Possible research titles

• Development of novel numerical methods for simulation of dynamic processes in complex media.

Supervisor’s research interests

My research work is connected with the development of novel numerical methods for simulation of dynamic processes in complex media. Many phenomena and technological processes are described by hyperbolic systems of equations: the earthquake initiation, the seismic survey of oil and gas deposits, the non-destructive testing of composite materials, etc. In our research group we are concentrated on the extension of the grid-characteristic method for more complicated medium models.
Acoustic, anisotropic elastic, fluid-saturated porous and non-linear continuum approaches and approximations are investigated. The internal research software is developed on C++ language supporting OpenMP, MPI and GPGPU systems. We are seeking for motivated young persons interested to expand scientific knowledge in the simulation area.

Research highlights

• Presentation of obtained scientific results at major international conferences: EAGE, SEG, etc.
• Participation in real-life research projects supported by RFBR, RSF and other scientific foundations
• Chance to achieve a good experience in a team of talented young people
• Collaboration with specialists from oil and gas companies

Main publications

• Golubev, V.I., Shevchenko, A.V., Petrov, I.B. Taking into Account Fluid Saturation of Bottom Sediments in Marine Seismic Survey (2019) Doklady Mathematics, 100 (2), pp. 488-490.
• Golubev, V.I., Voinov, O.Y., Petrov, I.B. Seismic Imaging of Fractured Elastic Media on the Basis of the Grid-Characteristic Method (2018) Computational Mathematics and Mathematical Physics, 58 (8), pp. 1309-1315.
• Beklemysheva, K.A., Vasyukov, A.V., Golubev, V.I., Zhuravlev, Y.I. On the Estimation of Seismic Resistance of Modern Composite Oil Pipeline Elements (2018) Doklady Mathematics, 97 (2), pp. 184-187.
• Golubev, V.I., Gilyazutdinov, R.I., Petrov, I.B., Khokhlov, N.I., Vasyukov, A.V. Simulation of dynamic processes in three-dimensional layered fractured media with the use of the grid-characteristic numerical method (2017) Journal of Applied Mechanics and Technical Physics, 58 (3), pp. 539-545.
• Study of Anisotropy of Seismic Response from Fractured Media July 2021 DOI:10.1007/978-981-16-2765-1_19 (http://dx.doi.org/10.1007/978-981-16-2765-1_19) In book: Intelligent Decision Technologies (pp.231-240)
• Golubev, V. I., и I. S. Nikitin. «Refined Schemes for Computing the Dynamics of Elastoviscoplastic Media». Computational Mathematics and Mathematical Physics 63, вып. 10 (2023 г.). https://doi.org/10.1134/s0965542523100032.
• Golubev, V. I., I. S. Nikitin, N. G. Burago, и Yu A. Golubeva. «Explicit–Implicit Schemes for Calculating the Dynamics of Elastoviscoplastic Media with a Short Relaxation Time». Differential Equations 59, вып. 6 (2023 г.). https://doi.org/10.1134/s0012266123060101.
• Golubev, V. I., I. S. Nikitin, A. V. Shevchenko, и I. B. Petrov. «Explicit–Implicit Schemes for Calculating Dynamics of Elastoviscoplastic Media with Softening». Differential Equations 60, вып. 6 (2024 г.). https://doi.org/10.1134/s0012266124060077.
• Golubev, Vasily I, и Ilia S Nikitin. «Numerical Schemes of Higher Approximation Orders for Dynamic Problems of Elastoviscoplastic Media», б. д.
• Golubev, Vasily, Ilia Nikitin, и Katerina Beklemysheva. «Model of fractured medium and nondestructive control of composite materials». Chinese Journal of Aeronautics 37, вып. 2 (1 февраль 2024 г.): 93–99. https://doi.org/10.1016/j.cja.2023.11.023.
• Golubev, Vasily, Alexey Vasykov, Ilia Nikitin, Andrey Stankevich, и Igor Petrov. «Continuum Model of Fractured Media in Direct and Inverse Seismic Problems». Continuum Mechanics and Thermodynamics 35, вып. 4 (2023 г.). https://doi.org/10.1007/s00161-022-01149-w.
• Guseva, E. K., V. I. Golubev, и I. B. Petrov. «Linear, Quasi-Monotonic and Hybrid Grid-Characteristic Schemes for Hyperbolic Equations». Lobachevskii Journal of Mathematics 44, вып. 1 (2023 г.). https://doi.org/10.1134/s1995080223010146.
• Institute of Computer Aided Design RAS, Ilia S. Nikitin, Vasily I. Golubev, и Moscow Institute of Physics and Technology (National Research University). «Explicit-Implicit Schemes for Calculating the Dynamics of Layered Media with Nonlinear Conditions at Contact Boundaries». Journal of Siberian Federal University. Mathematics & Physics 14, вып. 6 (декабрь 2021 г.): 768–78. https://doi.org/10.17516/1997-1397-2021-14-6-768-778.
• Malovichko, M. S., N. B. Yavich, A. M. Razorenova, V. I. Golubev, и N. A. Koshev. «PDE-Constrained Optimization for Electroencephalographic Source Reconstruction». Lobachevskii Journal of Mathematics 45, вып. 6 (2024 г.). https://doi.org/10.1134/s1995080224603266.
• Petrov, I. B., V. I. Golubev, Yu S. Ankipovich, и A. V. Favorskaya. «Numerical Modeling of Acoustic Processes in Gradient Media Using the Grid-Characteristic Method». Doklady Mathematics 106, вып. 3 (2022 г.). https://doi.org/10.1134/s1064562422700090.
• Petrov, I. B., V. I. Golubev, V. Yu Petrukhin, и I. S. Nikitin. «Simulation of Seismic Waves in Anisotropic Media». Doklady Mathematics 103, вып. 3 (2021 г.). https://doi.org/10.1134/s1064562421030145.
• Petrov, I. B., V. I. Golubev, A. V. Shevchenko, и I. S. Nikitin. «Approximation of Boundary Condition in Higher Order Grid-Characteristic Schemes». Doklady Mathematics 108, вып. 3 (2023 г.). https://doi.org/10.1134/s1064562423701375.
• Shevchenko, A. V., и V. I. Golubev. «Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems». Computational Mathematics and Mathematical Physics 63, вып. 10 (2023 г.). https://doi.org/10.1134/s096554252310010x. «Simulation of Seismic Wave Propagation in a Multicomponent Oil Deposit Model». Просмотрено 5 ноябрь 2024 г. https://doi.org/10.1142/S1758825120500842.
• Vasyukov, A. V., I. S. Nikitin, A. S. Stankevich, и Vasily I. Golubev. «DEEP CONVOLUTIONAL NEURAL NETWORKS IN SEISMIC EXPLORATION PROBLEMS». Interfacial Phenomena and Heat Transfer 10, вып. 3 (2022 г.). https://doi.org/10.1615/InterfacPhenomHeatTransfer.2022046367.
• Yavich, N. B., V. I. Golubev, и N. I. Khokhlov. «Fast Parallel Solver of Time-Harmonic Wave Equation with Topography». Lobachevskii Journal of Mathematics 45, вып. 1 (2024 г.). https://doi.org/10.1134/s1995080224010542.