Solving the Cauchy problem for an elliptic equation using Bat Algorithm
| dc.citation.epage | 1131 | |
| dc.citation.issue | 4 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 1119 | |
| dc.contributor.affiliation | Університет Абдельмалека Ессааді | |
| dc.contributor.affiliation | Abdelmalek Essaadi University | |
| dc.contributor.author | Дауді, Дж. | |
| dc.contributor.author | Таяні, Ч. | |
| dc.contributor.author | Daoudi, J. | |
| dc.contributor.author | Tajani, C. | |
| dc.coverage.placename | Львів | |
| dc.date.accessioned | 2025-03-10T09:21:52Z | |
| dc.date.created | 2023-02-28 | |
| dc.date.issued | 2023-02-28 | |
| dc.description.abstract | У цій статті подано метод розв’язування класу обернених задач для еліптичних рівнянь, відомих як проблема заповнення даних. Мета полягає в тому, щоб відновити відсутні дані на недоступній частині межі за допомогою вимірювань з доступної частини. Внутрішня складність цієї проблеми виникає через її некоректну природу, оскільки вона чутлива до змін у вхідних даних. Щоб вирішити цю задачу, запропонований підхід включає регулярізацію Тихонова для підвищення стійкості задачі. Щоб вирішити цю задачу, використовується метаевристичний підхід, зокрема, алгоритм кажанів (BA), заснований на ехолокаційній поведінці кажанів. Виконані чисельні результати показують, що алгоритм кажанів дає стійкі, збіжні та точні розв’язки. | |
| dc.description.abstract | This paper presents a method for solving a class of inverse problems for elliptic equations known as the data completion problem. The goal is to recover missing data on the inaccessible part of the boundary using measurements from the accessible part. The inherent difficulty of this problem arises from its ill-posed nature, as it is susceptible to variations in the input data. To address this challenge, the proposed approach integrates Tikhonov regularization to enhance the stability of the problem. To solve this problem, we use a metaheuristic approach, specifically, the Bat Algorithm (BA) inspired by the echolocation behavior of bats. The performed numerical results show that the Bat Algorithm yields stable, convergent, and accurate solutions. | |
| dc.format.extent | 1119-1131 | |
| dc.format.pages | 13 | |
| dc.identifier.citation | Daoudi J. Solving the Cauchy problem for an elliptic equation using Bat Algorithm / J. Daoudi, C. Tajani // Mathematical Modeling and Computing. — Lviv Politechnic Publishing House, 2023. — Vol 10. — No 4. — P. 1119–1131. | |
| dc.identifier.citationen | Daoudi J. Solving the Cauchy problem for an elliptic equation using Bat Algorithm / J. Daoudi, C. Tajani // Mathematical Modeling and Computing. — Lviv Politechnic Publishing House, 2023. — Vol 10. — No 4. — P. 1119–1131. | |
| dc.identifier.doi | doi.org/10.23939/mmc2023.04.1119 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/64064 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 4 (10), 2023 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 4 (10), 2023 | |
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| dc.relation.references | [2] Tajani C., Kajtih H., Daanoun A. Iterative method to solve a data completion problem for biharmonic equation for rectangular domain. Annals of West University of Timisoara – Mathematics and Computer Science. 55 (1), 129–147 (2017). | |
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| dc.relation.references | [15] Yang X.-S., He X. Bat algorithm: literature review and applications. International Journal of Bio-inspired Computation. 5 (3), 141–149 (2013). | |
| dc.relation.references | [16] Bolaji A., Khader A., Al-Betar M., Awadallah M. Artificial bee colony algorithm, its variants and applications: A survey. Journal of Theoretical & Applied Information Technology. 47 (2), 434–459 (2013). | |
| dc.relation.references | [17] Poli R., Kennedy J., Blackwell T. Particle swarm optimization: An overview. Swarm Intelligence. 1, 33–57 (2007). | |
