Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Vestnik YuUrGU. Ser. Mat. Model. Progr.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2023, Volume 16, Issue 3, Pages 35–50
DOI: https://doi.org/10.14529/mmp230303 (Mi vyuru693) 		 
Programming & Computer Software

Development and verification of a simplified hp-version of the least-squares collocation method for irregular domains

L. S. Bryndinab, V. A. Belyaeva, V. P. Shapeeva

a Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russian Federation
b Novosibirsk State University, Novosibirsk, Russian Federation
Full-text PDF (381 kB)
References:
PDF
HTML
DOI: https://doi.org/10.14529/mmp230303
Abstract: A new high-precision hp-version of the least-squares collocation method (hp-LSCM) for the numerical solution of elliptic problems in irregular domains is proposed, implemented, and verified. We use boundary irregular cells (i-cells) cut off from the cells of a rectangular grid by a boundary domain and their external parts for writing the collocation and matching equations in constructing an approximate solution. A separate solution is not constructed in small and (or) elongated non-independent i-cells. The solution is continued from neighboring independent cells, in which the outer (and inner in a multiply-connected domain) part of the domain boundary contained in these non-independent i-cells is used to write the boundary conditions. This approach significantly simplifies the computer implementation of the developed hp-LSCM in comparison with the previous well-recommended version without losing its efficiency. We show reducing the overdetermination ratio of a system of linear algebraic equations in comparison with its values in the traditional versions of LSCM when solving a biharmonic equation. The results are compared with those of other papers with a demonstration of the advantages of the new technique. We present the results of bending calculations of annular plates of various thicknesses in the framework of the Kirchhoff–Love and Reissner–Mindlin theories using hp-LSCM without shear locking.
Keywords: least-squares collocation method, Kirchhoff–Love theory, Reissner–Mindlin theory, biharmonic equation, irregular domain.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation
Received: 13.03.2023
Document Type: Article
UDC: 519.635.1+519.632.4+539.3
MSC: 35J40, 35J25, 35Q74
Language: Russian
Citation: L. S. Bryndin, V. A. Belyaev, V. P. Shapeev, “Development and verification of a simplified hp-version of the least-squares collocation method for irregular domains”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 16:3 (2023), 35–50
Citation in format AMSBIB
\Bibitem{BryBelSha23}
\by L.~S.~Bryndin, V.~A.~Belyaev, V.~P.~Shapeev
\paper Development and verification of a simplified hp-version of the least-squares collocation method for irregular domains
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2023
\vol 16
\issue 3
\pages 35--50
\mathnet{http://mi.mathnet.ru/vyuru693}
\crossref{https://doi.org/10.14529/mmp230303}
Linking options:
  • https://www.mathnet.ru/eng/vyuru693
  • https://www.mathnet.ru/eng/vyuru/v16/i3/p35
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:35
    Full-text PDF :14
    References:7
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024