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Numerical Method of Quasi-Isometric Parametrization for Two-Dimensional Curvilinear Domains

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Abstract

A method for constructing a quasi-isometric parametrization of a plane curvilinear quadrilateral is described. The parametrization is defined using a generalized Dirichlet variational functional. Based on its minimization, an algorithm for generating grids that implement a quasi-isometric parametrization of quadrilaterals with curved, but sufficiently smooth boundaries is developed. Primary attention is given to the numerical features of the proposed approach.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    S. K. Godunov

  2. Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    V. T. Zhukov & O. B. Feodoritova

Authors
  1. S. K. Godunov
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  2. V. T. Zhukov
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  3. O. B. Feodoritova
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Corresponding authors

Correspondence to S. K. Godunov, V. T. Zhukov or O. B. Feodoritova.

Additional information

Dedicated to Academician S.K. Godunov on the occasion of his 90th birthday

Translated by I. Ruzanova

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Godunov, S.K., Zhukov, V.T. & Feodoritova, O.B. Numerical Method of Quasi-Isometric Parametrization for Two-Dimensional Curvilinear Domains. Comput. Math. and Math. Phys. 60, 568–579 (2020). https://doi.org/10.1134/S096554252004020X

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  • DOI: https://doi.org/10.1134/S096554252004020X

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