On fast reconstruction of periodic structures with partial scattering data
This paper presents a numerical method for solving the inverse problem of reconstructing the shape of periodic structures from scattering data. This inverse problem is motivated by applications in the nondestructive evaluation of photonic crystals. The numerical method belongs to the class of sampli...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024303 |
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| _version_ | 1832590746097549312 |
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| author | John Daugherty Nate Kaduk Elena Morgan Dinh-Liem Nguyen Peyton Snidanko Trung Truong |
| author_facet | John Daugherty Nate Kaduk Elena Morgan Dinh-Liem Nguyen Peyton Snidanko Trung Truong |
| author_sort | John Daugherty |
| collection | DOAJ |
| description | This paper presents a numerical method for solving the inverse problem of reconstructing the shape of periodic structures from scattering data. This inverse problem is motivated by applications in the nondestructive evaluation of photonic crystals. The numerical method belongs to the class of sampling methods that aim to construct an imaging function for the shape of the periodic structure using scattering data. By extending the results of Nguyen, Stahl, and Truong [Inverse Problems, 39:065013, 2023], we studied a simple imaging function that uses half the data required by the numerical method in the cited paper. Additionally, this imaging function is fast, simple to implement, and very robust against noise in the data. Both isotropic and anisotropic cases were investigated, and numerical examples were presented to demonstrate the performance of the numerical method. |
| format | Article |
| id | doaj-art-5dbc16a978734e9bb7b58b7277757d8d |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-5dbc16a978734e9bb7b58b7277757d8d2025-01-23T07:53:01ZengAIMS PressElectronic Research Archive2688-15942024-11-0132116481650210.3934/era.2024303On fast reconstruction of periodic structures with partial scattering dataJohn Daugherty0Nate Kaduk1Elena Morgan2Dinh-Liem Nguyen3Peyton Snidanko4Trung Truong5College of Professional Programs, Southwest Baptist University, Bolivar, MO 65613, USADepartment of Mathematical Sciences, Kent State University, Kent, OH 44240, USADepartment of Mathematics, Marist College, Poughkeepsie, NY 12601, USADepartment of Mathematics, Kansas State University, Manhattan, KS 66506, USADepartment of Mathematics, Bradley University, Peoria, IL 61625, USADepartment of Mathematics and Physics, Marshall University, Huntington, WV 25755, USAThis paper presents a numerical method for solving the inverse problem of reconstructing the shape of periodic structures from scattering data. This inverse problem is motivated by applications in the nondestructive evaluation of photonic crystals. The numerical method belongs to the class of sampling methods that aim to construct an imaging function for the shape of the periodic structure using scattering data. By extending the results of Nguyen, Stahl, and Truong [Inverse Problems, 39:065013, 2023], we studied a simple imaging function that uses half the data required by the numerical method in the cited paper. Additionally, this imaging function is fast, simple to implement, and very robust against noise in the data. Both isotropic and anisotropic cases were investigated, and numerical examples were presented to demonstrate the performance of the numerical method.https://www.aimspress.com/article/doi/10.3934/era.2024303inverse scatteringperiodic structureimaging functionpartial data |
| spellingShingle | John Daugherty Nate Kaduk Elena Morgan Dinh-Liem Nguyen Peyton Snidanko Trung Truong On fast reconstruction of periodic structures with partial scattering data Electronic Research Archive inverse scattering periodic structure imaging function partial data |
| title | On fast reconstruction of periodic structures with partial scattering data |
| title_full | On fast reconstruction of periodic structures with partial scattering data |
| title_fullStr | On fast reconstruction of periodic structures with partial scattering data |
| title_full_unstemmed | On fast reconstruction of periodic structures with partial scattering data |
| title_short | On fast reconstruction of periodic structures with partial scattering data |
| title_sort | on fast reconstruction of periodic structures with partial scattering data |
| topic | inverse scattering periodic structure imaging function partial data |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024303 |
| work_keys_str_mv | AT johndaugherty onfastreconstructionofperiodicstructureswithpartialscatteringdata AT natekaduk onfastreconstructionofperiodicstructureswithpartialscatteringdata AT elenamorgan onfastreconstructionofperiodicstructureswithpartialscatteringdata AT dinhliemnguyen onfastreconstructionofperiodicstructureswithpartialscatteringdata AT peytonsnidanko onfastreconstructionofperiodicstructureswithpartialscatteringdata AT trungtruong onfastreconstructionofperiodicstructureswithpartialscatteringdata |