Fourier-Laplace analysis of the multigrid waveform relaxation method for hyperbolic equations

BIT Numerical Mathematics

Volumn 36, Issue 4, 1996, Pages 831-841

  Ta'asan, Shlomo ^a   Zhang, Hong ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b CLEMSON UNIVERSITY   (United States)

Author keywords

Fourier Laplace; Hyperbolic equation; Multigrid; Parabolic equation; Spectral radius; Steady state problem; Waveform relaxation

Indexed keywords

EID: 1542401178     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01733794     Document Type: Article

References (19)

1. M. Bjørhus, Semi-discrete subdomain iteration for hyperbolic systems, Technical Report Numerics no.4/1995, Department of Mathematics, University of Trondheim, Trondheim, Norway, 1995.
2. A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comp., 31 (1977), pp. 333-390.
3. A. Brandt, Multigrid solvers for non-elliptic and singular-perturbation steady-state problems, technical report, Weizmann Institute of Science, Rehovot, Israel, 1981.
4. G. Horton and S. Vandewalle, A space-time multigrid method for parabolic P.D.E.s, SIAM J. Sci. Comput., 16 (1995), pp. 848-864.
5. A. Jameson, Solution of the Euler equations for two dimensional transonic flow by multigrid method, Appl. Math. Comput., 13 (1983), pp. 327-355.
6. R. Jeltsch and B. Pohl, Waveform relaxation with overlapping splittings, SIAM J. Sci. Comput., 16 (1995), pp. 40-49.
7. B. Leimkuhler, U. Miekkala, and O. Nevanlinna, Waveform relaxation for linear RC circuits, Impact of Computing in Science and Engineering, 3 (1991), pp. 123-145.
8. E. Lelarasmee, A. Ruehli, and A. Sangiovanni-Vincentelli, The waveform relaxation method for time-domain analysis of large scale integrated circuits, IEEE Trans. Computer-Aided Design, 1 (1982), pp. 131-145.
9. C. Lubich and A. Ostermann, Multigrid dynamic iteration for parabolic equations, BIT, 27 (1987), pp. 216-234.
10. A. Lumsdaine, M. Reichelt, and J. White, Conjugate direction waveform methods for transient two-dimensional simulation of MOS devices, in Proceedings of the International Conference on Computer Aided Design, Santa Clara, CA, 1991, pp. 116-119.
11. U. Miekkala and O. Nevanlinna, Convergence of dynamic iteration methods for initial value problems, SIAM J. Sci. Stat. Comput., 8 (1987), pp. 459-482.
12. A. Newton and A. Sangiovanni-Vincentelli, Relaxation-based electrical simulation, IEEE Trans. Computer-Aided Design, 3 (1984), pp. 308-331.
13. P. Odent, L. Claesen, and H. De Man, Acceleration of relaxation based circuit simulation using a multiprocessor system, IEEE Trans. Computer-Aided Design, 9 (1990), pp. 1063-1072.
14. C. Oosterlee and P. Wesseling, Multigrid schemes for time-dependent incompressible Navier-Stokes equations, Impact of Computing in Science and Engineering, 5 (1993), pp. 153-175.
15. A. Ruehli and C. Zukowski, Convergence of waveform relaxation for RC circuits, in Semiconductors (part I and part II), F. Odeh, J. Cole, W. Coughran, P. Loyd, and J. White, eds., IMA Volumes in Mathematics and its Applications, Springer Verlag, 1992.
16. S. Taásan and H. Zhang, On the multigrid waveform relaxation method, SIAM J. Sci. Comput., 16 (1995), pp. 1092-1104.
17. S. Vandewalle, Parallel multigrid waveform relaxation for parabolic problems, Teubner Verlag, Stuttgart, 1993.
18. P. Wesseling, An Introduction to Multigrid Methods, John Wiley, Chichester, England, 1992.
19. E. Xia and R. Saleh, Parallel waveform-Newton algorithms for circuit simulation, IEEE Trans. Computer-Aided Design, 11 (1992), pp. 432-442.