Volume 47, Number 6, November-December 2013
|Page(s)||1821 - 1843|
|Published online||07 October 2013|
A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation
1 Inria Saclay
Ile-de-France, Palaiseau, France.
2 Inria Paris-Rocquencourt, Le Chesnay, France.
3 Université Paris 6, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France.
4 CETMEF, Margny-les-Compiègne, France.
We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some a priori error estimates controlled by the POD remainder – in the construction procedure – and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the FitzHugh − Nagumo 1D model. Finally, we give detailed illustrations of the approach in two parameter estimation applications, the first in a variational estimation framework with the FitzHugh − Nagumo model, and the second with a beating heart mechanical model for which we employ a sequential estimation method to characterize model parameters using real image data in a clinical case.
Mathematics Subject Classification: 65M60 / 35A35 / 35B45 / 93E10
Key words: Proper Orthogonal Decomposition / parameter variations / estimation / FitzHugh − Nagumo equations / cardiac modeling
© EDP Sciences, SMAI 2013
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