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SIAM Journal on Scientific Computing
Article . 2006 . Peer-reviewed
Data sources: Crossref
DBLP
Article . 2006
Data sources: DBLP
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A Numerical Study of the Probe Method

Authors: Klaus Erhard; Roland Potthast;

A Numerical Study of the Probe Method

Abstract

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source $\Phi(\cdot,z)$ with source point z to define an indicator function $\hat{I}(z)$ which can be reconstructed from Cauchy data or far field data. The indicator function $\hat{I}(z)$ can be shown to blow off when the source point z tends to the boundary $\partial D$, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
16
Average
Top 10%
Top 10%
Green