Selected computational aspects of the meshless finite difference method. The meshless finite difference method (MFDM) is nowadays a powerful engineering tool for numerical analysis of boundary value problems. Nowadays, its computational capabilities are not fully used mainly due to the lack of suitable commercial software. This paper briefly presents the current state-of-the-art of the MFDM solution approach as well as it deals with the selected computational aspects of the MFDM. A set of Matlab functions written by the author is attached to the paper. Techniques for generation of nodes, MFD stars, formulas, equations as well as local approximation technique and numerical integration schemes are discussed there. (netlib numeralgo na36)

References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Kużelewski, Andrzej; Zieniuk, Eugeniusz: The FMM accelerated PIES with the modified binary tree in solving potential problems for the domains with curvilinear boundaries (2021)
  2. Milewski, Sławomir: Higher order schemes introduced to the meshless FDM in elliptic problems (2021)
  3. Milewski, Sławomir: A Matlab software for approximate solution of 2D elliptic problems by means of the meshless Monte Carlo random walk method (2020)
  4. Milewski, Sławomir; Putanowicz, Roman: Higher order meshless schemes applied to the finite element method in elliptic problems (2019)
  5. Cecot, W.; Milewski, S.; Orkisz, J.: Determination of overhead power line cables configuration by FEM and meshless FDM (2018)
  6. Milewski, Sławomir: Combination of the meshless finite difference approach with the Monte Carlo random walk technique for solution of elliptic problems (2018)
  7. Suchde, Pratik; Kuhnert, Jörg; Tiwari, Sudarshan: On meshfree GFDM solvers for the incompressible Navier-Stokes equations (2018)
  8. Rüter, Marcus Olavi; Chen, Jiun-Shyan: An enhanced-strain error estimator for Galerkin meshfree methods based on stabilized conforming nodal integration (2017)
  9. Jaśkowiec, J.; Milewski, S.: Coupling finite element method with meshless finite difference method in thermomechanical problems (2016)
  10. Jaśkowiec, J.; Milewski, S.: The effective interface approach for coupling of the FE and meshless FD methods and applying essential boundary conditions (2015)
  11. Milewski, Sławomir: Selected computational aspects of the meshless finite difference method (2013)