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

Article type: Research Article

Authors: Benamou, J.-D.^; | Collino, F. | Marmorat, S.

Affiliations: INRIA, Domaine de Voluceau, Rocquencourt, France. E-mail: Jean-david.Benamou@inria.fr | CERFACS, Toulouse, France

Note: [] Corresponding author: J.-D. Benamou, INRIA, Domaine de Voluceau, Rocquencourt, France. E-mail: Jean-david. Benamou@inria.fr

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.

Keywords: plane waves, point source, inverse scattering

DOI: 10.3233/ASY-121157

Journal: Asymptotic Analysis, vol. 83, no. 1-2, pp. 157-187, 2013