Numerical methods for differential equations, finite element method, computational seismology, numerical methods in elasticity, domain decomposition methods, mathematical modeling

Papers
1. F. di Michele, А. Styahar, D. Pera, J. May, R. Aloisio, B. Rubino, P. Marcati. Fault shape effect on SH waves using finite element method, Springer, Journal of Seismology, 26 (2022), pp. 417-437, doi: https://doi.org/10.1007/s10950-022-10075-y
2. I. Prokopyshyn, A. Styahar. Numerical analysis of contact of the elastic bodies one of which has a discontinuous thin coating, Materials Science, Vol. 57, No. 5 (2022), pp. 734–744, doi: 10.1007/s11003-022-00602-0.
The same: І. Prokopyshyn, А. Styahar. Numerical investigation of a contact between elastic bodies, one of which has a thin nonuniform coating, Physicochemical Mechanics of Materials, no. 5 (2021), pp. 125–133 (in Ukrainian)
3. I. Prokopyshyn, A. Styahar. Investigation of contact between elastic bodies one of which has a thin coating connected with the body through a nonlinear Winkler layer by the domain decomposition methods, J. Math. Sci., 258, no. 4 (2021), pp. 477–506.
The same: І. Prokopyshyn, А. Styahar. Investigation by domain decomposition methods of a contact between elastic bodies, one of which has a thin coating, connected with a body through a nonlinear Winkler layer, Math. Methods and Ph.-Mech. Fields, 62, no. 1 (2019), pp. 92–111. (in Ukrainian)
4. I. Dyyak, M. Kopytko and A. Styahar. Parallelization of the algorithm for the numerical solution to the hyperelastic deformation problem, Digest of Lviv University, Series on Applied Mathematics and Informatics, 29 (2021), pp. 37–49 (in Ukrainian)
5. I. Dyyak, B. Rubino, Ya. Savula and A. Styahar. Numerical analysis of heterogenous mathematical model of elastic body with thin inclusion by combined BEM and FEM, Mathematical Modeling and Computing, 6, no. 2 (2019), pp. 239–250.
6. A. Styahar, Ya. Savula and I. Dyyak. Numerical analysis of the stress-strain state of a body with thin inclusion by the domain decomposition method, J. Math. Sci., 217, no. 3 (2016), pp. 283–298.
The same: A. Styahar, Ya. Savula and I. Dyyak. Numerical analysis of the stress-strain state for the body with thin inclusion using domain decomposition method, Math. Methods and Ph.-Mech. Fields, 57, no. 3 (2014), pp. 119–131. (in Ukrainian)
7. Ya. Savula, A. Styahar. Numerical analysis of two-dimensional inhomogeneous elasticity problem with geometric nonlinearity, Ph.-Math. Modeling and Informational Technologies, 21 (2015), pp. 198–204. (in Ukrainian)
8. A. Styahar, Ya. Savula. On the convergence of domain decomposition algorithm for the body with thin inclusion, Acta Mechanica et Automatica, 9, no. 1 (31) (2015), pp. 27–32.
9. A. Styahar. Numerical investigation of the Girkmann problem with FEM/BEM coupling using domain decomposition, Journal of Computational and Applied Mathematics, 2(116) (2014), pp. 141–151.
10. I. Dyyak, Ya. Savula and A. Styahar. Numerical investigation of a plain strain state for a body with thin cover using domain decomposition, Journal of Numerical and Applied Mathematics, 3(109) (2012), pp. 23–33.
11. I. Makar, Ya. Savula and A. Styahar. Numerical analysis of a multiscale model of the elastic body with the thin cover, Ph.-Math. Modeling and Informational Technologies, 15 (2012), pp. 49–55.
12. I. Mukha, N. Savula and A. Styahar. Analysis of the mathematical model of Tymoshenko, Digest of Lviv University, Series on Applied Mathematics and Informatics, 18 (2012), pp. 197–207. (in Ukrainian)

