Numerical Solution of an Inverse Problem for a General Hyperbolic Heat Equation Научная публикация
| Конференция |
XIV International Conference Optimization and Applications 18-22 сент. 2023 , Петровац, Черногория |
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| Сборник | Optimization and Applications : 14th International Conference, OPTIMA 2023, Petrovac, Montenegro, September 18–22, 2023, Revised Selected Papers Сборник, Springer. 2023. 390 c. ISBN 9783031478598. |
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| Журнал |
Communications in Computer and Information Science
ISSN: 1865-0929 |
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| Вых. Данные | Год: 2023, Страницы: 47-60 Страниц : 14 DOI: 10.1007/978-3-031-48751-4_4 | ||||||
| Ключевые слова | Inverse and ill-posed problems · Hyperbolic heat equation · Inexact gradient · Richardson’s method · Accelerated gradient methods · Regularization | ||||||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Российский научный фонд | 23-71-10068 |
Реферат:
In this paper we describe an algorithm of numerical solving of an inverse problem on a general case of a hyperbolic heat equation with additional second time derivative with a small parameter. The problem in this case is finding an initial distribution with given final distribution. This algorithm allows finding a solution to the problem for any admissible given precision. Algorithm allows evading difficulties analogous to the case of heat equation with inverted time. Furthermore, it allows finding an optimal grid size by learning on a relatively big grid size and small amount of iterations of a gradient method and later extrapolates to the required grid size using Richardson’s method. This algorithm allows finding an adequate estimate of Lipschitz constant for the gradient of the target functional. Finally, this algorithm may easily be applied to the problems with similar structure, for example in solving equations for plasma, social processes and various biological problems. The theoretical novelty of the paper consists in the developing of an optimal procedure of finding of the required grid size using Richardson extrapolation in context of ill-posed problems, and accelerated methods were applied to this problem.
Библиографическая ссылка:
Akindinov G.
, Krivorotko O.
, Matyukhin V.
Numerical Solution of an Inverse Problem for a General Hyperbolic Heat Equation
В сборнике Optimization and Applications : 14th International Conference, OPTIMA 2023, Petrovac, Montenegro, September 18–22, 2023, Revised Selected Papers. – Springer., 2023. – C.47-60. – ISBN 9783031478598. DOI: 10.1007/978-3-031-48751-4_4 Scopus OpenAlex
Numerical Solution of an Inverse Problem for a General Hyperbolic Heat Equation
В сборнике Optimization and Applications : 14th International Conference, OPTIMA 2023, Petrovac, Montenegro, September 18–22, 2023, Revised Selected Papers. – Springer., 2023. – C.47-60. – ISBN 9783031478598. DOI: 10.1007/978-3-031-48751-4_4 Scopus OpenAlex
Даты:
| Опубликована в печати: | 14 дек. 2023 г. |
| Опубликована online: | 14 дек. 2023 г. |
Идентификаторы БД:
| Scopus: | 2-s2.0-85180626127 |
| OpenAlex: | W4389681803 |