МЕГАГРАНТЫ

Лаборатория "Многомасштабные модели пониженного порядка"

О лаборатории

Наименование проекта
Многомасштабные модели пониженного порядка.

№ договора:

14.Y26.31.0013

Сайт лаборатории

Наименование организации
Федеральное государственное автономное образовательное учреждение высшего образования "Северо-Восточный федеральный университет имени М.К. Аммосова"

Область научных исследований
Компьютерные и информационные науки

Цели и зачади проекта заключаются в следующем:
1. проведение фундаментальных исследований и разработка инновационных математических и вычислительных концепций моделирования и анализа для задач в сильно неоднородных пористых средах;
2. разработка алгоритмов высокого качества для многомасштабного моделирования и их математический анализ, включая инновационные адаптивные методы многомасштабного понижения порядка модели, передовые методы дискретизации, эффективные алгоритмы расщепления; 3. разработка интегрированного программного инструментария для численного моделирования многомасштабных задач;
4. проведение точных и подробных исследований для отдельных прикладных задач (приложений);
5. объединение ряда математических подобластей под эгидой адаптивных методов многомасштабного понижения порядка модели; а также
6. разработка учебных программ и программ стажировок в области адаптивных многомасштабных моделей пониженного порядка с интегрированными математическими компонентами.

Ведущий учёный

Efendiev Y 

ФИО: Эфендиев Ялчин

 

Дата рождения 25.01.1971

Гражданство
США

Ученые степень и звание

Доктор философии

Место работы

Техасский университет A&M

Область научных интересов

Многомасштабные методы, вычислительная математика, пористая среда, численное усреднение, численный анализ

Достижения и награды

- действительный член Американского математического сообщества (Fellow of AMS), 2017
- премия AFS Distinguished Achievement Award for Graduate Mentoring, Техасский университет A&M
- пленарный докладчик, Международное сообщество по исследованию пористой среды (International Society of Porous Media), май 2015
- приглашенный докладчик (45 мин), Международный Конгресс математиков, 2014 (ICM)
- Mobil Chair in Computational Sciences, Texas A&M University
- пленарный докладчик, SIAM Geosciences 2011
- QRI Scholar
- премия Fraunhofer Bessel Award (Фонд Александра фон Гумбольдта), 2010
- премия W. P. Carey Prize за выдающуюся научную работу в области Прикладной математики, Калифорнийский Технологический Институт, 1999
- Saul Kaplun Memorial Fellowship, Калифорнийский Технологический Институт, 1995-1996
- главный редактор, Журнал вычислительной и прикладной математики
- член редколлегии ряда журналов, включая SIAM MMS, SPE Journal, Geomathematics


1. Y. Efendiev, Hardness of the elastic medium when a solid is turned in it , V-Mosk-Mekh (6), pp. 76-78 (1994)
2. A. Yu. Beliaev, Y. Efendiev, Homogenization of the Stokes equations with random potential, Math. Notes, v59 (3-4), pp. 361-372 (1996)
3. Y. Efendiev, T. Hou, X. Wu, Convergence of a nonconformal multiscale finite element method, SIAM in J. Num. Anal. 37, 888-910 (2000)
4. Y. Efendiev, X.H. Wu, Multiscale finite element methods for the problems with highly oscillatory coefficients, Numerische Math., vol.90(3), 2002
5. Y. Efendiev, M. Luskin, Stability of microstructures for some martensitic transformations, Mathematical and Computer Modelling, v.34 (2001), pp. 1289-1305
6. Y. Efendiev, M. R. Zachariah, A model for two component aerosol coagulation and phase separation: A method for changing the growth of nanoparticles, Chemical Engineering Science. 56, 5763 (2001)
7. Y. Efendiev, L. Durlofsky, S. Lee, Modeling of subgrid effects in coarse-scale simulations of transport in heterogeneous porous media, Water Resources Research, 36(8), 2000, 2031-2041

