APPLIED QUASIPOTENTIAL METHOD FOR SOLVING THE COEFFICIENT PROBLEMS OF PARAMETER IDENTIFICATION OF ANISOTROPIC MEDIA
Andrii Bomba
Rivne State Humanitarian University, Department of Informatics and Applied Mathematics (Ukraine)
http://orcid.org/0000-0001-5528-4192
Andrii Safonyk
safonik@ukr.netNational University of Water and Environmental Engineering, Department of Automation, Electrical Engineering and Computer-Integrated Technologies (Ukraine)
http://orcid.org/0000-0002-5020-9051
Olha Michuta
National University of Water and Environmental Engineering, Department of Applied Mathematics (Ukraine)
http://orcid.org/0000-0003-2886-0662
Mykhailo Boichura
National University of Water and Environmental Engineering, Department of Applied Mathematics (Ukraine)
http://orcid.org/0000-0002-9073-4037
Abstract
A numerical method of quasiconformal mappings for solving the coefficient problems of finding eigenvalues of the conductivity tensor having information about its directions in an anisotropic medium using applied quasipotential tomographic data is generalized. The corresponding algorithm is based on the alternate solving of problems on quasiconformal mappings and parameter identification. The results of numerical experiments of imitative restoration of environment structure are presented.
Keywords:
applied quasipotential tomography, quasiconformal mapping, identification, anisotropyReferences
Abascal J.-F. P. J., Lionheart W. R. B., Arridge S. R., Schweiger M., Atkinson D., Holder D. S.: Electrical impedance tomography in anisotropic media with known eigenvectors. Inverse Problems 27(6)/2011, 1–17.
Google Scholar
Bomba A. Ya., Boichura M. V.: Applied quasipotenrial method for solving coefficient problems of parametric Identification. Bulletin of NUWEE. Technical Sciences Series 4(76)/2017, 163–177 (in Ukrainian).
Google Scholar
Bomba A. Ya., Kashtan S. S., Pryhornytskyi D. O., Yaroshchak S. V.: Complex analysis methods. Editorial and Publishing Department of NUWEE, Rivne 2013 (in Ukrainian).
Google Scholar
Bomba A. Ya., Kroka L. L.: Numerical methods of quasiconformal mappings for solving problems of identifying of electrical conductivity coefficient in an applied potential tomography. Volyn Mathematical Bulletin. Applied Mathematics Series 11(20)/2014, 24–33 (in Ukrainian).
Google Scholar
Bomba A. Ya., Safonik A. P.: Mathematical Simulation of the Process of Aerobic Treatment of Wastewater under Conditions of Diffusion and Mass Transfer Perturbations. 2018. Journal of Engineering Physics and Thermophysics 91(2)/2018, 318–323.
Google Scholar
Crabb M.: EIT Reconstruction Algorithms for Respiratory Intensive Care. Ph.D. Thesis, University of Manchester, Manchester 2014.
Google Scholar
Herwanger J.V., Pain C.C., Binley A., De Oliveira C.R.E., Worthington M. H.: Anisotropic resistivity tomography. Geophysical Journal International 158(2)/2004, 409–425.
Google Scholar
Holder D.: Electrical Impedance Tomography. Methods, History and Applications. IOP Publishing, Bristol 2005.
Google Scholar
Lionheart W. R. B.: Conformal uniqueness results in anisotropic electrical impedance imaging Inverse Problems. Inverse Problems 13(1)/1997, 125–134.
Google Scholar
Martins T. C., Tsuzuki M. S. G.: Investigating Anisotropic EIT with Simulated Annealing. IFAC-PapersOnLine 50(1)/2017, 9961–9966.
Google Scholar
Michuta O., Vlasyuk A., Martyniuk P.: Mathematical Modeling of Influence of Chemical Erosin and non-Isothermal Conditions on the Filtration Consolidation of Saline Soils in Three-Dimensional Case. Visnyk of the Lviv University. Series Applied Mathematics and Computer Science 19/2013, 68–80.
Google Scholar
Ortega J. M., Rheinboldt W. C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, San Diego 1970.
Google Scholar
http://www.alglib.net (available: 28.11.2018).
Google Scholar
Authors
Andrii BombaRivne State Humanitarian University, Department of Informatics and Applied Mathematics Ukraine
http://orcid.org/0000-0001-5528-4192
Authors
Andrii Safonyksafonik@ukr.net
National University of Water and Environmental Engineering, Department of Automation, Electrical Engineering and Computer-Integrated Technologies Ukraine
http://orcid.org/0000-0002-5020-9051
Authors
Olha MichutaNational University of Water and Environmental Engineering, Department of Applied Mathematics Ukraine
http://orcid.org/0000-0003-2886-0662
Authors
Mykhailo BoichuraNational University of Water and Environmental Engineering, Department of Applied Mathematics Ukraine
http://orcid.org/0000-0002-9073-4037
Statistics
Abstract views: 207PDF downloads: 125
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Most read articles by the same author(s)
- Andrii Bomba, Yurii Klymyuk, Ihor Prysіazhnіuk, COMPUTER PREDICTION OF TECHNOLOGICAL REGIMES OF RAPID CONE-SHAPED ADSORPTION FILTERS WITH CHEMICAL REGENERATION OF HOMOGENEOUS POROUS LOADS , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 10 No. 4 (2020)
- Andrii Safonyk, Ihor Prysiazhniuk, Olena Prysiazhniuk, Oleksandr Naumchuk, MATHEMATICAL MODELING SINGULARLY PERTURBED PROCESSES OF WATER SOFTENING ON SODIUM-CATIONITE FILTERS , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 9 No. 1 (2019)
- Andrii Safonyk, MODELLING AND AUTOMATION OF PROCESS OF WATER PURIFICATION BY MAGNETIC FILTER , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 6 No. 1 (2016)
