A preconditioning technique for a class of PDE-constrained optimization problems
type: Item
instance of: scholarly article
title: A preconditioning technique for a class of PDE-constrained optimization problems
zbMATH Open document ID: 1293.65041
author: Michele Benzi
author: Eldad Haber
author: Lauren Taralli
published in: Advances in Computational Mathematics
publication date: 2011-12-14T00:00:00Z
review text: A preconditioning technique for the linear equations resulting in the application of the inexact Newton method to the solution of discretized PDE constrained optimization problems is presented. The block triangular preconditioner \(P\) is based on a perturbed version of the Gauß-Newton Hessian. \(P\) is used as preconditioner for FGMRES. The Schur complement systems arising in the inversion of \(P\) are solved by a PCG method with ML smoothed aggregation AMG as preconditioner. For numerical experiments, a simplified version of the Monge-Kantorovich mass transfer problem involving a hyperbolic PDE constraint is investigated. The inexact Newton method converges rapidly, the number of FGMRES iterations is low, even in the case where the solutions of the Schur complement systems are only approximated with low relative accuracy. The computational effort does not scale well with the problem size, due to some problems going back to the ML preconditioner. Nevertheless, the new approach seems to be competitive in comparison to reduced-Hessian based methods.
reviewed by: Martin Reißel
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49M05
Mathematics Subject Classification ID: 65F22
zbMATH DE Number: 5988495
zbMATH Keywords: preconditioning
zbMATH Keywords: Krylov subspace method
zbMATH Keywords: saddle point
zbMATH Keywords: PDE constrained optimization
zbMATH Keywords: Monge-Kantorovich problem
describes a project that uses: Trilinos
describes a project that uses: ML
MaRDI profile type: Publication
full work available at URL: s10444-011-9173-8
OpenAlex ID: W2050959344
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DOI: 10.1007/S10444-011-9173-8
description: scientific article; zbMATH DE number 5988495