ePubs
The open archive for STFC research publications
Home
About ePubs
Content Policies
News
Help
Privacy/Cookies
Suggest an Enhancement
Contact ePubs
Full Record Details
DOI
10.5286/raltr.2008018
Persistent URL
http://purl.org/net/epubs/work/43760
Record Status
Checked
Record Id
43760
Title
Optimal solvers for PDE-constrained optimization
Contributors
T Rees (Oxford U. Computing Lab)
,
HS Dollar (STFC Rutherford Appleton Lab.)
,
AJ Wathen (Oxford U. Computing Lab)
Abstract
Optimization problems with constraints which require the solution of a partial differential equation arise widely in many areas of the sciences and engineering, in particular in problems of design. The solution of such PDE-constrained optimization problems is usually a major computational task. Here we consider simple problems of type: distrubuted control problems in which the 2- and 3-dimensional Poisson problem is the PDE. The large dimensional linear systems which result from discretization and which need to be solved are of saddle-point type. We introduce two optimal preconditioners for these systems which lead to convergence of symmetric Krylov subspace iterative methods in a number of iterations which does not increase with the dimension of the discrete problem. These preconditioners are block structured and involve standard multigrid cycles. The optimality of the preconditioned iterative solver is proved theoretically and verified computationally in several test cases/ The theoretical proof indicates that these approaches may have much broader applicability for other partial differential equations.
Organisation
CSE
,
CSE-NAG
,
STFC
Keywords
PDE-constrained optimization
,
optimal control
,
linear systems
,
preconditioning
,
saddle-point problems
,
all-at-once methods
Funding Information
Related Research Object(s):
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Report
RAL Technical Reports
RAL-TR-2008-018. STFC, 2008.
rdwRAL2008018.pdf
2008
Showing record 1 of 1
Recent Additions
Browse Organisations
Browse Journals/Series
Login to add & manage publications and access information for OA publishing
Username:
Password:
Useful Links
Chadwick & RAL Libraries
SHERPA FACT
SHERPA RoMEO
SHERPA JULIET
Journal Checker Tool
Google Scholar