Результаты исследований

Пукбликации

Q1

Chung E. T., Vasilyeva M., Wang Y. A conservative local multiscale model reduction technique for Stokes flows in heterogeneous perforated domains //Journal of Computational and Applied Mathematics — ISSN: 0377-0427. – 2017. – V. 321. – P. 389-405, http://dx.doi.org/10.1016/j.cam.2017.03.004
Yang, K., Guha, N., Efendiev, Y., & Mallick, B. K. Bayesian and variational Bayesian approaches for flows in heterogeneous random media //Journal of Computational Physics — ISSN: 0021-9991. – 2017. – V. 345. – P. 275-293, http://dx.doi.org/10.1016/j.jcp.2017.04.034
Eric T. Chung, Wing Tat Leung, Maria Vasilyeva, Yating Wang. Multiscale model reduction for transport and flow problems in perforated domains // Journal of Computational and Applied Mathematics — ISSN: 0377-0427. — 2018. -V. 330. -P. 519-535, http://dx.doi.org/10.1016/j.cam.2017.08.017
I. Yucel Akkutlu, Yalchin Efendiev, Maria Vasilyeva, Yuhe Wang . Multiscale model reduction for shale gas transport in poroelastic fractured media// Journal of Computational Physics — ISSN: 0021-9991. — 2018. -V. 353. -P. 356-376, https://doi.org/10.1016/j.jcp.2017.10.023
P.N. Vabishchevich. Two-component domain decomposition scheme with overlapping subdomains for parabolic equations //Journal of Computational and Applied Mathematics — ISSN: 0377-0427. — 2018. -V. 340. -P. 664-675, https://doi.org/10.1016/j.cam.2017.09.015
Vasilyeva M., Vasil’ev V., Stepanov S. Generalized multiscale discontinuous Galerkin method for solving the heat problem with phase change //Journal of Computational and Applied Mathematics — ISSN: 0377-0427. — 2018. -V. 340. -P. 645-652, https://doi.org/10.1016/j.cam.2017.12.004

Web Of Science (Core Collection)

Akkutlu, I. Y., Efendiev, Y., Vasilyeva, M., Wang, Y. Multiscale model reduction for shale gas transport in a coupled discrete fracture and dual-continuum porous media //Journal of Natural Gas Science and Engineering — ISSN: 1875-5100. – 2017. — V. 48. -P. 65-76, http://dx.doi.org/10.1016/j.jngse.2017.02.040
Cho, Y., Gibson, Jr, R. L., Vasilyeva, M., Efendiev, Y. Generalized multi-scale finite elements for simulation of elastic wave propagation in fractured media //Geophysics — ISSN: 0016-8033, — 2017. -V. 83. P. 1-70, https://doi.org/10.1190/geo2017-0076.1
P.N. Vabishchevich. Splitting schemes for unsteady problems involving the grad-div operator //Applied Numerical Mathematics — ISSN: 0168-9274. — 2018. -V. 124. -P. 130-139, https://doi.org/10.1016/j.apnum.2017.10.005