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| dc.relation.references | [20] Evans L. C. Partial Differential Equations. Graduate Studies in Mathematics, vol. 19. American Mathematical Society, Providence (2010). | |
| dc.relation.references | [21] Yang X. Nature-Inspired Metaheuristic Algorithms. Luniver Press (2010). | |
| dc.relation.references | [22] Jayabarathi T., Raghunathan T., Gandomi A. H. The bat algorithm, variants and some practical engineering applications: A review. Nature-Inspired Algorithms and Applied Optimization, Studies in Computational Intelligence. 744, 313–330 (2018). | |
| dc.relation.references | [23] Alihodzic A., Tuba M. Improved bat algorithm applied to multilevel image thresholding. The Scientific World Journal. 2014, 176718 (2014). | |
| dc.relation.references | [24] Zhang J., Wang G. Image matching using a bat algorithm with mutation. Applied Mechanics and Materials. 203, 88–93 (2012). | |
| dc.relation.references | [25] Bahmani-Firouzi B., Azizipanah-Abarghooee R. Optimal sizing of battery energy storage for micro-grid operation management using a new improved bat algorithm. International Journal of Electrical Power & Energy Systems. 56, 42–54 (2014). | |
| dc.relation.references | [26] Strumberger I., Bacanin N., Tuba M. Constrained portfolio optimization by hybridized bat algorithm. 2016 7th International Conference on Intelligent Systems, Modelling and Simulation (ISMS). 83–88 (2016). | |
| dc.relation.referencesen | [1] Zemzemi N., Bourenane H., Cochet H. An iterative method for solving the inverse problem in electrocardiography imaging: from body surface to heart potential. Computing in Cardiology. 41, 717–720 (2014). | |
| dc.relation.referencesen | [2] Tajani C., Kajtih H., Daanoun A. Iterative method to solve a data completion problem for biharmonic equation for rectangular domain. Annals of West University of Timisoara – Mathematics and Computer Science. 55 (1), 129–147 (2017). | |
| dc.relation.referencesen | [3] Tromp J. Seismic wavefield imaging of Earth’s interior across scales. Nature Reviews Earth & Environment. 1, 40–53 (2020). | |
| dc.relation.referencesen | [4] Daniell P. Lectures on Cauchy’s problem in linear partial differential equations. By J. Hadamard. Pp. viii+316. 15 s.net. 1923. (Per Oxford University Press.). The Mathematical Gazette. 12 (171) 173–174 (1924). | |
| dc.relation.referencesen | [5] Andrieux S., Baranger T. N. An energy error-based method for the resolution of the Cauchy problem in 3D linear elasticity. Computer Methods in Applied Mechanics and Engineering. 197 (9–12), 902–920 (2008). | |
| dc.relation.referencesen | [6] Cimeti`ere A., Delvare F., Jaoua M., Pons F. Solution of the Cauchy problem using iterated Tikhonov regularization. Inverse Problems. 17 (3), 553–570 (2001). | |
| dc.relation.referencesen | [7] Bourgeois L. Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace’s equation. Inverse Problems. 22 (2), 413–440 (2006). | |
| dc.relation.referencesen | [8] Feng X., Eld´en L., Fu C. A quasi-boundary-value method for the Cauchy problem for elliptic equations with nonhomogeneous Neumann data. Journal of Inverse and Ill-posed Problems. 18 (6), 617–645 (2010). | |
| dc.relation.referencesen | [9] Tuan N. H., Trong D. D., Quan P. H. A note on a Cauchy problem for the Laplace equation: regularization and error estimates. Applied Mathematics and Computation. 217 (7), 2913–2922 (2010). | |
| dc.relation.referencesen | [10] Qian Z., Fu C.-L., Li Z.-P. Two regularization methods for a Cauchy problem for the Laplace equation. Journal of Mathematical Analysis and Applications. 338 (1), 479–489 (2008). | |
| dc.relation.referencesen | [11] Regi´nska T., Wakulicz A. Wavelet moment method for the Cauchy problem for the Helmholtz equation. Journal of Computational and Applied Mathematics. 223 (1), 218–229 (2009). | |
