Open AccessIdentification and stability of small-sized dislocations using a direct algorithm
Author(s) -
Batoul Abdelaziz,
Abdellatif El Badia,
Ahmad El Hajj
Publication year - 2022
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021046
Subject(s) - dislocation , generalization , curvilinear coordinates , algorithm , stability (learning theory) , mathematics , position (finance) , line (geometry) , boundary (topology) , point (geometry) , inverse , mathematical analysis , computer science , geometry , physics , condensed matter physics , finance , machine learning , economics
This paper considers the problem of identifying dislocation lines of curvilinear form in three-dimensional materials from boundary measurements, when the areas surrounded by the dislocation lines are assumed to be small-sized. The objective of this inverse problem is to reconstruct the number, the initial position and certain characteristics of these dislocations and establish, using certain test functions, a Hölder stability of the centers. This paper can be considered as a generalization of [ 9 ], where instead of reconstructing point-wise dislocations, as done in the latter paper, our aim is to recover the parameters of line dislocations by employing a direct algebraic algorithm.