Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation | Sciact - Система учета научной деятельности ИМ СО РАН

Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation Научная публикация

Журнал

SIAM Journal on Imaging Sciences
ISSN: 1936-4954

Вых. Данные

Год: 2023, Том: 16, Номер: 3, Страницы: 1762-1790 Страниц : 29 DOI: 10.1137/23M1565449

Ключевые слова

geodesic lines, Riemannian metric, Carleman estimate, coefficient inverse problem, global convergence, convexification, numerical studies

Авторы

Klibanov Michael V. ¹ , Li Jingzhi ² , Nguyen Loc H. ¹ , Romanov Vladimir ³ , Ya Zhipeng ²

Организации

1	Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223 USA.
2	Department of Mathematics & National Center for Applied Mathematics Shenzhen & SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, People’s Republic of China.
3	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0009

The first globally convergent numerical method for a coefficient inverse problem for the Riemannian radiative transfer equation (RRTE) is constructed. This is a version of the so-called convexification method, which has been pursued by this research group for a number of years for some other CIPs for PDEs. Those PDEs are significantly different from the RRTE. The presence of the Carleman weight function in the numerical scheme is the key element which insures the global convergence. Convergence analysis is presented along with the results of numerical experiments, which confirm the theory. RRTE governs the propagation of photons in the diffuse medium in the case when they propagate along geodesic lines between their collisions. Geodesic lines are generated by the spatially variable dielectric constant of the medium.

Klibanov M.V. , Li J. , Nguyen L.H. , Romanov V. , Ya Z.
Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation
SIAM Journal on Imaging Sciences. 2023. V.16. N3. P.1762-1790. DOI: 10.1137/23M1565449 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	13 апр. 2023 г.
Принята к публикации:	31 мая 2023 г.
Опубликована в печати:	29 авг. 2023 г.
Опубликована online:	29 авг. 2023 г.

Web of science:	WOS:001165602900002
Scopus:	2-s2.0-85175641623
РИНЦ:	63113720
OpenAlex:	W4386251050

БД	Цитирований
OpenAlex	2
Scopus	2
Web of science	1