[en] In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with a ne parameter dependence. The essential new ingredient is the dual (or adjoint) problem and the use of its solution in a sampling procedure to pick up “goal-orientedly” parameter samples. First, we introduce the reduced-basis recipe — Galerkin projection onto a space YN spanned by the reduced basis functions which are constructed from the solutions of the governing partial di erential equation at several selected points in parameter space. Second, we propose a new “goal-oriented” Proper Orthogonal Decomposition (POD)–Greedy sampling procedure to construct these associated ba-sis functions. Third, based on the assumption of a ne parameter dependence, we use the o ine-online computational procedures developed earlier to split the computational procedure into o ine and online stages. We verify the proposed computational procedure by applying it to a three-dimensional simulation dental implant problem. The good numeri-cal results show that our proposed procedure performs better than the standard POD–Greedy procedure in terms of the accuracy of output functionals.
Research center :
Institute of Mechanics and Advanced Materials, Cardiff University
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Hoang, Khac Chi
Kerfriden, Pierre
Bordas, Stéphane ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Language :
English
Title :
A goal-oriented reduced basis method for the wave equation in inverse analysis
Publication date :
March 2013
Event name :
International Conference on Computational Mechanics (CM13)
Event organizer :
Durham University and the UK Association of Computational Mechanics in Engineering (ACME)
Event place :
Durham, United Kingdom
Event date :
25-27 March 2013
By request :
Yes
Audience :
International
Main work title :
International Conference on Computational Mechanics CM13 Proceedings
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