Petrov Igor Borisovich

Publications in Math-Net.Ru

1. Calculating technogenic vibrations in urban environments using grid-characteristic method
   
   Computer Research and Modeling, 17:6 (2025),  1119–1129
2. Detecting large fractures in geological media using convolutional neural networks
   
   Computer Research and Modeling, 17:5 (2025),  889–901
3. On a grid-characteristic second order scheme for systems of hyperbolic equations with piecewise constant coefficients on non-fitted meshes
   
   Dokl. RAN. Math. Inf. Proc. Upr., 525 (2025),  83–90
4. Numerical solution of integro-differential equations of the theory of viscoelasticity with kernels of exponential and Rabotnov types
   
   Dokl. RAN. Math. Inf. Proc. Upr., 521 (2025),  88–95
5. Elastoplastic ice model with dynamic damage for simulation of non-linear processes during a low-speed impact
   
   J. Sib. Fed. Univ. Math. Phys., 18:2 (2025),  179–190
6. A compound elastoplastic model with hydrostatic core and fracturing for localization of nonlinear deformations in ice during a low-speed impact
   
   Sib. Zh. Vychisl. Mat., 28:3 (2025),  269–286
7. Grid-characteristic method with implicit schemes and contact conditions at the material interface
   
   Zh. Vychisl. Mat. Mat. Fiz., 65:11 (2025),  1955–1970
8. Acoustic waveform inversion with image-to-image Schrödinger bridges
   
   Zh. Vychisl. Mat. Mat. Fiz., 65:8 (2025),  1451–1466
9. Grid-characteristic method combined with discontinuous Galerkin method for simulation of wave propagation through linear elastic media in the three-dimensional case
   
   Zh. Vychisl. Mat. Mat. Fiz., 65:2 (2025),  222–234
10. Three-dimensional grid-characteristic schemes of high order of approximation
    
    Dokl. RAN. Math. Inf. Proc. Upr., 520:1 (2024),  11–18
11. Study of rheological ice models based on numerical simulation of low-velocity impact with a ball indentor
    
    Prikl. Mekh. Tekh. Fiz., 65:6 (2024),  181–194
12. Increasing the order of approximation for calculations of wave processes in a composite sample when using an unstructured computational grid
    
    Prikl. Mekh. Tekh. Fiz., 65:3 (2024),  152–160
13. Numerical computation of methane migration effect on seismic survey results in permafrost zones
    
    Zh. Vychisl. Mat. Mat. Fiz., 64:9 (2024),  1708–1717
14. Explicit-implicit numerical scheme for problems in the dynamics of elastoviscoplastic media with softening
    
    Zh. Vychisl. Mat. Mat. Fiz., 64:9 (2024),  1689–1698
15. Iterative PDE-constrained optimization for seismic full-waveform inversion
    
    Zh. Vychisl. Mat. Mat. Fiz., 64:5 (2024),  954–966
16. About the boundary condition approximation in the higher-order grid-characteristic schemes
    
    Dokl. RAN. Math. Inf. Proc. Upr., 514:1 (2023),  52–58
17. On obtaining initial approximation for full wave inversion problem using convolutional neural network
    
    Dokl. RAN. Math. Inf. Proc. Upr., 512 (2023),  58–64
18. Linear quasi-monotonous and hybrid grid-characteristic schemes for the numerical solution of linear acoustic problems
    
    Sib. Zh. Vychisl. Mat., 26:2 (2023),  135–147
19. Application of convolutional neural networks for search and determination of physical characteristics of inhomogeneities in geological media from seismic data
    
    Mathematical notes of NEFU, 30:1 (2023),  101–113
20. Raising convergence order of grid-characteristic schemes for 2D linear elasticity problems using operator splitting
    
    Computer Research and Modeling, 14:4 (2022),  899–910
21. Calculation of transverse wave speed in preloaded fibres under an impact
    
    Computer Research and Modeling, 14:4 (2022),  887–897
22. Numerical modeling of acoustic processes in gradient media using the grid-characteristic method
    
    Dokl. RAN. Math. Inf. Proc. Upr., 507 (2022),  51–56
23. Joint modeling of wave phenomena by applying the grid-characteristic method and the discontinuous Galerkin method
    
    Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022),  62–67
24. Erratum to: On numerical modeling of fiber deformation and destruction under impact load
    
    Dokl. RAN. Math. Inf. Proc. Upr., 505 (2022),  303
25. On numerical modeling of fiber deformation and destruction under impact load
    
    Dokl. RAN. Math. Inf. Proc. Upr., 504 (2022),  83–87
26. Using 2D/3D convolutional neural networks and direct numerical modeling for transcranial ultrasound problems
    
    Dal'nevost. Mat. Zh., 22:2 (2022),  255–256
27. Hybrid grid-characteristic schemes for arctic seismic problems
    
    Dokl. RAN. Math. Inf. Proc. Upr., 501 (2021),  67–73
28. Mathematical modeling of 3D dynamic processes near a fracture using the Schoenberg fracture model
    
    Dokl. RAN. Math. Inf. Proc. Upr., 500 (2021),  40–44
29. Simulation of seismic waves in anisotropic media
    
    Dokl. RAN. Math. Inf. Proc. Upr., 498 (2021),  59–64
30. Calculation of a railway with unsupported sleepers by a grid-characteristic method
    
    Prikl. Mekh. Tekh. Fiz., 62:2 (2021),  193–200
31. Simulation of dynamic processes in deformable medium with the grid-characteristic approach
    
    Russian Journal of Cybernetics, 2:2 (2021),  74–81
32. Computation of seismic resistance of an ice island by the grid-characteristic method on combined grids
    
    Zh. Vychisl. Mat. Mat. Fiz., 61:8 (2021),  1363–1377
33. On numerical solution of joint inverse geophysical problems with structural constraints
    
    Computer Research and Modeling, 12:2 (2020),  329–343
34. Numerical modelling of seismic waves spread in models with an ice field in the arctic shelf
    
    Computer Research and Modeling, 12:1 (2020),  73–82
35. Stability analysis of artificial ice islands by methods of mathematical modeling
    
    Dokl. RAN. Math. Inf. Proc. Upr., 495 (2020),  44–47
36. Problem of acoustic diagnostics of a damaged zone
    
    Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020),  92–96
37. Solution of the fracture detection problem by machine learning methods
    
    Dokl. RAN. Math. Inf. Proc. Upr., 491 (2020),  107–110
38. Model and calculation of the stress-strain state of a hydrate-containing medium during its partial thawing
    
    Keldysh Institute preprints, 2020, 099, 23 pp.
39. Modeling of thin fiber deformation and destruction under dynamic load
    
    Mat. Model., 32:5 (2020),  95–102
40. Grid-characteristic calculation of multistorey buildings destruction
    
    Mat. Model., 32:3 (2020),  102–114
41. The numerical modeling of the elastic waves propagation in the geological media with gas cavities using the grid-characteristic method
    
    Sib. Zh. Vychisl. Mat., 23:3 (2020),  325–338
42. Modeling technical and mathematical tasks of applied knowledge areas on computers
    
    Proceedings of ISP RAS, 32:6 (2020),  167–182
43. Boundary conditions for modeling the impact of wheels on railway track
    
    Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020),  1587–1603
44. Application of mathematical fracture models to simulation of exploration seismology problems by the grid-characteristic method
    
    Computer Research and Modeling, 11:6 (2019),  1077–1082
45. Application of the grid-characteristic method for mathematical modeling in dynamical problems of deformable solid mechanics
    
    Computer Research and Modeling, 11:6 (2019),  1041–1048
46. The application of grid-characteristic method in solution of fractured formations exploration seismology direct problems (review article)
    
    Mat. Model., 31:4 (2019),  33–56
47. Numerical modeling of seismic influence on underwater composite oil pipeline
    
    Mat. Model., 31:1 (2019),  103–113
48. Application of the grid-characteristic method for solving the problems of the propagation of dynamic wave disturbances in high-performance computing systems
    
    Proceedings of ISP RAS, 31:6 (2019),  237–252
49. The use of full-wave numerical simulation for the investigation of fractured zones
    
    Mat. Model., 30:11 (2018),  105–126
50. Numerical modeling of low-velocity impact on hybrid composite
    
