Effective medium theory for embedded sound-soft obstacles in an anisotropic inhomogeneous medium with applications
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912611570810880 |
|---|---|
| author | Diao, Huaian Meng, Qingle Sun, Zhiying |
| author_facet | Diao, Huaian Meng, Qingle Sun, Zhiying |
| contents | This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model commonly arises in the inverse scattering problem of simultaneously recovering the embedded obstacles and the surrounding medium. We propose a novel theoretical framework that demonstrates how embedded obstacles can be effectively approximated by an isotropic and lossy medium with specified physical parameters, wherein the total wave field exhibits decay properties related to these specified material parameters at the boundaries of the obstacles. This mathematical characterization of the wave in an effective medium model can be used to locate the underlying obstacles. Furthermore, we establish rigorous estimates to validate this approximation and provide a concrete example illustrating our theoretical results. Our proposed effective medium theory offers substantial applications within the context of the aforementioned inverse problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective medium theory for embedded sound-soft obstacles in an anisotropic inhomogeneous medium with applications Diao, Huaian Meng, Qingle Sun, Zhiying Mathematical Physics Analysis of PDEs 34L25, 78A46 This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model commonly arises in the inverse scattering problem of simultaneously recovering the embedded obstacles and the surrounding medium. We propose a novel theoretical framework that demonstrates how embedded obstacles can be effectively approximated by an isotropic and lossy medium with specified physical parameters, wherein the total wave field exhibits decay properties related to these specified material parameters at the boundaries of the obstacles. This mathematical characterization of the wave in an effective medium model can be used to locate the underlying obstacles. Furthermore, we establish rigorous estimates to validate this approximation and provide a concrete example illustrating our theoretical results. Our proposed effective medium theory offers substantial applications within the context of the aforementioned inverse problem. |
| title | Effective medium theory for embedded sound-soft obstacles in an anisotropic inhomogeneous medium with applications |
| topic | Mathematical Physics Analysis of PDEs 34L25, 78A46 |
| url | https://arxiv.org/abs/2509.23163 |