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Selected computational aspects of the meshless finite difference method

Author:

Sławomir MilewskiAuthors Info & Claims

Numerical Algorithms, Volume 63, Issue 1

Pages 107 - 126

https://doi.org/10.1007/s11075-012-9614-6

Published: 01 May 2013 Publication History

Abstract

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 current state-of-the-art of the MFDM solution approach as well as 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.

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Cited By

Jaśkowiec JMilewski S(2023)Coupling finite element method with meshless finite difference method by means of approximation constraintsComputers & Mathematics with Applications10.1016/j.camwa.2023.04.037142:C(208-224)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1016/j.camwa.2023.04.037
Slak JKosec G(2021)MedusaACM Transactions on Mathematical Software10.1145/345096647:3(1-25)Online publication date: 26-Jun-2021
https://dl.acm.org/doi/10.1145/3450966
Kużelewski AZieniuk E(2021)The FMM accelerated PIES with the modified binary tree in solving potential problems for the domains with curvilinear boundariesNumerical Algorithms10.1007/s11075-020-01066-688:3(1025-1050)Online publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1007/s11075-020-01066-6
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Selected computational aspects of the meshless finite difference method
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation

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cover image Numerical Algorithms

Numerical Algorithms Volume 63, Issue 1

May 2013

209 pages

ISSN:1017-1398

Issue’s Table of Contents

Copyright © Copyright © 2013 Springer Science+Business Media New York.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 May 2013

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Cited By

Jaśkowiec JMilewski S(2023)Coupling finite element method with meshless finite difference method by means of approximation constraintsComputers & Mathematics with Applications10.1016/j.camwa.2023.04.037142:C(208-224)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1016/j.camwa.2023.04.037
Slak JKosec G(2021)MedusaACM Transactions on Mathematical Software10.1145/345096647:3(1-25)Online publication date: 26-Jun-2021
https://dl.acm.org/doi/10.1145/3450966
Kużelewski AZieniuk E(2021)The FMM accelerated PIES with the modified binary tree in solving potential problems for the domains with curvilinear boundariesNumerical Algorithms10.1007/s11075-020-01066-688:3(1025-1050)Online publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1007/s11075-020-01066-6
Milewski S(2020)A Matlab software for approximate solution of 2D elliptic problems by means of the meshless Monte Carlo random walk methodNumerical Algorithms10.1007/s11075-019-00694-x83:2(565-591)Online publication date: 1-Feb-2020
https://dl.acm.org/doi/10.1007/s11075-019-00694-x
Rter MChen J(2017)An enhanced-strain error estimator for Galerkin meshfree methods based on stabilized conforming nodal integrationComputers & Mathematics with Applications10.1016/j.camwa.2017.06.05274:9(2144-2171)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1016/j.camwa.2017.06.052
Jakowiec JMilewski S(2016)Coupling finite element method with meshless finite difference method in thermomechanical problemsComputers & Mathematics with Applications10.5555/3044216.304434972:9(2259-2279)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.5555/3044216.3044349
Jaśkowiec JMilewski S(2015)The effective interface approach for coupling of the FE and meshless FD methods and applying essential boundary conditionsComputers & Mathematics with Applications10.1016/j.camwa.2015.06.02070:5(962-979)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1016/j.camwa.2015.06.020

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