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Multipoint Meshless FD Schemes Applied to Nonlinear and Multiscale Analysis

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 13353)


The paper presents computational schemes of the multipoint meshless method – the numerical modeling tool that allows accurate and effective solving of boundary value problems. The main advantage of the multipoint general version is its generality – the basic relations of derivatives from the unknown function depend on the domain discretization only and are independent of the type of problem being solved. This feature allows to divide the multipoint computational strategy into two stages and is advantageous from the calculation efficiency point of view. The multipoint method algorithms applied to such engineering problems as numerical homogenization of heterogeneous materials and nonlinear analysis are developed and briefly presented. The paper is illustrated by several examples of the multipoint numerical analysis.


  • Meshless FDM
  • Higher order approximation
  • Multipoint method
  • Homogenization
  • Nonlinear analysis
  • Elastic-plastic problem

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  • DOI: 10.1007/978-3-031-08760-8_5
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Correspondence to Irena Jaworska .

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Jaworska, I. (2022). Multipoint Meshless FD Schemes Applied to Nonlinear and Multiscale Analysis. In: Groen, D., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2022. ICCS 2022. Lecture Notes in Computer Science, vol 13353. Springer, Cham.

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  • Print ISBN: 978-3-031-08759-2

  • Online ISBN: 978-3-031-08760-8

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