Linearized Boundary Control Method for Density Reconstruction in Acoustic Wave Equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917673949986816 |
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| author | Oksanen, Lauri Yang, Tianyu Yang, Yang |
| author_facet | Oksanen, Lauri Yang, Tianyu Yang, Yang |
| contents | We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the linearized Neumann-to-Dirichlet map. A key ingredient in the derivation is a linearized Blagovescenskii's identity with a free parameter. When the linearization is at a constant background density, we derive two reconstructive algorithms with stability estimates based on the boundary control method. When the linearization is at a non-constant background density, we establish an increasing stability estimate for the recovery of the density perturbation. The proposed reconstruction algorithms are implemented and validated with several numerical experiments to demonstrate the feasibility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linearized Boundary Control Method for Density Reconstruction in Acoustic Wave Equations Oksanen, Lauri Yang, Tianyu Yang, Yang Analysis of PDEs 35R30, 35L05 We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the linearized Neumann-to-Dirichlet map. A key ingredient in the derivation is a linearized Blagovescenskii's identity with a free parameter. When the linearization is at a constant background density, we derive two reconstructive algorithms with stability estimates based on the boundary control method. When the linearization is at a non-constant background density, we establish an increasing stability estimate for the recovery of the density perturbation. The proposed reconstruction algorithms are implemented and validated with several numerical experiments to demonstrate the feasibility. |
| title | Linearized Boundary Control Method for Density Reconstruction in Acoustic Wave Equations |
| topic | Analysis of PDEs 35R30, 35L05 |
| url | https://arxiv.org/abs/2405.14989 |