Application of the grid-characteristic method for solving the problems of the propagation of dynamic wave disturbances in high-performance computing systems
https://doi.org/10.15514/ISPRAS-2019-31(6)-16
Abstract
The paper considers the application of various modern technologies of high-performance computing to accelerate the numerical solution of the problems of propagation of dynamic wave disturbances using the grid-characteristic method. Technologies are considered both for central processing units (CPUs) and for graphic processors (GPUs). Comparative results of applying MPI, OpenMP, CUDA technologies are presented. As examples of the work of the developed software package, a number of examples of calculating the problems of seismic and geophysics are given. Separately, the issue of parallelizing problems with the presence of contacts of many grids and the topography of the day surface using curvilinear grids is considered.
About the Authors
Nikolai Igorevich KhokhlovRussian Federation
candidate of physical and mathematical sciences, senior researcher, deputy head of the laboratory of applied computational geophysics
Igor Borisovich Petrov
Russian Federation
doctor of physical and mathematical sciences, professor, corresponding member of the Russian Academy of Sciences, head of the department of computer science
References
1. V.A. Biryukov, V.A. Miryakha, I.B. Petrov, and N.I. Khokhlov. Simulation of elastic wave propagation in geological media: Intercomparison of three numerical methods. Computational Mathematics and Mathematical Physics, vol. 56, no. 6, 2016, pp. 1086–1095.
2. Голубев В.И., Петров И.Б., Хохлов Н.И. Численное моделирование сейсмической активности сеточно-характеристическим методом. Журнал вычислительной математики и математической физики, том 53, № 10, 2013 г., стр. 1709 – 1720 / Golubev V.I., Petrov I.B., Khokhlov N.I. Numerical simulation of seismic activity by the grid-characteristic method. Computational Mathematics and Mathematical Physics, vol. 53, № 10, 2013, pp. 1523–1533.
3. P.L. Roe. Characteristic-Based Schemes for the Euler Equations. Annual Review of Fluid Mechanics, № 18, 1986, pp. 337-365.
4. LeVeque R.J. Finite volume methods for hyperbolic problems. Cambridge Texts in Applied Mathematics, vol. 31. Cambridge university press, 2002, 552 p.
5. LeVeque R.J. Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. Other Titles in Applied Mathematics, vol. 98. Siam, 2007, 328 p.
6. Strang G. On the construction and comparison of difference schemes. SIAM Journal on Numerical Analysis, vol. 5, no. 3, 1968, pp. 506–517.
7. Courant R., Isaacson E., Rees M. On the solution of nonlinear hyperbolic differential equations by finite differences. Communications on Pure and Applied Mathematics, vol. 5, no. 3, 1952, pp. 243–255.
8. Русанов В.В. Разностные схемы третьего порядка точности для сквозного счета разрывных решений. Доклады АН СССР, том 180, no. 6, 1968 г., стр. 1303–1305 / Rusanov V.V. Difference schemes of the third order of accuracy for the forward calculation of discontinuous solutions. Doklady Akademii Nauk SSSR, vol. 180, no. 6, pp. 1303–1305 (in Russian).
9. Favorskaya A.V., Petrov I.B. Grid-characteristic method. Innovations in Wave Processes Modelling and Decision Making. In Innovations in Wave Processes Modelling and Decision Making, Springer, 2018, pp. 117–160.
10. Dagum L., Menon R. OpenMP: an industry standard API for shared-memory programming. IEEE computational science and engineering, vol. 5, no. 1, 1998, pp. 46–55.
11. Nakata N., Tsuji T., Matsuoka T. Acceleration of computation speed for elastic wave simulation using a Graphic Processing Unit. Exploration Geophysics, vol. 42, no. 1, 2011, pp. 98–104.
12. Weiss R. M., Shragge J. Solving 3D anisotropic elastic wave equations on parallel GPU devices. Geophysics, vol. 78, no. 2, 2013, 22 p.
13. F. Rubio et al. Finite-difference staggered grids in GPUs for anisotropic elastic wave propagation simulation. Computers & geosciences, vol. 70, issue C, 2014, pp. 181–189.
14. Komatitsch D., Michéa D., Erlebacher G. Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA. Journal of Parallel and Distributed Computing, vol. 69, no. 5, 2009, pp. 451–460.
15. D. Komatitsch et al. Modeling the propagation of elastic waves using spectral elements on a cluster of 192 GPUs. Computer Science – Research and Development, vol. 25, no. 1/2, 2010, pp. 75–82.
16. Message Passing Interface Forum. MPI: a Message-Passing Interface Standard. Technical Report. University of Tennessee, 1994.
17. Якобовский М.В. Введение в параллельные методы решения задач: Учебное пособие. М., Издательство Московского университета, 2013, 328 стр. / Yakobovsky M.V. An Introduction to Parallel Problem Solving Methods: A Training Manual. M., Moscow University Publishers, 2013, 328 p.
18. Ivanov A.M., Khokhlov N.I. Efficient Inter-process Communication in Parallel Implementation of Grid-Characteristic Method. In Smart Innovation, Systems and Technologies, vol. 133, 2019, pp. 91–102.
19. Иванов А.М., Хохлов Н.И. Параллельная реализация сеточно-характеристического метода в случае явного выделения контактных границ. Компьютерные исследования и моделирование, том 10, № 5, 2018 г., стр. 667-678 / Ivanov A.M., Khokhlov N.I. Parallel implementation of the grid-characteristic method in the case of explicit contact boundaries. Computer Research and Modeling, vol. 10. № 5, 2018, pp. 667–678 (in Russian).
20. Khokhlov N. et al. Solution of Large-scale Seismic Modeling Problems. Procedia Computer Science, vol. 66, 2015, pp. 191–199.
21. Khokhlov N. et al. Applying OpenCL Technology for Modelling Seismic Processes Using Grid-Characteristic Methods. Communications in Computer and Information Science, vol. 678, 2016, pp. 577–588.
22. Golubev V.I. et al. Simulation of dynamic processes in three-dimensional layered fractured media with the use of the grid-characteristic numerical method. Journal of Applied Mechanics and Technical Physics, vol. 58. № 3, 2017, 539–545.
23. Aminzadeh F., Brac J., and Kunz T. 3D Salt and Overthrust models. In Distribution CD of Salt and Overthrust models, SEG/EAGE Modeling Series, No. 1, 1997.
24. Фаворская А.В., Петров И.Б. Численное моделирование волновых процессов в скальных массивах сеточно-характеристическим методом. Математическое моделирование, том 30, № 3, 2018 г., стр. 37–51 / Favorskaya A. V., Petrov I.B. Numerical Modeling of Wave Processes in Rocks by the Grid-Characteristic Method. Mathematical Models and Computer Simulations, vol. 10. issue 5, 2018, pp. 639–647.
Review
For citations:
Khokhlov N.I., Petrov I.B. Application of the grid-characteristic method for solving the problems of the propagation of dynamic wave disturbances in high-performance computing systems. Proceedings of the Institute for System Programming of the RAS (Proceedings of ISP RAS). 2019;31(6):237-252. (In Russ.) https://doi.org/10.15514/ISPRAS-2019-31(6)-16