A New Convergent Algorithm to Approximate Potentials from Fixed Angle Scattering Data

Barceló Valcárcel, Juan Antonio and Castro Barbero, Carlos Manuel and Luque, Teresa and Vilela Bendaña, María de la Cruz (2019). A New Convergent Algorithm to Approximate Potentials from Fixed Angle Scattering Data. "SIAM Journal on Applied Mathematics (SIAP)", v. 79 (n. 6); pp. 2688-2691. ISSN 1095-712X. https://doi.org/10.1137/18M1172247.

Description

Title: A New Convergent Algorithm to Approximate Potentials from Fixed Angle Scattering Data
Author/s:
  • Barceló Valcárcel, Juan Antonio
  • Castro Barbero, Carlos Manuel
  • Luque, Teresa
  • Vilela Bendaña, María de la Cruz
Item Type: Article
Título de Revista/Publicación: SIAM Journal on Applied Mathematics (SIAP)
Date: 2019
ISSN: 1095-712X
Volume: 79
Subjects:
Freetext Keywords: Inverse Problem, Helmholtz Equation, Scattering
Faculty: E.T.S.I. Caminos, Canales y Puertos (UPM)
Department: Matemática e Informática Aplicadas a la Ingenierías Civil y Naval
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We introduce a new iterative method to recover a real compact supported potential of the Schödinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the resolvent of the Schödinger operator by partial sums associated to its Born series. The main interest is that, unlike other iterative methods in the literature, each iteration is explicit (and therefore faster computationally) and a rigorous analytical result on the convergence of the iterations is proved. This result requires potentials with small norm in certain Sobolev spaces. As an application we show some numerical experiments that illustrate this convergence.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2017-85934-C3-3-PUnspecifiedUnspecifiedAnálisis semiclásico y numérico, control y problemas inversos
Government of SpainMTM2014-53850-P2UnspecifiedUnspecifiedUnspecified
Government of SpainMTM2014-57769-C3-1-PUnspecifiedUnspecifiedAnálisis con aplicaciones a problemas inversos

More information

Item ID: 64188
DC Identifier: http://oa.upm.es/64188/
OAI Identifier: oai:oa.upm.es:64188
DOI: 10.1137/18M1172247
Official URL: https://epubs.siam.org/doi/abs/10.1137/19M1278508
Deposited by: Memoria Investigacion
Deposited on: 01 Oct 2020 12:59
Last Modified: 01 Oct 2020 17:01
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