    Mat. Model., 30:11 (2018),  27–43
51. Discontinuous Galerkin method for simulation of ice flow impact on vertical cylinder offshore structure
    
    Mat. Model., 30:9 (2018),  111–134
52. Numerical modeling by grid-characteristic method of influence of ice formations on seismic replies
    
    Mat. Model., 30:8 (2018),  107–115
53. Problems of simulation of natural and anthropogenous processes in the Arctic zone of the Russian Federation
    
    Mat. Model., 30:7 (2018),  103–136
54. Modelling of the destruction of polymers under high energy impact
    
    Mat. Model., 30:7 (2018),  61–78
55. Numerical modeling of wave processes in the rocks by grid-characteristic method
    
    Mat. Model., 30:3 (2018),  37–51
56. Discontinuous Galerkin method for ice strength investigation
    
    Mat. Model., 30:2 (2018),  110–118
57. Seismic imaging of fractured elastic media on the basis of the grid-characteristic method
    
    Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018),  113–119
58. Grid-characteristic method on tetrahedral unstructured meshes with large topological inhomogeneities
    
    Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018),  62–72
59. Numerical problems of the modeling of natural and industrial processes in the Arctic zone of the Russian Federation
    
    Chebyshevskii Sb., 18:3 (2017),  428–443
60. Calculation of dynamic destruction in deformable bodies
    
    Mat. Model., 29:4 (2017),  45–58
61. Simulation of dynamic processes in three-dimensional layered cracked media with the use of the grid-characteristic numerical method
    
    Prikl. Mekh. Tekh. Fiz., 58:3 (2017),  190–197
62. Grid-characteristic method on embedded hierarchical grids and its application in the study of seismic waves
    
    Zh. Vychisl. Mat. Mat. Fiz., 57:11 (2017),  1804–1811
63. The development of fracture mathematical models for numerical solution of exploration seismology problems with use of grid-characteristic method
    
    Computer Research and Modeling, 8:6 (2016),  911–925
64. Modeling the influence of the Chelyabinsk meteorite's bow shock wave on the Earth surface
    
    Mat. Model., 28:8 (2016),  33–45
65. Numerical solution of exploration seismology problems in areas of fractures reservoirs
    
    Mat. Model., 28:7 (2016),  31–44
66. Compact grid-characteristic schemes of higher orders for 3D linear transport equation
    
    Mat. Model., 28:2 (2016),  123–132
67. Numerical modeling of composite materials failure using grid-characteristic method
    
    Mat. Model., 28:2 (2016),  97–110
68. The study of increased order grid-characteristic methods on unstructured grids
    
    Sib. Zh. Vychisl. Mat., 19:2 (2016),  223–233
69. Numerical study of wave propagation in porous media with the use of the grid-characteristic method
    
    Zh. Vychisl. Mat. Mat. Fiz., 56:9 (2016),  1645–1656
70. Numerical solution of seismic exploration problems in the Arctic region by applying the grid-characteristic method
    
    Zh. Vychisl. Mat. Mat. Fiz., 56:6 (2016),  1149–1163
71. Simulation of elastic wave propagation in geological media: Intercomparison of three numerical methods
    
    Zh. Vychisl. Mat. Mat. Fiz., 56:6 (2016),  1104–1114
72. Numerical modeling of straight 3d exploration seismology problems with use of grid-characteristic method on unstructured tetrahedral meshes
    
    Computer Research and Modeling, 7:4 (2015),  875–887
73. Numerical simulation of earthquakes' impact on facilities by grid-characteristic method
    
    Mat. Model., 27:12 (2015),  109–120
74. Numerical modeling of wave processes in layered media in the Arctic
    
    Mat. Model., 27:11 (2015),  63–75
75. Discontinuous Galerkin method for numerical simulation of dynamic processes in solids
    
    Mat. Model., 27:3 (2015),  96–108
76. Simulation of seismic processes inside the planet using hybrid grid-characteristic method
    
    Mat. Model., 27:2 (2015),  139–148
77. Application of the grid-characteristic method on unstructured tetrahedral meshes to the solution of direct problems in seismic exploration of fractured layers
    
    Zh. Vychisl. Mat. Mat. Fiz., 55:10 (2015),  1762–1772
78. Numerical simulation of dynamic processes in biomechanics using the grid-characteristic method
    
