A strategy to avoid ill-conditioned stars in the generalized finite difference method for solving one-dimensional problems

被引：4
作者：
Albuquerque-Ferreira, Augusto C. [1 ]
Urena, Miguel [2 ]
Ramos, Higinio [3 ]
机构：
[1] Univ Salamanca, Dept Comp Engn, Salamanca 37008, Spain
[2] Stat Spain INE, Madrid, Spain
[3] Univ Salamanca, Dept Appl Math, Salamanca, Spain
来源：
COMPUTATIONAL AND MATHEMATICAL METHODS | 2021年 / 3卷 / 06期
关键词：
fourth-order approximations; generalized finite difference method; ill-conditioned stars; parallel processing; SINGULAR-VALUE DECOMPOSITION; HEAT-CONDUCTION; SCHEME;
D O I：
10.1002/cmm4.1149
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we solve linear boundary value problems of second-order in ordinary differential equations with the generalized finite difference method and compare the numerical accuracy for different orders of approximations. We develop a strategy for dealing with ill-conditioned stars based on the condition number of the matrix of derivatives. In addition, we consider a scheme implemented with parallel processing for the formation of the stars and the calculation of the derivatives. We present some examples with high gradients in irregular discretizations exaggerated on purpose, to highlight the efficiency of the proposed strategy.
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页数：12
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共 31 条
  • [1] A singular-value decomposition (SVD)-based generalized finite difference (GFD) method for close-interaction moving boundary flow problems
    Ang, S. J.
    Yeo, K. S.
    Chew, C. S.
    Shu, C.
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 76 (12) : 1892 - 1929
  • [2] [Anonymous], 2012, NUMERICAL TREATMENT
  • [3] A posteriori error estimator and indicator in generalized finite differences.: Application to improve the approximated solution of elliptic PDEs
    Benito, J. J.
    Urena, F.
    Gavete, L.
    Alonso, B.
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2008, 85 (3-4) : 359 - 370
  • [4] On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using Generalized Finite Differences
    Benito, J. J.
    Garcia, A.
    Gavete, L.
    Negreanu, M.
    Urena, F.
    Vargas, A. M.
    [J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2020, 113 : 181 - 190
  • [5] An h-adaptive method in the generalized finite differences
    Benito, JJ
    Ureña, F
    Gavete, L
    Alvarez, R
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2003, 192 (5-6) : 735 - 759
  • [6] Influence of several factors in the generalized finite difference method
    Benito, JJ
    Ureña, F
    Gavete, L
    [J]. APPLIED MATHEMATICAL MODELLING, 2001, 25 (12) : 1039 - 1053
  • [7] An efficient way to assemble finite element matrices in vector languages
    Cuvelier, Francois
    Japhet, Caroline
    Scarella, Gilles
    [J]. BIT NUMERICAL MATHEMATICS, 2016, 56 (03) : 833 - 864
  • [8] Reduced-order strategy for meshless solution of plate bending problems with the generalized finite difference method
    Ferreira, Augusto Cesar Albuquerque
    Vieira Ribeiro, Paulo Marcelo
    [J]. LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES, 2019, 16 (01)
  • [9] Forsythe George E, 1960, Partial Differential, P5
  • [10] A note on the dynamic analysis using the generalized finite difference method
    Gavete, L.
    Urena, F.
    Benito, J. J.
    Salete, E.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 252 : 132 - 147
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