Issue |
ESAIM: COCV
Volume 2, 1997
|
|
---|---|---|
Page(s) | 307 - 327 | |
DOI | https://doi.org/10.1051/cocv:1997110 | |
Published online | 15 August 2002 |
The BC-method in Multidimensional Spectral Inverse Problem: Theory and Numerical Illustrations
1
belishev@pdmi.ras.ru
2
gotlib@io.spb.su
3
Sergei.Ivanov@pobox.spbu.ru
This work is devoted to numerical experiments for multidimensional Spectral Inverse Problems. We check the efficiency of the algorithm based on the BC-method, which exploits relations between Boundary Control Theory and Inverse Problems. As a test, the problem for an ellipse is considered. This case is of interest due to the fact that a field of normal geodesics loses regularity on a nontrivial separation set. The main result is that the BC-algorithm works quite successfully in spite of this complication. A theoretical introduction to the BC-method is included.
Résumé
Cette contribution concerne des expériences numériques sur le problème spectral inverse en plusieurs dimension d'espace. On vérifie l'efficacité d'un algorithme basé sur la méthode " BC " (Boundary Control ou Contrôle Frontière) qui exploite les relations existant entre la théorie du contrôle frontière et les problèmes inverses. Comme exemple on traite le cas d'une ellipse. Ce cas est intéressant car le champ des géodésiques normales perd sa régularité sur un " cut locus " non trivial. Le résultat essentiel est que l'algorithme BC donne de bons résultats malgré cette complication. Une introduction théorique à la méthode BC est incluse dans l'article.
Key words: Multidimensional inverse problem / Spectral data / Recovering of a density / Boundary control theory / BC-method / Geometrical optics / Numerical testing .
© EDP Sciences, SMAI, 1997
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