    Zh. Vychisl. Mat. Mat. Fiz., 55:8 (2015),  1380–1390
79. Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes
    
    Zh. Vychisl. Mat. Mat. Fiz., 55:3 (2015),  512–522
80. Numerical modeling of low energy strike at composite stringer panel
    
    Mat. Model., 26:9 (2014),  96–110
81. The monitoring state of a moving train using high performance systems and modern computational methods
    
    Mat. Model., 26:7 (2014),  19–32
82. Modeling of 3D seismic problems using high-performance computing
    
    Mat. Model., 26:1 (2014),  83–95
83. Combined grid-characteristic method for the numerical solution of three-dimensional dynamical elastoplastic problems
    
    Zh. Vychisl. Mat. Mat. Fiz., 54:7 (2014),  1203–1217
84. Grid-characteristic method on unstructured tetrahedral meshes
    
    Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014),  821–832
85. Computational modeling of a meteor entering atmosphere dense layersusing elastoplastic approximation
    
    Computer Research and Modeling, 5:6 (2013),  957–967
86. Numerical simulation of processes in rigid deformable media in the presence of dynamic contacts using grid-characteristic method
    
    Mat. Model., 25:11 (2013),  3–16
87. Simulation of wave responses from subvertical macrofracture systems using grid-characteristic method
    
    Mat. Model., 25:3 (2013),  89–104
88. Grid-characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step
    
    Mat. Model., 25:2 (2013),  42–52
89. Numerical simulation of seismic activity by the grid-characteristic method
    
    Zh. Vychisl. Mat. Mat. Fiz., 53:10 (2013),  1709–1720
90. High-performance computer simulation of wave processes in geological media in seismic exploration
    
    Zh. Vychisl. Mat. Mat. Fiz., 52:2 (2012),  330–341
91. Numerical study of anisotropy of wave responses from fractured reservoir by grid-characteristic method
    
    Mat. Model., 23:10 (2011),  97–106
92. Influence of natural disasters on ground facilities
    
    Mat. Model., 23:8 (2011),  46–54
93. Computation of dynamic processes in continuous media with a crack initiated by the near-surface disturbance using grid-characteristic method
    
    Mat. Model., 22:11 (2010),  109–122
94. Computational modeling of seysmoresponse in multilayered geologic medium by grid-characteristic method
    
    Mat. Model., 22:9 (2010),  13–22
95. Modeling of wave processes with smoothed particle hydrodynamics method
    
    Mat. Model., 21:7 (2009),  20–28
96. Computation of wave processes in nonuniform 3D constructions
    
    Mat. Model., 21:5 (2009),  3–9
97. Mathematical simulation of deformation and wave processes in multilayered structures
    
    Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009),  1690–1696
98. Numerical research of dynamic behavior of complicated constructions in impacts on rectangle and triangle grids
    
    Mat. Model., 19:9 (2007),  105–113
99. Simulation of deformation processes in complex construction under dynamic intensitive loadings
    
    Mat. Model., 18:5 (2006),  91–110
100. Numerical simulation of the consequences of a mechanical action on a human brain under a skull injury
     
     Zh. Vychisl. Mat. Mat. Fiz., 46:9 (2006),  1711–1720
101. О проблеме идентификации пользователя по почерку в биометрической системе контроля доступа
     
     Informatsionnye Tekhnologii i Vychslitel'nye Sistemy, 2005, no. 3,  61–70
102. Расчет динамических процессов в сооружениях при падении самолетов
     
     Informatsionnye Tekhnologii i Vychslitel'nye Sistemy, 2005, no. 1,  130–139
103. О численном моделировании биомеханических процессов в медицинской практике
     
     Informatsionnye Tekhnologii i Vychslitel'nye Sistemy, 2003, no. 1-2,  102–111
104. Computation of dynamical processes in eye during laser cataract extraction
     
     Mat. Model., 15:11 (2003),  37–44
105. Computational investigation of wave processes in perforated deformable media
     
     Mat. Model., 15:10 (2003),  89–94
106. Numerical analysis of wave processes and fracture in layered targets
     
     Zh. Vychisl. Mat. Mat. Fiz., 43:10 (2003),  1562–1579
107. Spatial patterns formed by chemotactic bacteria Escherichia coli
     