Others

Vabishchevich P.N., Vasil’ev A.O. Time step selection for the numerical solution of boundary value problems for parabolic equations // Computational Mathematics and Mathematical Physics. — 2017. — Vol. 57. —P. 843-853
Avvakumov A. V., Strizhov V. F., Vabishchevich P. N. et al. Spectral properties of dynamic processes in a nuclear reactor // Annals of Nuclear Energy . — 2017. — Vol. 99. — P. 68-79
Vasilyeva M.V., Vasilyev V. I., Krasnikov A. A., Nikiforov D.Y. Numerical Simulation of Single-Phase Fluid Flow in Fractured Porous Media // Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki. 2017. 159(1), pp. 100-115.
Fellerman, J., Brown, D.L., Vasilyeva, M. On Two-Scale Convergence of Fluid-Structure Interaction Problems with Applications to Poroelasticity // Poromechanics 2017 — Proceedings of the 6th Biot Conference on Poromechanics. 2017. pp. 125-132
Avvakumov A.V., Vabishchevich P.N., Vasil’ev A.O., Strizhev V.F. Numerical modeling of neutron diffusion non-stationary problems // Matematicheskoe Modelirovanie. — 2017. — Vol. 29 (7). — P. 44-62
Vladimir N. Glukhikh , Anna Y. Okhlopkova , Petr V. Sivtsev. Numerical Simulation of Deformations of Softwood Sawn Timber – 2017. (submitted, Lecture Notes in Computer Science (LNCS))
Vasilyeva M., Vasil’ev V., Krasnikov A., Nikiforov D. Numerical simulation of the one phase filtration problem in fractured porous media – 2017. (submitted)
Iliev O., Nikiforova M.A., Semenov Y.V., Zakharov P.E. Splitting Algorithm for Numerical Simulation of Li-ion Battery Electrochemical Processes. // AIP Conference Proceedings. — 2017. -V. 1907
Grigoriev V.V., Zakharov P.E. Numerical simulation of two-dimensional Rayleigh-Benard convection. // AIP Conference Proceedings. — 2017. -V. 1907
Sirditov I., Stepanov S. Mathematical modeling of the Heat Transfer for Determining the Depth of Thawing Basin Building with Long Service Live. // AIP Conference Proceedings. — 2017. -V. 1907
Sivtsev P., Stepanov S. Numerical modeling of stress-strain state of pipeline. // AIP Conference Proceedings. — 2017. -V. 1907
Vasil’ev V.I. Conjugate Gradient Method for Identification of a Spacewise Heat Source // Lecture Notes in Computer Science. — 2017
Sivtsev P.V. Numerical Simulation of Deformations of Softwood Sawn Timber // Lecture Notes in Computer Science. — 2017
Vabishchevich P.N., Vasilev A.O. Solution of the 3D Neutron Diffusion Benchmark by FEM // Lecture Notes in Computer Science. — 2017
Vasilyeva M.V., Stepanov S.P., Sirditov I.K. Reduced dimension model for heat transfer of ground heat exchange in permafrost // Journal of Physics: Conference Series. — 2017, -V. 937.
Vasil’ev V.I., Prokopiev G. Iterative solution of the inverse cauchy problem for elliptic equation by the conjugate gradient method // AIP Conference proceeding. — 2017. -V. 1895.
Vasilyeva M., Gavrilieva U. Numerical simulation of elastic waves using discontinuous Galerkin method in heterogeneous media // Vestnik NEFU. — 2017. -V. 58
Vasilyeva M., Prokopiev G. Numerical solution of the two-phase flow filtration problem with heterogeneous coefficients using finite element method // Vestnik NEFU. — 2017. -V. 59
Vasilyeva M., Kolesov A., Tirilgin A. Numerical modellung of the viscoporoelastic problems for soils – 2017. // Vestnik NEFU. — 2017. -V. 60.
Васильева М. В. и др. Численное моделирование задач термоупругости для конструкции с внутренним источником //Математические заметки СВФУ. – 2017. – Т. 24. – №. 3.
Спиридонов Д. А., Васильева М. В. Моделирование задач фильтрации в трещиноватых пористых средах посредством смешанного метода конечных элементов (встроенная модель трещин) //Математические заметки СВФУ. – 2017. – Т. 24. – №. 3.

