Extending a new two-grid waveform relaxation on a spatial finite element discretization

Habibi, Noora; Mesforush, Ali

doi:10.22034/cmde.2020.37349.1653

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	Extending a new two-grid waveform relaxation on a spatial finite element discretization
Computational Methods for Differential Equations
مقاله 15، دوره 9، شماره 4، دی 2021، صفحه 1148-1162 اصل مقاله (177.74 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.37349.1653
نویسندگان
Noora Habibi^* ؛ Ali Mesforush
Faculty of Applied Mathematics, Shahrood University Of Technology, P.O. Box 3619995161 Shahrood, Iran.
چکیده
In this work, a new two-grid method presented for the elliptic partial differential equations is generalized to the time-dependent linear parabolic partial differential equations. The new two-grid waveform relaxation method uses the numerical method of lines, replacing any spatial derivative by a discrete formula, obtained here by the finite element method. A convergence analysis in terms of the spectral radius of the corresponding two-grid waveform relaxation operator is also developed. Moreover, the efficiency of the presented method and its analysis are tested, applying the twodimensional heat equation.
کلیدواژه‌ها
Waveform relaxation method؛ Finite element method؛ Multigrid acceleration

مراجع
[1] N. S. Bakhvalov, On the convergence of a relaxation method with natural constraints on the elliptic operator, USSR Comput. Math. Math. Phys., 6 (1966), 101–135. [2] A. Brandt and O. E. Liven, Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, Revised Edition, SIAM, 2011. [3] A. Brandt, Multi-level adaptive techniques (MLAT) for fast numerical solution to boundary value problem, Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, Springer, (1973), 82–89. [4] A. Brandt, Multilevel adaptive solution to boundary value problems, Math. Comp., 31 (1977), 333–390. [5] A. Brandt, S. F. McCormick, and J. W. Ruge, Algebraic multigrid (AMG) for automatic multi- grid solutions with application to geodetic computations, Report, Institute for Computational Studies, Fort Collins, CO, (1984), 257–284. [6] R. P. Fedorenko, A relaxation method for solving elliptic difference equations, USSR Comput. Math. Phys., 1 (1962), 1092–1096. [7] R. P. Fedorenko, The speed of convergence of one iterative process, USSR Comput. Math. Math. Phys., 4 (1964), 227–235. [8] W. Hackbusch, Multigrid Methods and Applications, Springer, Berlin, 1985. [9] J. Janssen and S. Vandewalle, Multigrid waveform relaxation of spatial finite element meshes: the continuous-time case, SIAM J. NUMER. ANAL., 33(2) (1996), 456–474. [10] J. Janssen and S. Vandewalle, Multigrid waveform relaxation on spatial finite element meshes: the discrete-time case, SIAM J. SCI. COMPUT., 17(1) (1996), 133–155. [11] S. B. G. Karakoc and M. Neilan, A C0 finite element method for the biharmonic problem without extrinsic penalization, NUMER. METH. PART. D. E., 30(4) (2014), 1254–1278. [12] C. Lubich and A. Ostermann, Multi-grid dynamic iteration for parabolic equations, BIT, 27 (1987), 216–234. [13] U. Miekkala and O. Nevanlinna, Convergence of dynamic iteration methods for initial value problems, SIAM j. Sci. Statist. Comput., 8 (1987), 459–482. [14] H. Moghaderi, M. Dehghan, and M. Hajarian, A fast and efficient two-grid method for solving d-dimensional poisson equations, Numer Algor., (2015), 1–55. [15] U. Trottenberg, C. Oosterlee, and A. Schuller, Multigrid, Academic press, 2000. [16] S. Vandewalle, Parallel multigrid waveform relaxation for parabolic problems, B. G. Teubner Stuttgart, 1993.
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Extending a new two-grid waveform relaxation on a spatial finite element discretization