DEVELOPMENT AND VERIFICATION OF A SIMPLIFIED HP-VERSION OF THE LEAST-SQUARES COLLOCATION METHOD FOR IRREGULAR DOMAINS

被引:0
|
作者
Bryndin, L. S. [1 ,2 ]
Belyaev, V. A. [1 ]
Shapeev, V. P. [1 ]
机构
[1] SB RAS, Khristianovich Inst Theoret & Appl Mech, Novosibirsk, Russia
[2] Novosibirsk State Univ, Novosibirsk, Russia
关键词
least-squares collocation method; Kirchhoff-Love theory; Reissner-Mindlin theory; biharmonic equation; irregular domain; EQUATIONS;
D O I
10.14529/mmp230303
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:35 / 50
页数:16
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