Q1

Qiuqi Li, Yuhe Wang, Maria Vasilyeva, Multiscale model reduction for fluid infiltration simulation through dual-continuum porous media with localized uncertainties // Journal of Computational and Applied Mathematics. – Volume 336. – 2018. – Pages 127-146. – ISSN 0377-0427. — https://doi.org/10.1016/j.cam.2017.12.040.
M. Vasilyeva, A. Mistry, P. Mukherjee. Multiscale Model Reduction for Pore-scale Simulation of Li-ion batteries using GMsFEM // Journal of Computational and Applied Mathematics. – Volume 344. – 2018. – Pages 73-88.— ISSN 0377-0427. — https://doi.org/10.1016/j.cam.2018.05.016.
Eric T.Chung, Yalchin Efendiev, Wing Tat Leung, Maria Vasilyeva, Yating Wang. Non-local multi-continua upscaling for flows in heterogeneous fractured media // Journal of Computational Physics. — Volume 372. — 2018. — Pages 22-34. — ISSN 0021-9991. — https://doi.org/10.1016/j.jcp.2018.05.038.
Chung Eric T., Efendiev Yalchin, Leung Wing Tat. Fast online generalized multiscale finite element method using constraint energy minimization // Journal of Computational Physics . — Volume 355. — 2018. — Pages 450-463. — ISSN 0021-9991. — DOI: 10.1016/j.jcp.2017.11.022.
Eric T.Chung, Yalchin Efendiev, Wing Tat Leung, Shuai Ye. Generalized multiscale finite element methods for space–time heterogeneous parabolic equations // Computers and Mathematics with Applications. -Volume 76, Issue 2. -2018. -Pages 419-437. -ISSN: 0898-1221. https://doi.org/10.1016/j.camwa.2018.04.028.
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung. Constraint Energy Minimizing Generalized Multiscale Finite Element Method // Comput. Methods Appl. Mech. Engrg. -Volume 339. 2018. -Pages 298–319. -ISSN: 0045-7825. https://doi.org/10.1016/j.cma.2018.04.010.
Petr N. Vabishchevich, Two-level schemes for the advection equation // Journal of Computational Physics. — Volume 363. — 2018. — Pages 158-177. — ISSN 0021-9991. — https://doi.org/10.1016/j.jcp.2018.02.044.
Peter Minev, Shriram Srinivasan, Petr N.Vabishchevich. Flux formulation of parabolic equations with highly heterogeneous coefficients // Journal of Computational and Applied Mathematics. – Volume 340. – 2018. – Pages 582-601. — ISSN 0377-0427. DOI: 10.1016/j.cam.2017.09.015.
E.M. Rudoy, N.P. Lazarev, Domain decomposition technique for a model of an elastic body reinforced by a Timoshenko’s beam // Journal of Computational and Applied Mathematics. — Volume 334. — 2018. — Pages 18-26. — ISSN 0377-0427. — https://doi.org/10.1016/j.cam.2017.11.019.
M.V. Klibanov, A.E. Kolesov. Convexification of a 3-d coefficient inverse scattering problem // Computers and Mathematics with Applications. — 2018. — ISSN 0898-1221. — Published online, https://doi.org/10.1016/j.camwa.2018.03.016.
Michael V Klibanov, Aleksandr E Kolesov, Anders Sullivan and Lam Nguyen, A new version of the convexification method for a 1D coefficient inverse problem with experimental data // Inverse Problems. — Volume 34. — Number 11. ISSN 0266-5611, https://doi.org/10.1088/1361-6420/aadbc6
Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev, Jihoon Kim, Constrained energy minimization based upscaling for coupled flow and mechanics // Journal of Computational Physics, Volume 376, 2019, Pages 660-674, https://doi.org/10.1016/j.jcp.2018.09.054, ISSN 0021-9991
P. N. Vabishchevich, Computational identification of the lowest space-wise dependent coefficient of a parabolic equation // Applied mathematical modelling, Volume 65, 2019, pp. 361-376, ISSN 0307-904X, https://doi.org/10.1016/j.apm.2018.08.024
Eric T. Chung, Yalchin Efendiev, W. T. Leung. Generalized Multiscale Finite Element Methods with energy minimizing oversampling // International Journal for Numerical Methods in Engineering, Volume 117, 2019, pp 316-343, ISSN 0029-5981 DOI: 10.1002/nme.5958
Michael V. Klibanov, Aleksandr E. Kolesov, Dinh-Liem Nguyen, Convexification method for a coefficient inverse problem and its performance for experimental backscatter data for buried targets // SIAM journal on imaging sciences, Vol. 12, No. 1, pp. 576-603, ISSN 1936-4954. DOI. 10.1137/18M1191658

Web Of Science (Core Collection)

Chung E., Efendiev Y., Leung, WT. Constraint energy minimizing generalized multiscale finite element method in the mixed formulation // COMPUTATIONAL GEOSCIENCES. — Volume 22. Issue 3. — 2018. — Pages 677-693. — ISSN 1420-0597. —DOI: 10.1007/s10596-018-9719-7. (Q2).
P. N. Vabishchevich, P. E. Zakharov. Numerical Solution of Time-Dependent Problems with Different Time Scales // Computational Mathematics and Mathematical Physics — issn 0965-5425, 2018, Vol. 58, No. 10, pp. 1552–1561.
E. T. Chung, Ya. Efendiev, W. T. Leung, M. Wheeler. Nonlinear Nonlocal Multicontinua Upscaling Framework and Its Applications // International Journal for Multiscale Computational Engineering — issn 1940-4352, 2018, 16(5), pp. 487–507. doi:10.1615/intjmultcompeng.2018027832
E. N. Lazarev, V. Everstov. Optimal location of a rigid inclusion in equilibrium problems for inhomogeneous two-dimensional bodies with a crack // Zeitschrift für Angewandte Mathematik und Mechanik — issn 1521-4001, DOI: 10.1002/zamm.201800268
Alexander V Avvakumov, Valery F Strizhov, Petr N Vabishchevich, Alexander O Vasilev. State change modal method for numerical simulation of dynamic processes in a nuclear reactor // Progress in Nuclear Energy. -Volume 106. -2018. -Pages 240-261. -ISSN: 0149-1970. https://doi.org/10.1016/j.pnucene.2018.02.027.
Yongchae Cho, Richard L. Gibson, Jr., Shubin Fu, Yalchin Efendiev. Frequency-domain reverse-time migration with accelerated wave simulation via generalized multiscale finite element // Journal of Applied Geophysics -ISSN: 0926-9851, Volume 160, January 2019, Pages 103-120. https://doi.org/10.1016/j.jappgeo.2018.11.005

