Parallel multilevel solution of nonlinear shell structures
type: Item
instance of: scholarly article
title: Parallel multilevel solution of nonlinear shell structures
zbMATH Open document ID: 1097.74057
author: E. Ramm
author: Wolfgang A. Wall
author: Michael W. Gee
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2006-03-08T00:00:00Z
review text: Thin-walled-structures discretized by finite elements lead to ill-conditioned matrices, and therefore the performance of iterative solvers is generally poor. This situation further deteriorates when the thickness change of the shell is taken into account. Here a preconditioner for this challenging class of problems is presented combining two approaches in a parallel framework. The first approach is a mechanically motivated improvement called `scaled director conditioning' (SDC), and is able to remove the extra-ill conditioning that appears with three-dimensional shell formulations as compared to formulations that neglect thickness change of the shell. It is introduced at the element level and harmonizes well with the second approach utilizing a multilevel algorithm. The authors demonstrate that shell models based on relative displacements including thickness change beside their numerous advantages tend to be even worse conditioned than those based on rotational degrees of freedom. It is shown that this parametrization-dependent disadvantage of three-dimensional models can be eliminated by the scaled director conditioning approach. This means that the `spectral gap' between different models can easily be closed. The SDC approach is introduced into a three-dimensional, geometrically and materially nonlinear shell formulation and is applied along with a hybrid finite element discretization. The SDC approach is combined with a semi-algebraic multilevel preconditioner based on an aggregation concept. The combination of the two methods results in a stable iterative solution process capable of achieving good performance for a wide range of large-scale problems in nonlinear shell dynamics and statics.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K25
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 5009883
zbMATH Keywords: preconditioning
zbMATH Keywords: iterative solvers
zbMATH Keywords: scaled director conditioning
reviewed by: V. L. Leontiev
describes a project that uses: AztecOO
describes a project that uses: Aztec
MaRDI profile type: Publication
full work available at URL: j.cma.2004.07.043
OpenAlex ID: W2019861110
cites work: A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation
cites work: On the physical significance of higher-order kinematic and static variables in a three-dimensional shell formulation
cites work: Nonlinear shell formulations for complete three-dimensional constitutive laws including composites and laminates
cites work: A black-box iterative solver based on a two-level Schwarz method
cites work: Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept
cites work: A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method
cites work: Domain Decomposition Algorithms with Small Overlap
cites work: Q4240328
cites work: Generalized Aggregation Multilevel solver
cites work: Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element
cites work: Nonlinear finite element analysis of shells. I. Three-dimensional shells
cites work: Nonlinear finite element analysis of shells. II. Two-dimensional shells
cites work: Energy optimization of algebraic multigrid bases
cites work: Q4254887
cites work: Parallel iterative solvers in nonlinear shell analysis
cites work: On a stress resultant geometrically exact shell model. IV: Variable thickness shells with through-the-thickness stretching
cites work: A class of mixed assumed strain methods and the method of incompatible modes
cites work: Q4716273
cites work: Convergence of algebraic multigrid based on smoothed aggregation
cites work: Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
DOI: 10.1016/J.CMA.2004.07.043
description: scientific article; zbMATH DE number 5009883