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Title: On the non-linear integral equation method for the reconstruction of an inclusion in the elastic body
Authors: Chapko, R. S.
Yaman, Olha Ivanyshyn
Vavrychuk, V. G.
Keywords: Double connected elastostatic domain
boundary reconstruction
elastic potentials
boundary integral equations
trigonometric quadrature method
Newton method
Tikhonov regularization
Publisher: Ivan Franko National University of Lviv,
Abstract: We apply the non-linear integral equation approach based on elastic potentials for determining the shape of a bounded object in the elastostatic two-dimensional domain from given Cauchy data on its boundary. The iterative algorithm is developed for the numerical solution of obtained integral equations. We find the Frechet derivative for the corresponding operator and show unique solviability of the linearized system. Full discretization of the system is realized by a trigonometric quadrature method. Due to the inherited ill-possedness in the system of linear equations we apply the Tikhonov regularization. The numerical results show that the proposed method gives a good accuracy of reconstructions with an economical computational cost.
Description: Vavrychuk, Vasyl/0000-0002-8314-6931
WOS: 000471789500002
ISSN: 0868-6912
Appears in Collections:Mathematics / Matematik
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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