Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

Mark Asch; Marion Darbas; Jean-Baptiste Duval

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 4, page 1016-1034
  • ISSN: 1292-8119

Abstract

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We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing the centers of the imperfections. Numerical results, in 2- and 3-D, show the robustness and accuracy of the approach for retrieving randomly placed imperfections from both complete and partial boundary measurements.

How to cite

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Asch, Mark, Darbas, Marion, and Duval, Jean-Baptiste. "Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume." ESAIM: Control, Optimisation and Calculus of Variations 17.4 (2011): 1016-1034. <http://eudml.org/doc/272830>.

@article{Asch2011,
abstract = {We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing the centers of the imperfections. Numerical results, in 2- and 3-D, show the robustness and accuracy of the approach for retrieving randomly placed imperfections from both complete and partial boundary measurements.},
author = {Asch, Mark, Darbas, Marion, Duval, Jean-Baptiste},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {wave equation; exact controllability; inverse problem; finite elements; Fourier inversion; conductivity imperfections; finite element solution; exact controllability method},
language = {eng},
number = {4},
pages = {1016-1034},
publisher = {EDP-Sciences},
title = {Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume},
url = {http://eudml.org/doc/272830},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Asch, Mark
AU - Darbas, Marion
AU - Duval, Jean-Baptiste
TI - Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2011
PB - EDP-Sciences
VL - 17
IS - 4
SP - 1016
EP - 1034
AB - We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing the centers of the imperfections. Numerical results, in 2- and 3-D, show the robustness and accuracy of the approach for retrieving randomly placed imperfections from both complete and partial boundary measurements.
LA - eng
KW - wave equation; exact controllability; inverse problem; finite elements; Fourier inversion; conductivity imperfections; finite element solution; exact controllability method
UR - http://eudml.org/doc/272830
ER -

References

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