Others

Maria Vasilyeva, Eric T. Chung, Wing Tat Leung, Valentin Alekseev Nonlocal multicontinuum (NLMC) upscaling of mixed dimensional coupled flow problem for embedded and discrete fracture models (submitted GEM — International Journal on Geomathematics)
Eric T. Chung, Yalchin Efendiev, Yanbo Li. Space-time GMsFEM for transport equations, GEM — International Journal on Geomathematics, 2018, Volume 9, Issue 2, pp 265–292
В.И. Васильев, М.В. Васильева, Д.Я. Никифоров. Численное решение задачи фильтрации в трещиноватой среде с использованием декомпозиции областей // Сибирский журнал индустриальной математики
В.Н. Алексеев, В.И. Васильев, М.В. Васильева, С.П. Степанов. Математические модели смешанной размерности процессов тепломассопереноса в системе-грунт труба // Сибирские электронные математические известия
В.И. Васильев, М.В. Васильева, А.В. Григорьев. Математическое моделирование задачи двухфазовой фильтрации в неоднородных трещиновато-пористых средах с использованием модели двойной пористости // Ученые записки Казанского университета, физико-математические науки
V. Alekseev, U. Gavrileva, D. Spiridonov, M. Vasilyeva. Numerical simulation of the transport and flow problems in perforated domains using Generalized Multiscale Finite Element method / AIP Conference Proceedings, 2018. 2025 (1), 100001
U. Gavrilieva, V. Alekseev, M. Vasilyeva. Numerical homogenization for wave propagation in fractured media / AIP Conference Proceedings, 2018. 2025 (1), 100002.
Aleksey Tyrylgin, Valentin Alekseev, Denis Spiridonov, Maria Vasilyeva, Qingfu Zhang. Mathematical modeling of the fluid flow and geo-mechanics in the fractured porous media using Generalized Multiscale Finite Element Method. / AIP Conference Proceedings, 2018. 2025 (1), 100009
D. Spiridonov, M. Vasilyeva. Multiscale model reduction of the flow problem in fractured porous media using Mixed Generalized Multiscale Finite Element method / AIP Conference Proceedings, 2018. 2025 (1), 100008
V. Alekseev, A. Tyrylgin, M. Vasilyeva. Generalized Multiscale Finite Element Method for elasticity problem in fractured media (submitted FDM: T&A proceeding)
Tyrylgin, M. Vasilyeva, D. Brown. Generalized Multiscale Finite Element Method for poroelasticity problems in heterogeneous media (submitted FDM: T&A proceeding)
U. Gavrilieva, V. Alekseev, M. Vasilyeva, J.D.De Basabe, Y.Efendiev, R.L.Gibson, Jr. Generalized Multiscale Discontinuous Galerkin Method for Helmholtz problem in fractured media (submitted FDM: T&A proceeding)
D. Spiridonov, M. Vasilyeva. Generalized Multiscale Finite Element method for unsaturated filtration problem in heterogeneous medium (submitted FDM: T&A proceeding)
Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev, Wing Tat Leung, Yating Wang. Upscaled model for mixed dimensional coupled flow problem in fractured porous media using Non-local multicontinuum (NLMC) method (submitted FDM: T&A proceeding)
P. Sivtsev, A. Grigorev. Numerical modeling of multiphysics blood filtration problem in liver lobule / AIP Conference Proceedings, 2018. 2025, 070003.
Kardashevskiy, V. Vasilev, V. Popov. Numerical reconstruction of the right-hand side with separable variables of the parabolic equation / AIP Conference Proceedings, 2018. 2025 (1), 100011
P. Sivtsev, A. Sivtseva. Numerical simulation of deformations of basalt roving (submitted FDM: T&A proceeding)
Kardashevskiy, V. Vasilev, V. Popov. The conjugate gradient method for the Dirichlet problem and its modifications (submitted FDM: T&A proceeding)
М.В. Васильева, В.И. Васильев, А.А. Тырылгин. Консервативная разностная схема для задач фильтрации в трещиноватых средах / Математические заметки СВФУ, 2018. Том 25, № 4
П. Е. Захаров, М. А. Никифорова. Численное моделирование термо-электрихимических процессов в li-ion аккумуляторах / Математические заметки СВФУ, 2018. Том 25, № 4

