Conditioning analysis of separate displacement preconditioners for some nonlinear elasticity systems

Authors:
O. Axelsson;J. Karátson
Affiliations:
Department of Mathematics, University of Nijmegen, 6525ED Nijmegen, The Netherlands;Department of Applied Analysis, ELTE University, H-1053 Budapest, Hungary
Venue:
Mathematics and Computers in Simulation
Year:
2004

Citing 11
Cited 1

On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations

Advances in Applied Mathematics
Equivalence of finite element methods for problems in elasticity

SIAM Journal on Numerical Analysis
A domain-decomposed solver for nonlinear elasticity

Computer Methods in Applied Mechanics and Engineering
Iterative solution methods

Iterative solution methods
Korn's inequalities and their applications in continuum mechanics

SIAM Review
Minimum Residual Adaptive Multilevel Finite Element Procedure for the Solution of Nonlinear Stationary Problems

SIAM Journal on Numerical Analysis
Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables
On iterative solvers in structural mechanics; separate displacement orderings and mixed variable methods

Mathematics and Computers in Simulation - Special issue from IMACS sponsored conference: “Modelling '98”
Multilevel algorithms for 3D simulation of nonlinear elasticity problems

Mathematics and Computers in Simulation - Special issue from IMACS sponsored conference: “Modelling '98”
Computer Solution of Large Sparse Positive Definite

Computer Solution of Large Sparse Positive Definite
Iteration number for the conjugate gradient method

Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics

Mesh Independent Convergence Rates Via Differential Operator Pairs

Large-Scale Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Separate displacement preconditioners are studied in the context of outer-inner iterations for a model in 3D nonlinear elasticity. Such a preconditioner, already known to be efficient for linear models, arises as the discretization of three independent Laplacian operators. In this paper the resulting condition number is investigated with focus on independence of parameters. Estimates are given which show that the condition number is uniformly bounded w.r.t. both the studied Newton iterate and the chosen discretization. Finally, it is sketched that ill-conditioning caused by nearly incompressible material parameters can be handled by a suitable mixed formulation.