Potential field modeling by combination of near-boundary and contact elements with non-classical finite differences in a heterogeneous medium
| dc.citation.epage | 384 | |
| dc.citation.issue | 2 | |
| dc.citation.journalTitle | Математичне моделювання та обчислення | |
| dc.citation.spage | 373 | |
| dc.citation.volume | 11 | |
| dc.contributor.affiliation | Національний університет “Львівська політехніка” | |
| dc.contributor.affiliation | Lviv Polytechnic National University | |
| dc.contributor.author | Журавчак, Л. М. | |
| dc.contributor.author | Zhuravchak, L. M. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-10-20T08:10:25Z | |
| dc.date.created | 2024-02-27 | |
| dc.date.issued | 2024-02-27 | |
| dc.description.abstract | У статті наведено узагальнену схему для знаходження розв’язків задач теорії потенціалу в двовимірних кусково-однорідних середовищах, які містять локальні області з залежними від координат фізичними характеристиками. Для опису додаткового впливу цих локальних областей, поряд з непрямими методами приграничних і контактних елементів, використано некласичний метод скінченних різниць, який базується на асиметричних скінченно-різницевих співвідношеннях. Проведено програмну реалізацію розробленого підходу для знаходження потенціалу електричного поля постійного струму в гірському неоднорідному хребті. | |
| dc.description.abstract | In this paper, a generalized scheme for finding solutions of potential theory problems in two-dimensional piecewise-homogeneous media containing local regions with coordinate-dependent physical characteristics has been presented. To describe the additional influence of these local areas, along with the indirect methods of near-boundary and contact elements, a non-classical finite-difference method based on asymmetric finite-difference relations has been used. The software implementation of the developed approach for finding the potential of the direct current electric field in a mountain heterogeneous ridge has been carried out. Approaches to solving elliptic problems that simulate stationary processes in piecewise-homogeneous media with ideal contact conditions at the interfaces and mixed boundary conditions have been considered. They analytically take into account the condition of continuity of the unknown functions (potential, temperature) and are based on the combination of indirect methods of near-boundary and contact elements. Using the software developed, computational experiments have been carried out for the problem of exploration and forecasting of oil and gas deposits in a mountain range by the method of electrical profiling. | |
| dc.format.extent | 373-384 | |
| dc.format.pages | 12 | |
| dc.identifier.citation | Zhuravchak L. M. Potential field modeling by combination of near-boundary and contact elements with non-classical finite differences in a heterogeneous medium / L. M. Zhuravchak // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 373–384. | |
| dc.identifier.citationen | Zhuravchak L. M. Potential field modeling by combination of near-boundary and contact elements with non-classical finite differences in a heterogeneous medium / L. M. Zhuravchak // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 373–384. | |
| dc.identifier.doi | doi.org/10.23939/mmc2024.02.373 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/113814 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та обчислення, 2 (11), 2024 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 2 (11), 2024 | |
| dc.relation.references | [1] Dmitriev V. I., Nesmeyanova N. I. Integral equation method in three-dimensional problems of lowfrequency electrodynamics. Computational Mathematics and Modeling. 3, 313–317 (1992). | |
| dc.relation.references | [2] Zhdanov M. S., Dmitriev V. I., Gribenko A. V. Integral electric current method in 3-D electromagnetic modeling for large conductivity contrast. IEEE Transactions on Geoscience and Remote Sensing. 45 (5), 1282–1290 (2007). | |
| dc.relation.references | [3] Banerjee P. K., Butterfield R. Boundary Element Methods in Engineering Science. London, McGraw-Hill (1981). | |
