Nonlinear preconditioned conjugate gradient and least-squares finite elements
type: Item
instance of: scholarly article
title: Nonlinear preconditioned conjugate gradient and least-squares finite elements
zbMATH Open document ID: 0633.65112
DOI: 10.1016/0045-7825(87)90020-X
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1987-01-01T00:00:00Z
review text: An extension of the authors' least-squares formulation for nonlinear first order systems of differential equations is presented. The similarity of the element matrices with the standard Galerkin approach is still retained. However, since the least-squares method is used, this formulation yields to a symmetric self-adjoint matrix. Since the solution scheme adopted is the nonlinear preconditioned conjugate gradient algorithm, a special preconditioner is constructed. The numerical analyses presented considers the steady inviscid compressible flow equation as model problems. Comparisons include element-by-element implementations of conjugate gradients and steep descent algorithms with several preconditioners as an iterative driver and nonlinear conjugate gradients. Although the authors' preconditioner is insensitive to the mesh size, the comparisons made seems to favour the Jacobi conjugate gradient iterative driver. However, the problems solved are still too small to clarify what is the best solution strategy.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 4030909
zbMATH Keywords: nonlinear first order systems
zbMATH Keywords: least-squares method
zbMATH Keywords: nonlinear preconditioned
zbMATH Keywords: steady inviscid compressible flow equation
zbMATH Keywords: Comparisons
zbMATH Keywords: steep descent algorithms
author: Graham F. Carey
author: Bo-Nan Jiang
reviewed by: N. F. F. Ebecken
MaRDI profile type: Publication
cites work: Q4171541
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full work available at URL: 0045-7825(87)90020-x
OpenAlex ID: W2077588135
description: scientific article; zbMATH DE number 4030909