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

被引：2

作者：

Benamou, J. -D. ^{[1
]}

Collino, F. ^{[2
]}

Marmorat, S. ^{[1
]}

机构：

[1] INRIA, Domaine De Voluceau, Rocquencourt, France

[2] CERFACS, F-31057 Toulouse, France

来源：

ASYMPTOTIC ANALYSIS | 2013年 / 83卷 / 1-2期

关键词：

plane waves; point source; inverse scattering; FAST MULTIPOLE METHOD; SCATTERING PROBLEMS; TRUNCATION; DISCOVERY;

D O I：

10.3233/ASY-121157

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：157 / 187

页数：31

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