A group-theoretic approach to computational bifurcation problems with symmetry
type: Item
instance of: scholarly article
title: A group-theoretic approach to computational bifurcation problems with symmetry
zbMATH Open document ID: 0668.73041
DOI: 10.1016/0045-7825(88)90049-7
author: Timothy J. Healey
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1988-01-01T00:00:00Z
review text: The author presents a group-theoretic approach to the computation of global solution branches, limit points, and bifurcation points of parameter-dependent equations of the form (1) \(f(u,\lambda)={\mathbb{O}}\), where f: \({\mathbb{R}}^ n\times {\mathbb{R}}\to {\mathbb{R}}^ n\) is a smooth, vector-valued function possessing some equivariance properties, \(u\in {\mathbb{R}}^ n\) is the vector of the state variables, and \(\lambda\in {\mathbb{R}}\) is some parameter. The basic idea consists in reducing problem (1) on the basis of the equivariance properties observed. Afterwards the reduced problems can be analyzed by standard methods. The author impressively demonstrates the efficiency of his technique in analyzing a lattice-dome structure with hexagonal symmetry in detail.
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 74Kxx
Mathematics Subject Classification ID: 74A99
Mathematics Subject Classification ID: 58E07
zbMATH DE Number: 4094951
zbMATH Keywords: group invariance
zbMATH Keywords: global solution branches
zbMATH Keywords: limit points
zbMATH Keywords: bifurcation points
zbMATH Keywords: parameter-dependent equations
zbMATH Keywords: equivariance properties
zbMATH Keywords: lattice- dome structure
zbMATH Keywords: hexagonal symmetry
reviewed by: Ulrich Langer
MaRDI profile type: Publication
full work available at URL: 0045-7825(88)90049-7
OpenAlex ID: W1988010545
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description: scientific article; zbMATH DE number 4094951