Direct Method for Identification of Two Coefficients of Acoustic Equation
We consider the coefficient inverse problem for the 2D acoustic equation. The problem is recovering the speed of sound in the medium (which depends only on the depth) and the density (function of both variables). We describe the method, based on the Gelfand–Levitan–Krein approach, which allows us to...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-07-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/13/3029 |
| _version_ | 1797591239503118336 |
|---|---|
| author | Nikita Novikov Maxim Shishlenin |
| author_facet | Nikita Novikov Maxim Shishlenin |
| author_sort | Nikita Novikov |
| collection | DOAJ |
| description | We consider the coefficient inverse problem for the 2D acoustic equation. The problem is recovering the speed of sound in the medium (which depends only on the depth) and the density (function of both variables). We describe the method, based on the Gelfand–Levitan–Krein approach, which allows us to obtain both functions by solving two sets of integral equations. The main advantage of the proposed approach is that the method does not use the multiple solution of direct problems, and thus has quite low CPU time requirements. We also consider the variation of the method for the 1D case, where the variation of the wave equation is considered. We illustrate the results with numerical experiments in the 1D and 2D case and study the efficiency and stability of the approach. |
| first_indexed | 2024-03-11T01:34:39Z |
| format | Article |
| id | doaj.art-e0b1750baf904a4fbde69ad853c64c7d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:34:39Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e0b1750baf904a4fbde69ad853c64c7d2023-11-18T17:04:48ZengMDPI AGMathematics2227-73902023-07-011113302910.3390/math11133029Direct Method for Identification of Two Coefficients of Acoustic EquationNikita Novikov0Maxim Shishlenin1Sobolev Institute of Mathematics, 630090 Novosibirsk, RussiaSobolev Institute of Mathematics, 630090 Novosibirsk, RussiaWe consider the coefficient inverse problem for the 2D acoustic equation. The problem is recovering the speed of sound in the medium (which depends only on the depth) and the density (function of both variables). We describe the method, based on the Gelfand–Levitan–Krein approach, which allows us to obtain both functions by solving two sets of integral equations. The main advantage of the proposed approach is that the method does not use the multiple solution of direct problems, and thus has quite low CPU time requirements. We also consider the variation of the method for the 1D case, where the variation of the wave equation is considered. We illustrate the results with numerical experiments in the 1D and 2D case and study the efficiency and stability of the approach.https://www.mdpi.com/2227-7390/11/13/3029acoustic equationinverse problemsdirect methodsintegral equations |
| spellingShingle | Nikita Novikov Maxim Shishlenin Direct Method for Identification of Two Coefficients of Acoustic Equation Mathematics acoustic equation inverse problems direct methods integral equations |
| title | Direct Method for Identification of Two Coefficients of Acoustic Equation |
| title_full | Direct Method for Identification of Two Coefficients of Acoustic Equation |
| title_fullStr | Direct Method for Identification of Two Coefficients of Acoustic Equation |
| title_full_unstemmed | Direct Method for Identification of Two Coefficients of Acoustic Equation |
| title_short | Direct Method for Identification of Two Coefficients of Acoustic Equation |
| title_sort | direct method for identification of two coefficients of acoustic equation |
| topic | acoustic equation inverse problems direct methods integral equations |
| url | https://www.mdpi.com/2227-7390/11/13/3029 |
| work_keys_str_mv | AT nikitanovikov directmethodforidentificationoftwocoefficientsofacousticequation AT maximshishlenin directmethodforidentificationoftwocoefficientsofacousticequation |