogolyubov, “Effective FDTD modeling of microwave ceramics”, 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS), IEEE, 2017, 2732–2733  crossref  isi  scopus
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