| dc.relation.references | [4] Brebbia C. A., Telles J. C. F., Wrobel L. C. Boundary Element Techniques. Theory and Applications in Engineering. Springer-Verlag, Berlin – Heidelberg – New York – Tokyo (1984). | |
| dc.relation.references | [5] Mukanova B., Modin I. The Boundary Element Method in Geophysical Survey. Springer, Cham (2018). | |
| dc.relation.references | [6] Najarzadeh L., Movahedian B., Azhari M. Numerical solution of scalar wave equation by the modified radial integration boundary element method. Engineering Analysis with Boundary Elements. 105, 267–278 (2019). | |
| dc.relation.references | [7] Zhang Y., Qu W., Chen J. A new regularized BEM for 3D potential problems. SCIENTIA SINICA Physica, Mechanica & Astronomica. 43 (3), 297–308 (2013). | |
| dc.relation.references | [8] Zhang J., Weicheng L., Yunqiao D., Chuanming J. A double-layer interpolation method for implementation of BEM analysis of problems in potential theory. Applied Mathematical Modelling. 51, 250–269 (2017). | |
| dc.relation.references | [9] Zhuravchak L. Computation of pressure change in piecewise-homogeneous reservoir for elastic regime by indirect near-boundary element method. 2019 IEEE 14th International Conference on Computer Sciences and Information Technologies (CSIT). 141–144 (2019). | |
| dc.relation.references | [10] Zhuravchak L. M., Zabrodska N. V. Using of partly-boundary elements as a version of the indirect near-boundary element method for potential field modeling. Mathematical Modeling and Computing. 8 (1), 1–10 (2021). | |
| dc.relation.references | [11] Zhuravchak L. Combination of near-boundary and contact elements in modeling stationary processes in piecewise-homogeneous objects. 2020 IEEE 15th International Conference on Computer Sciences and Information Technologies (CSIT). 411–414 (2020). | |
| dc.relation.references | [12] Zhuravchak L. M., Zabrodska N. V. Nonstationary thermal fields in inhomogeneous materials with nonlinear behavior of the components. Materials Science. 46 (1), 36–46 (2010). | |
| dc.relation.references | [13] Zhuravchak L. M., Kruk O. S. Consideration of the nonlinear behavior of environmental material and a three-dimensional internal heat sources in mathematical modeling of heat conduction. Mathematical Modeling and Computing. 2 (1), 107–113 (2015). | |
| dc.relation.references | [14] Anshuman A., Eldho T. I. Coupled flow and transport simulation involving rate-limited adsorption in highly heterogeneous unconfined aquifers using a local strong form meshless method. Engineering Analysis with Boundary Elements. 145, 1–12 (2022). | |
| dc.relation.references | [15] Habibirad A., Hesameddini E., Shekari Y. A suitable hybrid meshless method for the numerical solution of time-fractional fourth-order reaction–diffusion model in the multi-dimensional case. Engineering Analysis with Boundary Elements. 145, 149–160 (2022). | |
| dc.relation.references | [16] Qu W., Chen W., Fu Z. Solutions of 2D and 3D non-homogeneous potential problems by using a boundary element-collocation method. Engineering Analysis with Boundary Elements. 60, 2–9 (2015). | |
| dc.relation.referencesen | [1] Dmitriev V. I., Nesmeyanova N. I. Integral equation method in three-dimensional problems of lowfrequency electrodynamics. Computational Mathematics and Modeling. 3, 313–317 (1992). | |
| dc.relation.referencesen | [2] Zhdanov M. S., Dmitriev V. I., Gribenko A. V. Integral electric current method in 3-D electromagnetic modeling for large conductivity contrast. IEEE Transactions on Geoscience and Remote Sensing. 45 (5), 1282–1290 (2007). | |
| dc.relation.referencesen | [3] Banerjee P. K., Butterfield R. Boundary Element Methods in Engineering Science. London, McGraw-Hill (1981). | |
| dc.relation.referencesen | [4] Brebbia C. A., Telles J. C. F., Wrobel L. C. Boundary Element Techniques. Theory and Applications in Engineering. Springer-Verlag, Berlin – Heidelberg – New York – Tokyo (1984). | |
