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Volume 40, Issue 3
Application of the Factorization Method to Recover Cuts with Oblique Derivative Boundary Condition

Jun Guo, Jian He & Jin Li

DOI: 10.4208/jcm.2010-m2019-0188

J. Comp. Math., 40 (2022), pp. 373-395.

Published online: 2022-02

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  • 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.

  • Keywords

Direct and inverse scattering, Oblique derivative, Crack, The factorization method.

  • AMS Subject Headings

35R30, 35P25, 78A46

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hssxgj@126.com (Jun Guo)

17885309@qq.com (Jian He)

lxjin25@163.com (Jin Li)

  • BibTex
  • RIS
  • TXT
@Article{JCM-40-373, author = {Guo , JunHe , Jian and Li , Jin}, title = {Application of the Factorization Method to Recover Cuts with Oblique Derivative Boundary Condition}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2010-m2019-0188}, url = {http://global-sci.org/intro/article_detail/jcm/20242.html} }
TY - JOUR T1 - Application of the Factorization Method to Recover Cuts with Oblique Derivative Boundary Condition AU - Guo , Jun AU - He , Jian AU - Li , Jin JO - Journal of Computational Mathematics VL - 3 SP - 373 EP - 395 PY - 2022 DA - 2022/02 SN - 40 DO - http://doi.org/10.4208/jcm.2010-m2019-0188 UR - https://global-sci.org/intro/article_detail/jcm/20242.html KW - Direct and inverse scattering, Oblique derivative, Crack, The factorization method. AB -

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.

Guo , JunHe , Jian and Li , Jin. (2022). Application of the Factorization Method to Recover Cuts with Oblique Derivative Boundary Condition. Journal of Computational Mathematics. 40 (3). 373-395. doi:10.4208/jcm.2010-m2019-0188
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