| dc.relation.referencesen | [12] H`ao D. N., Lesnic D. The Cauchy problem for Laplace’s equation via the conjugate gradient method. IMA Journal of Applied Mathematics. 65 (2), 199–217 (2000). | |
| dc.relation.referencesen | [13] Marin L., Elliott L., Heggs P., Ingham D., Lesnic D., Wen X. Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation. International Journal for Numerical Methods in Engineering. 60 (11), 1933–1947 (2004). | |
| dc.relation.referencesen | [14] Marin L., Elliott L., Heggs P. J., Ingham D. B., Lesnic D., Wen X. BEM solution for the Cauchy problem associated with Helmholtz-type equations by the Landweber method. Engineering Analysis with Boundary Elements. 28 (9), 1025–1034 (2004). | |
| dc.relation.referencesen | [15] Yang X.-S., He X. Bat algorithm: literature review and applications. International Journal of Bio-inspired Computation. 5 (3), 141–149 (2013). | |
| dc.relation.referencesen | [16] Bolaji A., Khader A., Al-Betar M., Awadallah M. Artificial bee colony algorithm, its variants and applications: A survey. Journal of Theoretical & Applied Information Technology. 47 (2), 434–459 (2013). | |
| dc.relation.referencesen | [17] Poli R., Kennedy J., Blackwell T. Particle swarm optimization: An overview. Swarm Intelligence. 1, 33–57 (2007). | |
| dc.relation.referencesen | [18] Mirjalili S., Mirjalili S. M., Lewis A. Grey Wolf Optimizer. Advances in Engineering Software. 69, 46–61 (2014). | |
| dc.relation.referencesen | [19] Sastry K., Goldberg D. E., Kendall G. Genetic algorithms. Search methodologies: Introductory tutorials in optimization and decision support techniques. 93–117 (2014). | |
| dc.relation.referencesen | [20] Evans L. C. Partial Differential Equations. Graduate Studies in Mathematics, vol. 19. American Mathematical Society, Providence (2010). | |
| dc.relation.referencesen | [21] Yang X. Nature-Inspired Metaheuristic Algorithms. Luniver Press (2010). | |
| dc.relation.referencesen | [22] Jayabarathi T., Raghunathan T., Gandomi A. H. The bat algorithm, variants and some practical engineering applications: A review. Nature-Inspired Algorithms and Applied Optimization, Studies in Computational Intelligence. 744, 313–330 (2018). | |
| dc.relation.referencesen | [23] Alihodzic A., Tuba M. Improved bat algorithm applied to multilevel image thresholding. The Scientific World Journal. 2014, 176718 (2014). | |
| dc.relation.referencesen | [24] Zhang J., Wang G. Image matching using a bat algorithm with mutation. Applied Mechanics and Materials. 203, 88–93 (2012). | |
| dc.relation.referencesen | [25] Bahmani-Firouzi B., Azizipanah-Abarghooee R. Optimal sizing of battery energy storage for micro-grid operation management using a new improved bat algorithm. International Journal of Electrical Power & Energy Systems. 56, 42–54 (2014). | |
| dc.relation.referencesen | [26] Strumberger I., Bacanin N., Tuba M. Constrained portfolio optimization by hybridized bat algorithm. 2016 7th International Conference on Intelligent Systems, Modelling and Simulation (ISMS). 83–88 (2016). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2023 | |
| dc.subject | обернена задача | |
| dc.subject | рівняння Гельмгольца | |
| dc.subject | рівняння Лапласа | |
| dc.subject | оптимізація | |
| dc.subject | регулярізація Тихонова | |
| dc.subject | алгоритм кажанів | |
| dc.subject | inverse problem | |
| dc.subject | Helmholtz equation | |
| dc.subject | Laplace equation | |
| dc.subject | optimization | |
| dc.subject | Thikhonov regularization | |
| dc.subject | bat algorithm | |
| dc.title | Solving the Cauchy problem for an elliptic equation using Bat Algorithm | |
| dc.title.alternative | Розв’язування задачі Коші для еліптичного рівняння за допомогою алгоритму кажанів | |
| dc.type | Article |
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