Skip to main content
Top
Published in:
Cover of the book

2018 | OriginalPaper | Chapter

1. Theory and Practice of Wave Processes Modelling

Authors : Alena V. Favorskaya, Igor B. Petrov

Published in: Innovations in Wave Processes Modelling and Decision Making

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Favorskaya AV, Petrov IB (2016) A study of high-order grid-characteristic methods on unstructured grids. Numer Anal Appl 9(2):171–178 Favorskaya AV, Petrov IB (2016) A study of high-order grid-characteristic methods on unstructured grids. Numer Anal Appl 9(2):171–178
2.
go back to reference 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, Muratov MV, Biryukov VA, Sannikov AV (2014) Grid-characteristic method on unstructured tetrahedral grids. Dokl Math 90(3):781–783
3.
go back to reference 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 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
4.
go back to reference 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 (2016) Wave responses from oil reservoirs in the Arctic shelf zone. Doklady Earth Sciences 466 (2):214–217
5.
go back to reference Favorskaya AV, Petrov IB (2017) Numerical modeling of dynamic wave effects in rock masses. Dokl Math 95(3):287–290 Favorskaya AV, Petrov IB (2017) Numerical modeling of dynamic wave effects in rock masses. Dokl Math 95(3):287–290
6.
go back to reference 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 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
7.
go back to reference 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 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
8.
go back to reference Magomedov KM, Kholodov AS (1988) Grid characteristic methods. Nauka, Moscow Magomedov KM, Kholodov AS (1988) Grid characteristic methods. Nauka, Moscow
9.
go back to reference Kholodov AS (1978) Construction of difference schemes with positive approximation for hyperbolic equations. USSR Comput Math Math Phys 18(6):116–132 Kholodov AS (1978) Construction of difference schemes with positive approximation for hyperbolic equations. USSR Comput Math Math Phys 18(6):116–132
10.
go back to reference 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 (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
11.
go back to reference Kholodov AS, Kholodov YaA (2006) Monotonicity criteria for difference schemes designed for hyperbolic equations. Comput Math Math Phys 46(9):1560–1588 Kholodov AS, Kholodov YaA (2006) Monotonicity criteria for difference schemes designed for hyperbolic equations. Comput Math Math Phys 46(9):1560–1588
12.
go back to reference Alekseenko AE, Kholodov AS, Kholodov YA (2016) Boundary control problems for quasilinear systems of hyperbolic equations. Comput Math Math Phys 56(6):916–931 Alekseenko AE, Kholodov AS, Kholodov YA (2016) Boundary control problems for quasilinear systems of hyperbolic equations. Comput Math Math Phys 56(6):916–931
13.
go back to reference 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 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
14.
go back to reference 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 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
15.
go back to reference 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 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
16.
go back to reference 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 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
17.
go back to reference Zhdanov MS (2002) Geophysical inverse theory and regularization problems. Methods in Geochemistry and Geophysics, vol 36, Elsevier, Netherlands Zhdanov MS (2002) Geophysical inverse theory and regularization problems. Methods in Geochemistry and Geophysics, vol 36, Elsevier, Netherlands
18.
go back to reference 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 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
19.
go back to reference Morse PM, Feshbach H (1953) Methods of theoretical physics. McGraw-Hill Book Co. Inc, New York, Toronto, London Morse PM, Feshbach H (1953) Methods of theoretical physics. McGraw-Hill Book Co. Inc, New York, Toronto, London
20.
go back to reference Moser TJ (2012) Review of ray-Born forward modeling for migration and diffraction analysis Stud Geophys Geod 56(2):411–432 Moser TJ (2012) Review of ray-Born forward modeling for migration and diffraction analysis Stud Geophys Geod 56(2):411–432
21.
go back to reference Cervený V, Klimeš L, Pšenčík I (2007) Seismic ray method: recent developments. Adv Geophys 48:1–126 Cervený V, Klimeš L, Pšenčík I (2007) Seismic ray method: recent developments. Adv Geophys 48:1–126
22.
go back to reference Thierry P, Operto S, and Lambar´e G (1999) Fast 2-D ray—born migration/inversion in complex media. Geophysics 64(1):162–181 Thierry P, Operto S, and Lambar´e G (1999) Fast 2-D ray—born migration/inversion in complex media. Geophysics 64(1):162–181
23.
go back to reference Beydoun WB, Mendes M (1989) Elastic ray-Born L2-migration/inversion. Geophys J Int 97(1):151–160 Beydoun WB, Mendes M (1989) Elastic ray-Born L2-migration/inversion. Geophys J Int 97(1):151–160
24.
go back to reference Beylkin G, Burridge R (1990) Linearized inverse scattering problems in acoustics and elasticity. Wave Motion 12(1):15–52 Beylkin G, Burridge R (1990) Linearized inverse scattering problems in acoustics and elasticity. Wave Motion 12(1):15–52
25.
go back to reference Favorskaya MN, Buryachenko VV (2018) Warping techniques in video stabilization. Intell Syst Ref Librar 135:177–215 Favorskaya MN, Buryachenko VV (2018) Warping techniques in video stabilization. Intell Syst Ref Librar 135:177–215
26.
go back to reference Favorskaya MN, Jain LC (2017) Large scene rendering. Intell Syst Ref Librar 122:281–320 Favorskaya MN, Jain LC (2017) Large scene rendering. Intell Syst Ref Librar 122:281–320
27.
go back to reference 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, Buryachenko V, Tomilina A (2017) Structure-based improvement of scene warped locally in digital video stabilization. Proc Comput Sci 112:1062–1071
28.
go back to reference 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 (2016) Recognition of pedestrian active events by robust to noises boost algorithm. Adv Intell Syst Comput 357:863–873
29.
go back to reference Favorskaya M, Jain LC, Proskurin A (2016) Unsupervised clustering of natural images in automatic image annotation systems. Intell Syst Ref Lib 108:23–155 Favorskaya M, Jain LC, Proskurin A (2016) Unsupervised clustering of natural images in automatic image annotation systems. Intell Syst Ref Lib 108:23–155
Metadata
Title
Theory and Practice of Wave Processes Modelling
Authors
Alena V. Favorskaya
Igor B. Petrov
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-76201-2_1

Premium Partner