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Iterative solvers for 3D linear and nonlinear elasticity problems: Displacement and mixed formulations
Author(s) -
El maliki Abderrahman,
Fortin Michel,
Tardieu Nicolas,
Fortin André
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2894
Subject(s) - preconditioner , discretization , finite element method , linear elasticity , krylov subspace , mathematics , iterative method , elasticity (physics) , linear system , nonlinear system , quadratic equation , mathematical optimization , mathematical analysis , geometry , structural engineering , materials science , physics , quantum mechanics , engineering , composite material
We present new iterative solvers for large‐scale linear algebraic systems arising from the finite element discretization of the elasticity equations. We focus on the numerical solution of 3D elasticity problems discretized by quadratic tetrahedral finite elements and we show that second‐order accuracy can be obtained at very small overcost with respect to first‐order (linear) elements. Different Krylov subspace methods are tested on various meshes including elements with small aspect ratio. We first construct a hierarchical preconditioner for the displacement formulation specifically designed for quadratic discretizations. We then develop efficient tools for preconditioning the 2 × 2 block symmetric indefinite linear system arising from mixed (displacement‐pressure) formulations. Finally, we present some numerical results to illustrate the potential of the proposed methods. Copyright © 2010 John Wiley & Sons, Ltd.