Efficient Numerical Reconstruction of Wave Equation Sources via Droplet-Induced Asymptotics
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918299593342976 |
|---|---|
| author | Hou, Shutong Sini, Mourad Wang, Haibing |
| author_facet | Hou, Shutong Sini, Mourad Wang, Haibing |
| contents | In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the resulting wave field perturbation measured at a single external point over time. The method enables stable source reconstructions where conventional approaches fail due to ill-posedness, with potential applications in medical imaging and non-destructive testing. Key contributions include:
1. Implementation of a theoretically justified asymptotic expansion, from [33], using the eigensystem of the Newtonian operator, with error analysis for the spectral truncation.
2. Novel numerical schemes for solving the time-domain Lippmann-Schwinger equation and reconstructing the source via Riesz basis expansions and mollification-based numerical differentiations.
3. Reconstruction requiring only single-point measurements, overcoming traditional spatial data limitations.
4. 3D numerical experiments demonstrating accurate source recovery under noise (SNR of the order $1/a$), with error analysis for the droplet size (of the order $a$) and the number of spectral modes $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15787 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient Numerical Reconstruction of Wave Equation Sources via Droplet-Induced Asymptotics Hou, Shutong Sini, Mourad Wang, Haibing Numerical Analysis 35R30, 65M32, 35C20 In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the resulting wave field perturbation measured at a single external point over time. The method enables stable source reconstructions where conventional approaches fail due to ill-posedness, with potential applications in medical imaging and non-destructive testing. Key contributions include: 1. Implementation of a theoretically justified asymptotic expansion, from [33], using the eigensystem of the Newtonian operator, with error analysis for the spectral truncation. 2. Novel numerical schemes for solving the time-domain Lippmann-Schwinger equation and reconstructing the source via Riesz basis expansions and mollification-based numerical differentiations. 3. Reconstruction requiring only single-point measurements, overcoming traditional spatial data limitations. 4. 3D numerical experiments demonstrating accurate source recovery under noise (SNR of the order $1/a$), with error analysis for the droplet size (of the order $a$) and the number of spectral modes $N$. |
| title | Efficient Numerical Reconstruction of Wave Equation Sources via Droplet-Induced Asymptotics |
| topic | Numerical Analysis 35R30, 65M32, 35C20 |
| url | https://arxiv.org/abs/2601.15787 |