MPI PARALLEL IMPLEMENT OF A WAVE EQUATION USING AN IMPLICIT FINITE DIFFERENCE SCHEME
Abstract
In this paper we will discuss the parallel implementation of the two-dimensional acoustic wave equation using the implicit difference method. As the programming environment used the distributed memory model of parallel computation and MPI (Message Passing Interface) system. The parallel approach is based on the parallelization of the tridiagonal matrix and uses the Yanenko method. The performance of the parallel algorithm has been studied using distributed computing method, and performed on supercomputer cluster.It has been observed that the parallel implementation provides a significant reduction in the computation time when compared with the serial implementation algorithm.
About the Authors
A. Altybay
Al-Farabi Kazakh National University
Kazakhstan
Kazakhstan
N. Tokmagambetov
Al-Farabi Kazakh National University
Kazakhstan
Kazakhstan
References
1. G. Cohen. High-Order Numerical Methods for Transient Wave Equations, Springer, NewYork, 2002.
2. N. N. Yanenko. The Method of Fractional Steps, Springer-Verlag Berlin Heidelberg, 1971.
3. H.K. Rouf. 1971, Implicit Finite Di_erence Time Domain Methods. Theory and Applications/ Hasan Khaled Rouf. -LAP Lambert Academic, 208,2011.
4. D. M. Causon, C. G. Mingham, L. Qian. Developments In Multi-Fluid Finite Volume Free Surface Capturing Methods, Advances in Numerical Simulation of Nonlinear Water Waves, 11, 397-427, 2010.
5. M. Dehghan, A. Mohebbi. The combination of collocation, finite difference, and multigrid methods for solution of the two-dimensional wave equation, Number. Methods Partial Differential Equation, 24, 897-910, 2008.
6. H.F. Ding, Y.X. Zhang. A new fourth-order compact finite difference scheme for the two dimensional second-order hyperbolic equation, J. Comput. Appl. Math., 72, 626-632, 2009.
7. A. P.Engsig-Karup, , B. Harry, , H. B. Bingham, , and O. Lindberg. An efficient exible-order model for 3D nonlinear water waves, J. Comput. Phys., 228:6, 2100-2118, 2009.
8. D. Greaves. Application Of The Finite Volume Method To The Simulation Of Nonlinear Water Waves, Advances in Numerical Simulation of Nonlinear Water Waves, 11, 357-396, 2010.
9. J.Grue, D.Fructus. Model For Fully Nonlinear Ocean Wave Simulations Derived Using Fourier Inversion Of Integral Equations In 3D, Advances in Numerical Simulation of Non-linear Water Waves, 11, 1-42, 2010.
10. H. O. Kreiss, N.A. Petersson, J. Ystrom. Di_erence approximation for the second-order wave equation, SIAM J. Numer. Anal. 40, 1940-1967, 2002.
11. H. L. Liao and Z. Z. Sun. A two-level compact ADI method for solving second-order wave equations, Int. J. Comput. Math. 90:7, 1471-1488,2013
12. J.M. Liu , K.M. Tang. A new unconditionally stable ADI compact scheme for the two spacedimensional linear hyperbolic equation, Int. J. Comput. Math. 87:10, 2259-2267,2010.
13. J. C. Munoz, M. Ruzhansky, and N. Tokmagambetov. Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters. J. Math. Pures Appl., 123:127-147, – 2019.
14. J. C. Munoz, M. Ruzhansky, and N. Tokmagambetov. Acoustic and shallow water wave propagations with irregular dissipation. Funct. Anal. Appl., to appear.
15. M. Ruzhansky, N. Tokmagambetov. Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic _eld. Lett. Math. Phys., 107(4):591-618, 2017.
16. M. Ruzhansky, N. Tokmagambetov. Wave equation for operators with discrete spectrum and irregular propagation speed. Arch. Ration. Mech. Anal., 226(3):1161-1207, 2017.
17. M. Ruzhansky, N. Tokmagambetov. On a very weak solution of the wave equation for a Hamiltonian in a singular electromagnetic _eld. Math. Notes, 103(5-6):856-858, 2018.
18. M. Ruzhansky, N. Tokmagambetov. Wave Equation for 2D Landau Hamiltonian. Appl. Comput. Math., 18(1):69-78, 2019.
19. I. S. Sapronov, A. N. Bykov. Parallel’no-konveyernyy algoritm [Pipelined Thomas algorithm]// Atom., 44, 24-25, 2009.
20. N. N. Yanenko, A. N. Konovalov, A. N. Bugrov, G. V. Shustov. Ob organizatsii parallel’nykh vychisleni i “rasparallelivanii” progonki [On organization of parallel computations and parallelization of the tridiagonal matrix algorithm]. Numerical Methods of Continuum Mechanics. 9(7):139-146, 1978.
21. G. Ducrozet, F. Bonnefoy, D. L. Touze, P. Ferrant. Open-source solver for nonlinear waves in open ocean based on High-Order Spectral method, Comp. Phys. Comm., 203, 245-254, 2016.
Review
For citations:
Altybay A., Tokmagambetov N. MPI PARALLEL IMPLEMENT OF A WAVE EQUATION USING AN IMPLICIT FINITE DIFFERENCE SCHEME. Herald of the Kazakh-British technical university. 2020;17(1):110-116.
Views:
292
Email this article 