An investigation of overlapping domain decomposition methods for one-dimensional dispersive long wave equations

Advances in Water Resources

Volumn 27, Issue 11, 2004, Pages 1111-1133

  Glimsdal, Sylfest ^a,b   Pedersen, Geir K ^b   Langtangen, H P ^a,b  

^a SIMULA RESEARCH LABORATORY   (Norway)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

Boussinesq equations; Domain decomposition; Numerical instabilities; Schwarz iterations; Weakly dispersive waves

Indexed keywords

BOUNDARY CONDITIONS; FILTRATION; PARAMETER ESTIMATION; PROBLEM SOLVING; WATER RESOURCES; WATER WAVES; WAVE PROPAGATION;

DECOMPOSITION METHODS; FINITE ELEMENT FORMULATIONS; GRID SIZES;

DECOMPOSITION;

BOUSSINESQ EQUATION; MATHEMATICAL METHOD; WATER WAVE; WAVE PROPAGATION;

EID: 8144231096     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2004.07.008     Document Type: Article

References (32)

1. K. Alapaty R. Mathur T. Odman Intercomparison of spatial interpolation schemes for use in nested grid models Month. Weath. Rev. 126 1998 243-249
2. D. Amitai A. Averbuch M. Israeli S. Itzikowitz Implicit-explicit parallel asynchronous solver of parabolic PDEs SIAM J. Sci. Comput. 19 4 1998 1366-1404
3. Cai X, Pedersen G, Langtangen HP. A parallel multi-subdomain strategy for solving the Boussinesq water wave equations. Advances in Water Resources [submitted]
4. X.-C. Cai Jr. M.A. Casarin Jr. F.W. Elliot O.B. Widlund Overlapping Schwarz algorithms for solving Helmholtz's equation AMS Contemp. Math. 218 1998 391-399
5. C.N. Dawson T.F. Dupont Explicit/implicit conservative domain decomposition procedures for parabolic problems based on block-centered finite differences SIAM J. Numer. Anal 31 4 1994 1045-1061
6. A. de La Bourdonnaye C. Fahrat A. Macedo F. Magoulès F.-X. Roux A non-overlapping domain decompoisition method for the exterior Helmholtz problem AMS Contemp. Math. 218 1998 42-66
7. Dean EJ, Glowinsky R. Domain decomposition of wave problems using mixed finite element method. In: Bjørstad PE, Espedal MS, Keyes DE, editors. In: Ninth International Conference on Domain Decomposition Methods, DDM.org; 1998. p. 326-33
8. C. Fahrat A. Macedo M. Lesoinne A two-level domain decompoisition method for the iterative solution of high frequency exterior Helmholtz problems Numer. Math. 85 2000 283-308
9. A.D. Fox S.J. Maskell Two-way interactive nesting of primitive equation ocean models with topography J. Phys. Oceanogr. 25 1995 2977-2996
10. I. Ginis R.A. Richardson L.M. Rothstein Design of multiply nested primitive equation ocean model Month. Weath. Rev. 126 1998 1054-1079
11. B. Gjevik G. Pedersen E. Dybesland C.B.C. Harbitz P.M.A. Miranda M.A. Baptista et al. Modeling tsunamis from earthquake sources near Gorringe Bank southwest of Portugal J. Geophys. Res. 102 013 1997 927-949
12. Kaplan E. A shallow water model distributed using domain decomposition. In: Bjørstad PE, Espedal MS, Keyes DE, editors, Ninth International Conference on Domain Decomposition Methods, pages 761-767. DDM.org, 1998
13. H.P. Langtangen Computational partial differential equations-numerical methods and Diffpack programming Textbooks in Computational Science and Engineering 2nd ed 2003 Springer Berlin
14. H.P. Langtangen G. Pedersen Computational models for weakly dispersive nonlinear water waves Comput. Methods Appl. Mech. Eng. 160 1998 337-358
15. D.K. Lilly Numerical solutions for the shape-preserving two-dimensional thermal convection element J. Atmos. Sci. 21 1964 83-98
16. C.C. Mei The applied dynamics of ocean surface waves 1989 World Scientific Singapore
17. L.-Y. Oey P. Chen A nested-grid ocean model: With application to the simulation of meanders and eddies in the Norwegian coastal current J. Geophys. Res. 97 1992 20063-20086
18. G. Pedersen Three-dimensional wave patterns generated by moving disturbances at transcritical speeds J. Fluid Mech. 196 39-63 1988
19. G. Pedersen Finite difference representations of nonlinear waves Int. J. Numer. Methods Fluids 13 1991 671-690
20. G. Pedersen An optical theory for discrete media Wave Motion 32 2000 79-92
21. Pedersen G. A note on tsunami generation by earthquakes. Preprint Series in Applied Mathematics 4, Deparment of Mathematics, University of Oslo, Norway; 2001
22. G. Pedersen Energy conservation and physical optics for discrete long wave equations Wave Motion 37 2003 81-100
23. Pedersen G, Langtangen HP. Effects of dispersion on generation and propagation of tsunamis. In: Proceedings of the International Conferance on Tsunamis, Paris, France; 1999
24. Pedersen G, Rygg OB. Numerical solution of the three dimensional Boussinesq equations for dispersive surface waves. Preprint Series in Applied Mathematics, Department of Mathematics, University of Oslo; 1987
25. D.H. Peregrine Equations for water waves and the approximation behind them. In: R.E. Meyer (Eds.). Waves on beaches 1972 Academic Press New York 357-412
26. P. Rao A parallel hydrodynamic model for shallow water equations Appl. Math. Computat. 150 1 2004 291-302
27. B.F. Smith P.E. Bjørstad W.D. Gropp Domain decomposition, parallel multilevel methods for elliptic partial differential equations 1996 Cambridge University Press
28. M.A. Spall W.R. Holland A nested primitive equation model for oseanic applications J. Phys. Oceanogr. 21 1991 205-220
29. A. Weiser M.F. Wheeler On convergence of block-centered finite differences for elliptic problems SIAM J. Numer. Anal. 25 2 1988 351-375
30. T.Y. Wu Long waves in ocean and coastal waters Proc. ASCE J. Eng. Mech. Div. 107 1981 501-522
31. D.-L. Zhang H.-R. Chang N.L. Seaman T.T. Warner J.M. Fritsch A two-way interactive nesting procedure with variable terrain resolution Month. Weath. Rev. 114 1986 1330-1339
32. O.C. Zienkiewicz R.L. Taylor The finite element method (3 volumes) 5th ed. 2000 McGraw-Hill New York