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Method of Fictitious Domains and Homotopy as a New Alternative to Multidimensional Partial Differential Equations in Domains of Any Shape

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Ukrainian Mathematical Journal Aims and scope

The ideas of the method of fictitious domains and homotopy are combined with an aim to reduce the solution of boundary-value problems for multidimensional partial differential equations (PDE) in domains of any shape to an exponentially convergent sequence of PDE in a parallelepiped (or, in the 2D case, in a rectangle). This enables us to decrease the required computer time due to the elimination of the necessity of triangulation of the domain by a grid with N inner nodes (thus, the Delaunay algorithm in the 2D case requires \( \mathcal{O} \)(N log N) operations).

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Authors and Affiliations

  1. Duale Hochschule Gera-Eisenach, Gera, Germany

    I. P. Gavrilyuk

  2. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    V. L. Makarov

Authors
  1. I. P. Gavrilyuk
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  2. V. L. Makarov
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Correspondence to I. P. Gavrilyuk.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 2, pp. 191–208, February, 2020.

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Gavrilyuk, I.P., Makarov, V.L. Method of Fictitious Domains and Homotopy as a New Alternative to Multidimensional Partial Differential Equations in Domains of Any Shape. Ukr Math J 72, 211–231 (2020). https://doi.org/10.1007/s11253-020-01777-y

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  • DOI: https://doi.org/10.1007/s11253-020-01777-y

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