| dc.relation.referencesen | [5] Mukanova B., Modin I. The Boundary Element Method in Geophysical Survey. Springer, Cham (2018). | |
| dc.relation.referencesen | [6] Najarzadeh L., Movahedian B., Azhari M. Numerical solution of scalar wave equation by the modified radial integration boundary element method. Engineering Analysis with Boundary Elements. 105, 267–278 (2019). | |
| dc.relation.referencesen | [7] Zhang Y., Qu W., Chen J. A new regularized BEM for 3D potential problems. SCIENTIA SINICA Physica, Mechanica & Astronomica. 43 (3), 297–308 (2013). | |
| dc.relation.referencesen | [8] Zhang J., Weicheng L., Yunqiao D., Chuanming J. A double-layer interpolation method for implementation of BEM analysis of problems in potential theory. Applied Mathematical Modelling. 51, 250–269 (2017). | |
| dc.relation.referencesen | [9] Zhuravchak L. Computation of pressure change in piecewise-homogeneous reservoir for elastic regime by indirect near-boundary element method. 2019 IEEE 14th International Conference on Computer Sciences and Information Technologies (CSIT). 141–144 (2019). | |
| dc.relation.referencesen | [10] Zhuravchak L. M., Zabrodska N. V. Using of partly-boundary elements as a version of the indirect near-boundary element method for potential field modeling. Mathematical Modeling and Computing. 8 (1), 1–10 (2021). | |
| dc.relation.referencesen | [11] Zhuravchak L. Combination of near-boundary and contact elements in modeling stationary processes in piecewise-homogeneous objects. 2020 IEEE 15th International Conference on Computer Sciences and Information Technologies (CSIT). 411–414 (2020). | |
| dc.relation.referencesen | [12] Zhuravchak L. M., Zabrodska N. V. Nonstationary thermal fields in inhomogeneous materials with nonlinear behavior of the components. Materials Science. 46 (1), 36–46 (2010). | |
| dc.relation.referencesen | [13] Zhuravchak L. M., Kruk O. S. Consideration of the nonlinear behavior of environmental material and a three-dimensional internal heat sources in mathematical modeling of heat conduction. Mathematical Modeling and Computing. 2 (1), 107–113 (2015). | |
| dc.relation.referencesen | [14] Anshuman A., Eldho T. I. Coupled flow and transport simulation involving rate-limited adsorption in highly heterogeneous unconfined aquifers using a local strong form meshless method. Engineering Analysis with Boundary Elements. 145, 1–12 (2022). | |
| dc.relation.referencesen | [15] Habibirad A., Hesameddini E., Shekari Y. A suitable hybrid meshless method for the numerical solution of time-fractional fourth-order reaction–diffusion model in the multi-dimensional case. Engineering Analysis with Boundary Elements. 145, 149–160 (2022). | |
| dc.relation.referencesen | [16] Qu W., Chen W., Fu Z. Solutions of 2D and 3D non-homogeneous potential problems by using a boundary element-collocation method. Engineering Analysis with Boundary Elements. 60, 2–9 (2015). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2024 | |
| dc.subject | непрямий метод приграничних елементів | |
| dc.subject | непрямий метод контактних елементів | |
| dc.subject | кусково-однорідний об’єкт | |
| dc.subject | локальна область неоднорідності матеріалу | |
| dc.subject | некласичні скінченні різниці | |
| dc.subject | електричне профілювання | |
| dc.subject | двовимірна задача теорії потенціалу | |
| dc.subject | indirect near-boundary element method | |
| dc.subject | indirect contact element method | |
| dc.subject | piecewise-homogeneous object | |
| dc.subject | local area of material inhomogeneity | |
| dc.subject | non-classical finite differences | |
| dc.subject | electrical profiling | |
| dc.subject | two-dimensional problem of potential theory | |
| dc.title | Potential field modeling by combination of near-boundary and contact elements with non-classical finite differences in a heterogeneous medium | |
| dc.title.alternative | Моделювання потенціального поля поєднанням приграничних та контактних елементів з некласичними скінченними різницями в неоднорідному середовищі | |
| dc.type | Article |
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