Reference : A goal-oriented reduced basis method for the wave equation in inverse analysis
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A goal-oriented reduced basis method for the wave equation in inverse analysis
Hoang, Khac Chi mailto []
Kerfriden, Pierre mailto []
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
International Conference on Computational Mechanics CM13 Proceedings
International Conference on Computational Mechanics (CM13)
25-27 March 2013
Durham University and the UK Association of Computational Mechanics in Engineering (ACME)
United Kingdom
[en] second-order hyperbolic partial di ; reduced basis method ; goal-oriented estimates ; dual problem ; adjoint problem ; POD–Greedy algorithm
[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.
Institute of Mechanics and Advanced Materials, Cardiff University
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