     Mat. Model., 14:10 (2002),  17–26
108. Wave processes in nonlinear active media
     
     Mat. Model., 12:1 (2000),  38–44
109. Grid characteristic method of dynamic deformation calculation on irregular grids
     
     Mat. Model., 11:7 (1999),  118–127
110. High impact modeling with smooth particle hydrodynamics
     
     Mat. Model., 11:1 (1999),  88–100
111. Simultaneous numerical solution of the compressed plasma effects and railgun electrodes problems
     
     Mat. Model., 5:10 (1993),  48–56
112. Numerical investigation of oblique collision of hard sphere with two-layer elastic-plastic slab
     
     Mat. Model., 4:3 (1992),  20–27
113. On the numerical analysis of three-dimensional problems of compression waves flow about an obstacle or a slot in elastoplastic half-space
     
     Dokl. Akad. Nauk SSSR, 314:4 (1990),  817–820
114. Calculation of dynamic deformation and distructure of elastic-plastic body by grid-characteristic methods
     
     Mat. Model., 2:11 (1990),  10–29
115. Calculation of short acoustic puls diffraction on a hole of the complicated form in the filling with elastic covering
     
     Mat. Model., 2:8 (1990),  51–59
116. About numerical solution of the three-dimensional shock problems
     
     Mat. Model., 2:2 (1990),  58–72
117. On the use of hybrid grid-characteristic schemes for the numerical solution of three-dimensional problems in the dynamics of a deformable solid
     
     Zh. Vychisl. Mat. Mat. Fiz., 30:8 (1990),  1237–1244
118. Numerical study of wave processes induced by the bulk energy absorption in targets of finite thickness
     
     Dokl. Akad. Nauk SSSR, 308:5 (1989),  1065–1069
119. Numerical modelling of the behaviour of elastic and elasto-plastic bodies in the presence of strong energy fluxes
     
     Mat. Model., 1:7 (1989),  1–12
120. On a numerical solution of related problems of supersonic flow over deformable shells of finite thickness
     
     Zh. Vychisl. Mat. Mat. Fiz., 27:8 (1987),  1233–1243
121. Computation of dynamic-deformation processes in elastoplastic solids with allowance for continual failure
     
     Dokl. Akad. Nauk SSSR, 285:6 (1985),  1344–1347
122. Numerical modeling of the process of penetration of a rigid body of revolution into an elastoplastic barrier
     
     Prikl. Mekh. Tekh. Fiz., 25:4 (1984),  132–139
123. Regularization of discontinuous numerical solutions of equations of hyperbolic type
     
     Zh. Vychisl. Mat. Mat. Fiz., 24:8 (1984),  1172–1188
124. Numerical investigation of certain dynamical problems of the mechanics of a deformable solid body by the grid-characteristic method
     
     Zh. Vychisl. Mat. Mat. Fiz., 24:5 (1984),  722–739


125. Academician Oleg Mikhailovich Belotserkovskii (on his 100th birthday)
     
     Mat. Model., 37:6 (2025),  194–196
126. Boris Nikolaevich Chetverushkin (on his eightieth birthday)
     
     Uspekhi Mat. Nauk, 79:4(478) (2024),  181–187
127. The life and scientific career of Academician O.M. Belotserkovskii
     
     Computer Research and Modeling, 14:4 (2022),  697–700
128. Editor’s note
     
     Computer Research and Modeling, 14:4 (2022),  695–696
129. In memory of Aleksandr Sergeevich Kholodov
     
     Mat. Model., 30:1 (2018),  135–136
130. In memory of A. S. Kholodov
     
     Computer Research and Modeling, 9:5 (2017),  677–678
131. In memory of O. M. Belotserkovskii
     
     Mat. Model., 28:2 (2016),  3–5
132. In memory of Academician of the RAS Oleg Mikhailovich Belotserkovskii
     
     Zh. Vychisl. Mat. Mat. Fiz., 56:6 (2016),  921–926
133. In memory of Radiĭ Petrovich Fedorenko (1930–2010)
     
     Zh. Vychisl. Mat. Mat. Fiz., 50:8 (2010),  1532–1536