A quantitative sampling method for elastic and electromagnetic sources
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916647814561792 |
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| author | Liu, Xiaodong Shi, Qingxiang |
| author_facet | Liu, Xiaodong Shi, Qingxiang |
| contents | This work is dedicated to a novel sampling method for accurately reconstructing elastic and electromagnetic sources from the far field patterns. We show that the proposed indicators in the form of integrals with full far field patterns are exactly the source functions. These facts not only give constructive uniqueness proofs of the inverse source problems, but also establish the theoretical basis of the proposed sampling methods. Furthermore, we derive the stability estimates for the corresponding discrete indicators using the far field patterns with finitely many observations and frequencies. We have also proposed the indicators with partial far field patterns and proved their validity for providing the derivative information of the unknown sources. Numerical examples are presented to verify the accuracy and stability of the proposed quantitative sampling method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A quantitative sampling method for elastic and electromagnetic sources Liu, Xiaodong Shi, Qingxiang Numerical Analysis 35P25, 78A46, 74B05 This work is dedicated to a novel sampling method for accurately reconstructing elastic and electromagnetic sources from the far field patterns. We show that the proposed indicators in the form of integrals with full far field patterns are exactly the source functions. These facts not only give constructive uniqueness proofs of the inverse source problems, but also establish the theoretical basis of the proposed sampling methods. Furthermore, we derive the stability estimates for the corresponding discrete indicators using the far field patterns with finitely many observations and frequencies. We have also proposed the indicators with partial far field patterns and proved their validity for providing the derivative information of the unknown sources. Numerical examples are presented to verify the accuracy and stability of the proposed quantitative sampling method. |
| title | A quantitative sampling method for elastic and electromagnetic sources |
| topic | Numerical Analysis 35P25, 78A46, 74B05 |
| url | https://arxiv.org/abs/2503.06581 |