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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 8, Pages 1345–1358 (Mi zvmmf607)  

This article is cited in 3 scientific papers (total in 3 papers)

Hamilton–Jacobi equation-based algorithms for approximate solutions to certain problems in applied geometry

D. I. Ivanova, I. E. Ivanova, I. A. Kryukovb

a Moscow Aviation Institute (State University of Aerospace Technologies)
b A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: Two important applied geometry problems are solved numerically. One is that of determining the nearest boundary distance from an arbitrary point in a domain. The other is that of determining (in a shortest-path metric) the distance between two points with the obstacles boundaries traversed inside the domain. These problems are solved by the time relaxation method as applied to a nonlinear Hamilton–Jacobi equation. Two major approaches are taken. In one approach, an equation with elliptic operators on the right-hand side is derived by changing the variables in the eikonal equation with viscous terms. In the other approach, first- and second-order monotone Godunov schemes are constructed taking into account the hyperbolicity of the nonlinear eikonal equation. One- and two-dimensional problems are solved to demonstrate the performance of the developed numerical algorithms and to examine their properties. Application problems are solved as examples.

Key words: eikonal equation, applied geometry, wall distance function.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:8, 1297–1310

Bibliographic databases:
UDC: 519.674
Received: 15.11.2004

Citation: D. I. Ivanov, I. E. Ivanov, I. A. Kryukov, “Hamilton–Jacobi equation-based algorithms for approximate solutions to certain problems in applied geometry”, Zh. Vychisl. Mat. Mat. Fiz., 45:8 (2005), 1345–1358; Comput. Math. Math. Phys., 45:8 (2005), 1297–1310

Citation in format AMSBIB
\by D.~I.~Ivanov, I.~E.~Ivanov, I.~A.~Kryukov
\paper Hamilton--Jacobi equation-based algorithms for approximate solutions to certain problems in applied geometry
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 8
\pages 1345--1358
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 8
\pages 1297--1310

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    This publication is cited in the following articles:
    1. I. E. Ivanov, I. A. Kryukov, “Chislennoe modelirovanie techenii mnogokomponentnogo gaza s silnymi razryvami svoistv sredy”, Matem. modelirovanie, 19:12 (2007), 89–100  mathnet  zmath  elib
    2. S. I. Kabanikhin, O. I. Krivorotko, “Chislennoe reshenie uravneniya eikonala”, Sib. elektron. matem. izv., 10 (2013), 28–34  mathnet
    3. S. I. Kabanikhin, O. I. Krivorotko, “A numerical algorithm for computing tsunami wave amplitude”, Num. Anal. Appl., 9:2 (2016), 118–128  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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