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An Algebraic Multigrid Method for Compressible and Nearly Incompressible Elasticity Problem in Two Dimensions

Author: OuYangZuo
Tutor: ShuShi
School: Xiangtan University
Course: Computational Mathematics
Keywords: Locking phenomena High Two-level approach Polished operator Reduced integration
CLC: O241.82
Type: Master's thesis
Year: 2008
Downloads: 24
Quote: 1
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Abstract


This paper studies the two-dimensional elastic pressure and almost incompressible algebraic multigrid (AMG) based on the part geometry and analysis information law . First , the study of the phenomenon of elastic material self-locking (Locking) \Then , for the two-dimensional elastic pressure problem four finite element equation , the two - level method node basis function compactly supported , algebraic criterion to establish a correspondence between certain decision variable indicators belongs geometry node type . Based on these results , four times per node basis function algebra to solve linear per - node basis function , said the key problem . Further select different polished sub ??, such as Gauss-Seidel (GS) and a special block of the Gauss- Seidel ( LBGS ) iteration to obtain the two - level method of finite element equation solving four TL-GS and TL- LBGS law . TL-GS method for rigorous theoretical analysis prove its convergence with the elastic modulus E grid scale h and Poisson's ratio ν independent conclusions. Numerical experiments show that the new method of solving the elastic pressure (ν ≤ 04) four finite element equation has good computational efficiency and robustness than classic AMG law has obvious advantages . In addition , numerical experiments verify the the TL-LBGS largely reduced p TL-GS convergence . Finally , for the two-dimensional elastic almost incompressible problem ( ν → 0.5 ) four finite element equations using reduced integration scheme to construct a coarse level matrix rigidity reduced , and then select different polished sub ??design a few species suitable for solving the the nearly incompressible two - level method . Further , by calling the the existing AMG law quickly solving the coarse level equations ( linear element equations ) , so as to establish the method of solving finite element equations of the four AMG numerical results show that , based on reduced integration scheme AMG method for solving almost impossible the pressure elastic four finite element equations efficiency has been greatly improved .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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