File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1088/1361-6420/ace548
- Scopus: eid_2-s2.0-85167509557
- Find via
Supplementary
-
Citations:
- Scopus: 0
- Appears in Collections:
Article: A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation
Title | A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation |
---|---|
Authors | |
Keywords | diffusion–advection equations initial source identification inverse problem non-smooth optimization optimal control primal-dual algorithm sparse control |
Issue Date | 1-Sep-2023 |
Publisher | IOP Publishing |
Citation | Inverse Problems, 2023, v. 39, n. 9 How to Cite? |
Abstract | We consider the problem of identifying a sparse initial source condition to achieve a given state distribution of a diffusion–advection partial differential equation after a given final time. The initial condition is assumed to be a finite combination of Dirac measures. The locations and intensities of this initial condition are required to be identified. This problem is known to be exponentially ill-posed because of the strong diffusive and smoothing effects. We propose a two-stage numerical approach to treat this problem. At the first stage, to obtain a sparse initial condition with the desire of achieving the given state subject to a certain tolerance, we propose an optimal control problem involving sparsity-promoting and ill-posedness-avoiding terms in the cost functional, and introduce a generalized primal-dual algorithm for this optimal control problem. At the second stage, the initial condition obtained from the optimal control problem is further enhanced by identifying its locations and intensities in its representation of the combination of Dirac measures. This two-stage numerical approach is shown to be easily implementable and its efficiency in short time horizons is promisingly validated by the results of numerical experiments. Some discussions on long time horizons are also included. |
Persistent Identifier | http://hdl.handle.net/10722/348357 |
ISSN | 2023 Impact Factor: 2.0 2023 SCImago Journal Rankings: 1.185 |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Biccari, Umberto | - |
dc.contributor.author | Song, Yongcun | - |
dc.contributor.author | Yuan, Xiaoming | - |
dc.contributor.author | Zuazua, Enrique | - |
dc.date.accessioned | 2024-10-09T00:30:59Z | - |
dc.date.available | 2024-10-09T00:30:59Z | - |
dc.date.issued | 2023-09-01 | - |
dc.identifier.citation | Inverse Problems, 2023, v. 39, n. 9 | - |
dc.identifier.issn | 0266-5611 | - |
dc.identifier.uri | http://hdl.handle.net/10722/348357 | - |
dc.description.abstract | We consider the problem of identifying a sparse initial source condition to achieve a given state distribution of a diffusion–advection partial differential equation after a given final time. The initial condition is assumed to be a finite combination of Dirac measures. The locations and intensities of this initial condition are required to be identified. This problem is known to be exponentially ill-posed because of the strong diffusive and smoothing effects. We propose a two-stage numerical approach to treat this problem. At the first stage, to obtain a sparse initial condition with the desire of achieving the given state subject to a certain tolerance, we propose an optimal control problem involving sparsity-promoting and ill-posedness-avoiding terms in the cost functional, and introduce a generalized primal-dual algorithm for this optimal control problem. At the second stage, the initial condition obtained from the optimal control problem is further enhanced by identifying its locations and intensities in its representation of the combination of Dirac measures. This two-stage numerical approach is shown to be easily implementable and its efficiency in short time horizons is promisingly validated by the results of numerical experiments. Some discussions on long time horizons are also included. | - |
dc.language | eng | - |
dc.publisher | IOP Publishing | - |
dc.relation.ispartof | Inverse Problems | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | diffusion–advection equations | - |
dc.subject | initial source identification | - |
dc.subject | inverse problem | - |
dc.subject | non-smooth optimization | - |
dc.subject | optimal control | - |
dc.subject | primal-dual algorithm | - |
dc.subject | sparse control | - |
dc.title | A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation | - |
dc.type | Article | - |
dc.identifier.doi | 10.1088/1361-6420/ace548 | - |
dc.identifier.scopus | eid_2-s2.0-85167509557 | - |
dc.identifier.volume | 39 | - |
dc.identifier.issue | 9 | - |
dc.identifier.eissn | 1361-6420 | - |
dc.identifier.issnl | 0266-5611 | - |