Iterative solvers for 3D linear and nonlinear elasticity problems: Displacement and mixed formulations |
| |
Authors: | Abderrahman El maliki Michel Fortin Nicolas Tardieu André Fortin |
| |
Affiliation: | 1. GIREF, Département de mathématiques et de statistique, Pavillon Vachon, 1045 Avenue de la médecine, Université Laval, Qué., Canada G1V 0A6;2. LaMSID, UMR EDF/CNRS 2832, 1 avenue du Général de Gaulle, F‐92140 Clamart, France |
| |
Abstract: | 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. |
| |
Keywords: | hierarchical quadratic basis hierarchical preconditioner linear and nonlinear elasticity mixed formulation block symmetric indefinite preconditioner conjugate gradient‐like methods |
|
|