Conference Proceedings

13. F. di Michele, D. Pera, J. May, V. Kastelic, M. Carafa, А. Styahar, B. Rubino, R. Aloisio, P.Marcati. On the possible use of the not-honoring method to include a real thrust into 3D physical based simulations, 21st International Conference on Computational Science and Its Applications (ICCSA), 13-16 September 2021, Cagliari, Italy, pp. 268-275, DOI 10.1109/ICCSA54496.2021.00044
14. I. Prokopyshyn, A. Styahar. Contact interaction between elastic bodies, one of which has a nonuniform thin coating, 15-th International Symposium of Ukrainian Mechanical Engineers in Lviv. Proceedings, 20-21 May 2021, Lviv, Ukraine, pp. 29–30, online. (in Ukrainian)
15. R. Martynyak, A. Styahar. Numerical investigation of multiscale elasticity problems for the bodies with thin covers, VIII International Scientific and Technical Conference: Actual Problems of Applied Mechanics and Strength of Structures, 12 June 2020, Zaporizhia, Ukraine, online, http://mmodel.znu.edu.ua/konferencia (in Ukrainian)
16. I. Prokopyshyn, A. Styahar. Domain decomposition methods for the problem of imperfect contact between massive and thin elastic bodies, Modern Problems of Mechanics and Mathematics. Collection of scientific papers. Volume 2, 22-25 May 2018, Lviv, Ukraine, pp. 83–84. (in Ukrainian)
17. Ya. Savula, A. Styahar. Numerical solution of the multiscale elasticity problems, Ukrainian Conference on Applied Mathematics: Conference proceedings, 28-30 September 2017, Lviv, Ukraine, p. 96.
18. Ya. Savula, A. Styahar. Multiscale modeling of deformation processes for the bodies with thin covers and inclusions, Modern Problems of Applied Mathematics and Informatics: XX National Scientific Conference: Conference Materials, 7-9 April 2014, Lviv, Ukraine, pp. 27–28.
19. Ya. Savula, A. Styahar. Numerical investigation of Girkman problem, VI International Scientific Conference “Modern Problems of Mathematical Modeling, Prediction and Optimization”, 4-5 April 2014, Kamyanets-Podilskyy, Ukraine, pp. 138–139.
20. А. Styahar. Numerical solution of Girkman problem by FEM/BEM coupling using domain decomposition, Modern Problems of Applied Mathematics and Informatics: XIX National Scientific Conference: Conference Materials, 3-4 October 2013, Lviv, Ukraine, p. 123. (in Ukrainian)
21. I. Dyyak, Ya. Savula and A. Styahar. Numerical investigation of a stress-strain state for a body with thin inclusion, VI International Scientific Conference Dedicated to the Memory of І. Lyashko “Computational and Applied Mathematics”, 5-6 September 2013, Kyiv, Ukraine, pp. 22–25.
22. Ya. Savula, І. Dyyak and А. Styahar. Numerical solution of the problems of the Girkman type and for the bodies with inclusion, Modern Problems of Mechanics and Mathematics. Scientific Works, 21-25 May 2013, Lviv, Ukraine, pp. 103–104. (in Ukrainian)
23. Ya. Savula, І. Makar and А. Styahar. Numerical solution of Girkman-type problems and problems for the bodies with cover, Modern Problems of Mathematical Modeling and Numerical Methods: Conference Materials, 22-23 February 2013, Rivne, Ukraine, p. 130. (in Ukrainian)
24. Ya. Savula, A. Styahar. Numerical simulation of the bodies with thin covers and inclusions using FEM/BEM coupling with domain decomposition algorithm, VIII International Conference on Porous Materials: Theory and Experiment (INTERPOR), 18-21 September 2012, Lviv, Ukraine, pp. 105–106.
25. Ya. Savula, I. Dyyak, I. Makar and A. Styahar. Applications of FEM/BEM coupling on heterogeneous structures using domain decomposition, European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), 10-14 September 2012, Vienna, Austria.
26. Ya. Savula, А. Styahar. Numerical solution of structural mechanics problems by FEM/BEM coupling using domain decomposition, Modern Problems of Applied Mathematics and Informatics: XVII National Scientific Conference: Conference Materials, 6-7 October 2011, Lviv, Ukraine, p. 91. (in Ukrainian)
27. І. Dyyak, Ya. Savula, Yu. Yashchuk and А. Styahar. Numerical solution of structural mechanics problems using mortar FEM functions, Mathematical Modeling and Mathematical Physics: Conference Materials, 21-24 September 2011, Kremenchuk, Ukraine, pp. 32–33. (in Ukrainian)

2007 – B.Sc. in Applied Mathematics (with Honors), Ivan Franko National University of Lviv.

2008 – M.Sc. in Applied Mathematics (with Honors), Ivan Franko National University of Lviv.

2008-2010 – M.Sc. in Mathematical Modelling, Mathmods programme, University of L’Aquila (Italy), University of Nice – Sophia Antipolis (France), University of Hamburg (Germany).

2010-2013 – Ph. D. Student at Ivan Franko National University of Lviv, specialty: mathematical modeling and computational methods.

2015 – Ph.D. in Mathematical Modelling and Numerical Methods, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine.

Working Experience

Since 2020 – Associate Professor at Department of Applied Mathematics, Ivan Franko National University of Lviv.

2016-2019 – Postdoctoral Researcher at DISIM, University of L’Aquila, Italy.

2012-2016 – Assistant Professor at Department of Applied Mathematics, Ivan Franko National University of Lviv.

Teaching:

– lectures and exercise classes in mathematical modeling and simulation (also for InterMaths students, in English);
– exercise classes in functional analysis, numerical methods, numerical methods of mathematical physics, algorithms and computational processes.

Internships:

May-July, 2009 -INRIA, Sophia Antipolis, Nice, France

Awards and Scholarships

2016 – President’s of Ukraine Award for Young Scientists.

1st semester
2nd semester