Abstract
This chapter presents a brief description of chapters devoted to the innovations in wave processes modelling and decision making (grid-characteristic method and applications). Grid-characteristic method is a direct finite-difference numerical method for obtaining full-wave solution of hyperbolic systems of equations. One can use different types of grids such as the regular, triangular, tetrahedral, and nested grids. This method is often used for modelling of the acoustic and isotropic/anisotropic elastic waves in heterogeneous media. Also, the original analytical algorithms for interpolation on the unstructured triangular and tetrahedral meshes are developed. The study of wave processes might be used in different applied areas, e.g. geophysics, non-destructive testing of different objects and materials, ultrasonic testing, seismic stability investigation, and ultrasonic operations modelling. Original investigation of composite materials delamination and non-destructive testing is done. The geological faults zones study is performed. Also, the migration techniques of acoustic and elastic fields are developed.
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References
Favorskaya AV, Petrov IB (2016) A study of high-order grid-characteristic methods on unstructured grids. Numer Anal Appl 9(2):171–178
Petrov IB, Favorskaya AV, Muratov MV, Biryukov VA, Sannikov AV (2014) Grid-characteristic method on unstructured tetrahedral grids. Dokl Math 90(3):781–783
Petrov IB, Favorskaya AV, Sannikov AV, Kvasov IE (2013) Grid-characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step. Math Models Comput Simul 5(5):409–415
Favorskaya AV, Petrov IB (2016) Wave responses from oil reservoirs in the Arctic shelf zone. Doklady Earth Sciences 466 (2):214–217
Favorskaya AV, Petrov IB (2017) Numerical modeling of dynamic wave effects in rock masses. Dokl Math 95(3):287–290
Favorskaya A, Petrov I, Golubev V, Khokhlov N (2017) Numerical simulation of earthquakes impact on facilities by grid-characteristic method. Proc Comp Sci 112:1206–1215
Petrov IB, Favorskaya AV, Khokhlov NI, Miryakha VA, Sannikov AV, Golubev VI (2015) Monitoring the state of the moving train by use of high performance systems and modern computation methods. Math Models Comput Simul 7(1):51–61
Magomedov KM, Kholodov AS (1988) Grid characteristic methods. Nauka, Moscow
Kholodov AS (1978) Construction of difference schemes with positive approximation for hyperbolic equations. USSR Comput Math Math Phys 18(6):116–132
Kholodov AS (1980) The construction of difference schemes of increased order of accuracy for equations of hyperbolic type. USSR Comput Math Math Phys 20(6):234–253
Kholodov AS, Kholodov YaA (2006) Monotonicity criteria for difference schemes designed for hyperbolic equations. Comput Math Math Phys 46(9):1560–1588
Alekseenko AE, Kholodov AS, Kholodov YA (2016) Boundary control problems for quasilinear systems of hyperbolic equations. Comput Math Math Phys 56(6):916–931
Belotserkovskii OM, Popov FD, Tolstykh AI, Fomin VN, Kholodov AS (1970) Numerical solution of some problems in gas dynamics. USSR Comput Math and Math Phys 10(2):158–177
Beklemysheva KA, Petrov IB, Favorskaya AV (2014) Numerical simulation of processes in solid deformable media in the presence of dynamic contacts using the grid-characteristic method. Math Models Comput Simul 6(3):294–304
Vasyukov AV, Ermakov AS, Potapov AP, Petrov IB, Favorskaya AV, Shevtsov AV (2014) Combined grid-characteristic method for the numerical solution of three-dimensional dynamical elastoplastic problems. Comput Math Math Phys 54(7):1176–1189
Petrov I, Vasyukov A, Beklemysheva K, Ermakov A, Favorskaya A (2016) Numerical modeling of non-destructive testing of composites. Proc Comput Sci 96:930–938
Zhdanov MS (2002) Geophysical inverse theory and regularization problems. Methods in Geochemistry and Geophysics, vol 36, Elsevier, Netherlands
Luo Y, Tromp J, Denel B, Calandra H (2013) 3D coupled acoustic-elastic migration with topography and bathymetry based on spectral-element and adjoint methods. Geophysics 78(4):193–202
Morse PM, Feshbach H (1953) Methods of theoretical physics. McGraw-Hill Book Co. Inc, New York, Toronto, London
Moser TJ (2012) Review of ray-Born forward modeling for migration and diffraction analysis Stud Geophys Geod 56(2):411–432
Cervený V, Klimeš L, Pšenčík I (2007) Seismic ray method: recent developments. Adv Geophys 48:1–126
Thierry P, Operto S, and Lambar´e G (1999) Fast 2-D ray—born migration/inversion in complex media. Geophysics 64(1):162–181
Beydoun WB, Mendes M (1989) Elastic ray-Born L2-migration/inversion. Geophys J Int 97(1):151–160
Beylkin G, Burridge R (1990) Linearized inverse scattering problems in acoustics and elasticity. Wave Motion 12(1):15–52
Favorskaya MN, Buryachenko VV (2018) Warping techniques in video stabilization. Intell Syst Ref Librar 135:177–215
Favorskaya MN, Jain LC (2017) Large scene rendering. Intell Syst Ref Librar 122:281–320
Favorskaya M, Buryachenko V, Tomilina A (2017) Structure-based improvement of scene warped locally in digital video stabilization. Proc Comput Sci 112:1062–1071
Favorskaya M, Jain LC (2016) Recognition of pedestrian active events by robust to noises boost algorithm. Adv Intell Syst Comput 357:863–873
Favorskaya M, Jain LC, Proskurin A (2016) Unsupervised clustering of natural images in automatic image annotation systems. Intell Syst Ref Lib 108:23–155
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Favorskaya, A.V., Petrov, I.B. (2018). Theory and Practice of Wave Processes Modelling. In: Favorskaya, A., Petrov, I. (eds) Innovations in Wave Processes Modelling and Decision Making. Smart Innovation, Systems and Technologies, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-76201-2_1
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