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Numerical Study of the RBF-FD Level Set Based Method for Partial Differential Equations on Evolving-in-Time Surfaces

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Meshfree Methods for Partial Differential Equations IX (IWMMPDE 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 129))

Abstract

In this article we present a Radial Basis Function (RBF)-Finite Difference (FD) level set based method for the numerical solution of partial differential equations (PDEs) of the reaction-diffusion-convection type on an evolving-in-time hypersurface Γ(t). In a series of numerical experiments we study the accuracy and robustness of the proposed scheme and demonstrate that the method is applicable to practical models.

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Author information

Authors and Affiliations

  1. Institute for Applied Mathematics, TU Dortmund, Dortmund, Germany

    Andriy Sokolov & Stefan Turek

  2. Department of Mathematics, University of Giessen, Giessen, Germany

    Oleg Davydov

Authors
  1. Andriy Sokolov
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  2. Oleg Davydov
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  3. Stefan Turek
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Corresponding author

Correspondence to Andriy Sokolov .

Editor information

Editors and Affiliations

  1. Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Michael Griebel

  2. Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Marc Alexander Schweitzer

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Sokolov, A., Davydov, O., Turek, S. (2019). Numerical Study of the RBF-FD Level Set Based Method for Partial Differential Equations on Evolving-in-Time Surfaces. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations IX. IWMMPDE 2017. Lecture Notes in Computational Science and Engineering, vol 129. Springer, Cham. https://doi.org/10.1007/978-3-030-15119-5_7

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