Numerical Microlocal analysis of 2-D noisy harmonic plane and circular waves

Abstract : We present a mathematical and numerical analysis of the stability and accuracy of the NMLA (Numerical MicroLocal Analysis) method [J. Comput. Phys. 199(2) (2004), 717-741] and its discretization.We restrict to homogeneous space and focus on the two simplest cases: (1) Noisy plane wave packets, (2) Noisy point source solutions. A stability result is obtained through the introduction of a new "impedance" observable. The analysis of the point source case leads to a modified second order (curvature dependent) correction of the algorithm. Since NMLA is local, this second order improved version can be applied to general data (heterogeneous media). See [J. Comput. Phys. 231(14) (2012), 4643-4661] for a an application to a source discovery inverse problem.
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Submitted on : Tuesday, January 28, 2014 - 5:06:47 PM
Last modification on : Thursday, February 7, 2019 - 5:49:37 PM

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Jean-David Benamou, Francis Collino, Simon Marmorat. Numerical Microlocal analysis of 2-D noisy harmonic plane and circular waves. Asymptotic Analysis, IOS Press, 2013, 83 (1-2), pp.157--187. ⟨10.3233/ASY-121157⟩. ⟨hal-00937691⟩

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