Q1

Denis Spiridonov, Maria Vasilyeva, Wing Tat Leung, A Generalized Multiscale Finite Element Method (GMsFEM) for perforated domain flows with Robin boundary conditions // Journal of Computational and Applied Mathematics. – Volume 357. – 2019. – Pages 319-328. – ISSN 0377-0427. — https://doi.org/10.1016/j.cam.2019.03.007.
Maria Vasilyeva, Eric T. Chung, Wing Tat Leung, Yating Wang, Denis Spiridonov, Upscaling method for problems in perforated domains with non-homogeneous boundary conditions on perforations using Non-Local Multi-Continuum method (NLMC) // Journal of Computational and Applied Mathematics. – Volume 357. – 2019. – Pages 215-227. – ISSN 0377-0427. — https://doi.org/10.1016/j.cam.2019.02.030.
Maria Vasilyeva, Eric T. Chung, Siu Wun Cheung, Yating Wang, Georgy Prokopev, Nonlocal multicontinua upscaling for multicontinua flow problems in fractured porous media // Journal of Computational and Applied Mathematics. – Volume 355. – 2019. – Pages 258-267. – ISSN 0377-0427. — https://doi.org/10.1016/j.cam.2019.01.024.
Raimondas Cˇiegis, Petr N. Vabishchevich, High order numerical schemes for solving fractional powers of elliptic operators // Journal of Computational and Applied Mathematics. – ISSN 0377-0427.

Web Of Science (Core Collection)

M. Vasilyeva, J. D. De Basabe, Y. Efendiev, R. L. Gibson, Multiscale model reduction of the wave propagation problem in viscoelastic fractured media // Geophysical Journal International, Volume 217, Issue 1, Pages 558–571, – ISSN 0956-540X. https://doi.org/10.1093/gji/ggz043

Others

Jingyan Zhang, Siu Wun Cheung, Yalchin Efendiev, and Eduardo Gildin, Eric T. Chung. Deep Model Reduction-Model Learning for Reservoir Simulation // Society of Petroleum Engineers. https://doi.org/10.2118/193912-MS
Leung, W. T., Chung, E. T., Efendiev, Y., Vasilyeva, M., & Wheeler, M. (2019, March 29). Nonlinear Upscaling of Two-Phase Flow Using Non-Local Multi-Continuum Approach // Society of Petroleum Engineers. doi:10.2118/193889-MS
S. Stepanov, A. Grigorev, M. Vasilyeva, D. Nikiforov and D. Spiridonov, Multiscale model reduction of fluid flow based on the dual porosity model // Journal of Physics: Conference Series. — 2019, -V. 1158, doi:10.1088/1742-6596/1158/4/042025.
A. Tyrylgin, D. Spiridonov and M. Vasilyeva, Numerical homogenization for poroelasticity problem in heterogeneous media // Journal of Physics: Conference Series. — 2019, -V. 1158, doi:10.1088/1742-6596/1158/4/042030.
M. Vasilyeva, and A. Tyrylgin, Convolutional neural network for fast prediction of the effective properties of domains with random inclusions // Journal of Physics: Conference Series. — 2019, -V. 1158, doi:10.1088/1742-6596/1158/4/042034.
D. Y. Nikiforov and S. P. Stepanov, Numerical simulation of the embedded discrete fractures by the finite element method // Journal of Physics: Conference Series. — 2019, -V. 1158, doi:10.1088/1742-6596/1158/3/032038.
V. I. Vasil’ev, A. M. Kardashevsky and V V Popov, An inverse problem for determination of the right part of parabolic equation by conjugate gradient method // Journal of Physics: Conference Series. — 2019, -V. 1158, doi:10.1088/1742-6596/1158/4/042033.
Ammosov, D., Vasilyeva, M., Babaei, M. and Chung, E, A coupled dual continuum and discrete fracture model for subsurface heat recovery with thermoporoelastic effects // Mathematical notes of NEFU, 2019. V 26, № 1, Pages 94 — 106, https://doi.org/10.25587/SVFU.2019.101.27250.
Su Ling-De, Vasil’ev Vasily I., Iterative identification of the spacewise-dependent right-hand side in a parabolic equation // Mathematical notes of NEFU, 2019. V 26, № 1, Pages 82 — 93, https://doi.org/10.25587/SVFU.2019.101.27249.

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