A goal-oriented reduced basis method for the wave equation in inverse analysis
Abstract
In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with affine 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 spanned by the reduced basis functions which are constructed from the solutions of the governing partial differential 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 basis functions. Third, based on the assumption of affine parameter dependence, we use the offline-online computational procedures developed earlier to split the computational procedure into offline and online stages. We verify the proposed computational procedure by applying it to a three-dimensional simulation dental implant problem. The good numerical results show that our proposed procedure performs better than the standard POD--Greedy procedure in terms of the accuracy of output functionals.
Cite
@article{arxiv.1305.3519,
title = {A goal-oriented reduced basis method for the wave equation in inverse analysis},
author = {Khac Chi Hoang and Pierre Kerfriden and Stephane P. A. Bordas},
journal= {arXiv preprint arXiv:1305.3519},
year = {2013}
}