scholarly journals Equivalence of Finite Elements for Nearly Incompressible Elasticity

1977 ◽  
Vol 44 (1) ◽  
pp. 181-183 ◽  
Author(s):  
T. J. R. Hughes
Keyword(s):  
Finite Elements ◽  
Incompressible Elasticity ◽  
Nearly Incompressible Elasticity

scholarly journals Isogeometric Collocation: A Mixed Displacement-Pressure Method for Nearly Incompressible Elasticity

2021 ◽  
Vol 129 (1) ◽  
pp. 1-26
Author(s):  
S. Morganti ◽  
F. Fahrendorf ◽  
L. De Lorenzis ◽  
J. A. Evans ◽  
T. J. R. Hughes ◽  
...  
Keyword(s):  
Pressure Method ◽  
Incompressible Elasticity ◽  
Nearly Incompressible Elasticity

Preconditioning Methods for the Penalty Function FEM Discretizations of 3D Nearly Incompressible Elasticity Problems

2016 ◽  
Vol 13 (05) ◽  
pp. 1650029
Author(s):  
Yingxiong Xiao ◽  
Zhenyou Li ◽  
Lei Zhou
Keyword(s):  
Penalty Function ◽  
Mixed Boundary ◽  
Fem Analysis ◽  
Three Dimensions ◽  
Preconditioned Conjugate Gradient ◽  
System Of Equations ◽  
Elasticity Problems ◽  
Overall Efficiency ◽  
Incompressible Elasticity ◽  
Nearly Incompressible Elasticity

Penalty function finite element method (FEM) is an efficient method for the solution of the nearly incompressible elasticity problems in three dimensions. In order to improve the overall efficiency, some faster solvers for the corresponding FEM system of equations must be presented. Since the resulting system of equations is symmetric positive definite and highly ill-conditioned, the preconditioned conjugate gradient (PCG) method is one of the most efficient methods for solving such FEM equations. In this paper, we have first presented some types of efficient PCG methods including [Formula: see text]-PCG and [Formula: see text]-PCG with two different block diagonal inverses as a preconditioner, respectively, and including the RS-GAMG-PCG based on the global matrix for the penalty function FEM equations of three-dimensional (3D) nearly incompressible elasticity problems with mixed boundary conditions. Furthermore, we apply these methods to the solution of the penalty function quadratic discretizations for the cantilever and the Cook’s membrane problems. The numerical results have shown that much more efficient PCG methods for 3D nearly incompressible problems can be obtained by using the known information that is easily available in most FEM applications, for instance, the type of the partial differential equations (PDEs) considered and the number of physical unknowns residing in each grid, and by combining the coarsening techniques used in the classic algebraic multigrid (AMG) method. This will greatly improve the overall efficiency of the penalty function FEM analysis.

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