Numerical Solution of an Inverse Problem for a General Hyperbolic Heat Equation Full article
| Conference |
XIV International Conference Optimization and Applications 18-22 Sep 2023 , Петровац, Черногория |
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| Source | Optimization and Applications : 14th International Conference, OPTIMA 2023, Petrovac, Montenegro, September 18–22, 2023, Revised Selected Papers Compilation, Springer. 2023. 390 c. ISBN 9783031478598. |
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| Journal |
Communications in Computer and Information Science
ISSN: 1865-0929 |
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| Output data | Year: 2023, Pages: 47-60 Pages count : 14 DOI: 10.1007/978-3-031-48751-4_4 | ||||||
| Tags | Inverse and ill-posed problems · Hyperbolic heat equation · Inexact gradient · Richardson’s method · Accelerated gradient methods · Regularization | ||||||
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 23-71-10068 |
Abstract:
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.
Cite:
Akindinov G.
, Krivorotko O.
, Matyukhin V.
Numerical Solution of an Inverse Problem for a General Hyperbolic Heat Equation
In compilation 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
In compilation 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
Dates:
| Published print: | Dec 14, 2023 |
| Published online: | Dec 14, 2023 |
Identifiers:
| Scopus: | 2-s2.0-85180626127 |
| OpenAlex: | W4389681803 |