Application of the Factorization Method to Recover Cuts with Oblique Derivative Boundary Condition

Application of the Factorization Method to Recover Cuts with Oblique Derivative Boundary Condition

Year:    2022

Author:    Jun Guo, Jian He, Jin Li

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 3 : pp. 373–395

Abstract

Direct and inverse problems for the scattering of cracks with mixed oblique derivative boundary conditions from the incident plane wave are considered, which describe the scattering phenomenons such as the scattering of tidal waves by spits or reefs. The solvability of the direct scattering problem is proven by using the boundary integral equation method. In order to show the equivalent boundary integral system is Fredholm of index zero, some relationships concerning the tangential potential operator is used. Due to the mixed oblique derivative boundary conditions, we cannot employ the factorization method in a usual manner to reconstruct the cracks. An alternative technique is used in the theoretical analysis such that the far field operator can be factorized in an appropriate form and fulfills the range identity theorem. Finally, we present some numerical examples to demonstrate the feasibility and effectiveness of the factorization method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2010-m2019-0188

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 3 : pp. 373–395

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Direct and inverse scattering Oblique derivative Crack The factorization method.

Author Details

Jun Guo

Jian He

Jin Li