Sampling type methods for an inverse waveguide problem

Peter Monk; Virginia Selgas

doi:10.3934/ipi.2012.6.709

Article Contents

2012, Volume 6, Issue 4: 709-747. Doi: 10.3934/ipi.2012.6.709

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Sampling type methods for an inverse waveguide problem

Peter Monk^1, and
Virginia Selgas^2,

1.
Department of Mathematics, University of Delaware, Newark, DE 19716
2.
Departamento de Matemáticas, Escuela Politécnica de Ingeniería de Gijón, Universidad de Oviedo, 33203 Gijón

Received: October 31, 2011

Revised: July 31, 2012

Published: October 2012

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Abstract

We consider the problem of locating a penetrable obstacle in an acoustic waveguide from measurements of pressure waves due to point sources inside the waveguide. More precisely, we assume that we are given the scattered field and its normal derivative for any source point and receiver placed on a pair of surfaces known as the source and the measurement surfaces, respectively. A novel feature of this work is that the obstacle is allowed to touch the boundary of the pipe.
We first analyze the associated interior transmission problem. Then, we adapt and analyze the Reciprocity Gap Method (RGM) and the Linear Sampling Method (LSM) to deal with the inverse problem. We also study the relationship between these two methods and provide numerical results.

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Mathematics Subject Classification: 65N21, 74F10.

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