A factorization method for the inverse scattering of the wave equation

Pekka Tietäväinen

A factorization method for the inverse scattering of the wave equation

Julkaisun otsikon käännös: A factorization method for the inverse scattering of the wave equation

Pekka Tietäväinen

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Doctoral Thesis › Monograph

Abstrakti

In this work the reconstruction problem of the scattering of the wave equation is considered. Our approach is to start from Colton-Kirch factorization method, derive a similar method for the time harmonic Robin problem, and use this to create a reconstruction for the wave equation. The new results presented in this work are the factorization reconstruction method for the time harmonic Robin scattering; the error limits that predict the trustworthiness of this reconstruction for various frequencies; and the factorization for the scattering of the wave equation, which includes two tests to determine whether a point is located in the scatterer.

Julkaisun otsikon käännös	A factorization method for the inverse scattering of the wave equation
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Nevanlinna, Olavi, Vastuuprofessori Lassas, Matti, Ohjaaja, Ulkoinen henkilö
Kustantaja	Aalto University
Painoksen ISBN	978-952-60-4232-9
Sähköinen ISBN	978-952-60-4233-6
Tila	Julkaistu - 2011
OKM-julkaisutyyppi	G4 Monografiaväitöskirja

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http://urn.fi/URN:ISBN:978-952-60-4233-6

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title = "A factorization method for the inverse scattering of the wave equation",

abstract = "In this work the reconstruction problem of the scattering of the wave equation is considered. Our approach is to start from Colton-Kirch factorization method, derive a similar method for the time harmonic Robin problem, and use this to create a reconstruction for the wave equation. The new results presented in this work are the factorization reconstruction method for the time harmonic Robin scattering; the error limits that predict the trustworthiness of this reconstruction for various frequencies; and the factorization for the scattering of the wave equation, which includes two tests to determine whether a point is located in the scatterer.",

keywords = "inverse problems, factorization, Robin boundary conditions, wave equation, Helmholtz equation, scattering, inverse problems, factorization, Robin boundary conditions, wave equation, Helmholtz equation, scattering",

author = "Pekka Tiet{\"a}v{\"a}inen",

year = "2011",

language = "English",

isbn = "978-952-60-4232-9",

series = "Aalto University publication series DOCTORAL DISSERTATIONS",

publisher = "Aalto University",

number = "66",

address = "Finland",

school = "Aalto University",

}

TY - BOOK

T1 - A factorization method for the inverse scattering of the wave equation

AU - Tietäväinen, Pekka

PY - 2011

Y1 - 2011

N2 - In this work the reconstruction problem of the scattering of the wave equation is considered. Our approach is to start from Colton-Kirch factorization method, derive a similar method for the time harmonic Robin problem, and use this to create a reconstruction for the wave equation. The new results presented in this work are the factorization reconstruction method for the time harmonic Robin scattering; the error limits that predict the trustworthiness of this reconstruction for various frequencies; and the factorization for the scattering of the wave equation, which includes two tests to determine whether a point is located in the scatterer.

AB - In this work the reconstruction problem of the scattering of the wave equation is considered. Our approach is to start from Colton-Kirch factorization method, derive a similar method for the time harmonic Robin problem, and use this to create a reconstruction for the wave equation. The new results presented in this work are the factorization reconstruction method for the time harmonic Robin scattering; the error limits that predict the trustworthiness of this reconstruction for various frequencies; and the factorization for the scattering of the wave equation, which includes two tests to determine whether a point is located in the scatterer.

KW - inverse problems

KW - factorization

KW - Robin boundary conditions

KW - wave equation

KW - Helmholtz equation

KW - scattering

KW - inverse problems

KW - factorization

KW - Robin boundary conditions

KW - wave equation

KW - Helmholtz equation

KW - scattering

M3 - Doctoral Thesis

SN - 978-952-60-4232-9

T3 - Aalto University publication series DOCTORAL DISSERTATIONS

PB - Aalto University

ER -

A factorization method for the inverse scattering of the wave equation

Abstrakti

Pääsy asiakirjaan

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