Overlapping Schwarz Methods for Unstructured Spectral Elements

Journal of Computational Physics

Volumn 160, Issue 1, 2000, Pages 298-317

  Pavarino, Luca F ^a   Warburton, Timothy ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Domain decomposition; Overlapping Schwarz methods; Spectral elements; Unstructured meshes

Indexed keywords

ITERATIVE METHODS; NAVIER STOKES EQUATIONS; NUMERICAL METHODS;

DISCRETIZATIONS; DOMAIN DECOMPOSITIONS; DOMAIN-DECOMPOSITION METHODS; OVERLAPPING SCHWARZ; OVERLAPPING SCHWARZ METHOD; SCHWARZ METHOD; SPECTRAL ELEMENT; THREE DIMENSIONS; TWO-DIMENSIONS; UNSTRUCTURED MESHES;

DOMAIN DECOMPOSITION METHODS;

EID: 0346246272     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6463     Document Type: Article

References (43)

1. Babuška I., Suri M. The p and h-p versions of the finite element method, basic principles and properties. SIAM Rev. 36:1994;578.
2. Bernardi C., Maday Y. Spectral methods. Handbook of Numerical Analysis, Volume V: Techniques of Scientific Computing (Part 2). 1997;209.
3. Bica I. Iterative Substructuring Algorithms for the p-version Finite Element Method for Elliptic Problems. September 1997.
4. Casarin M. Quasi-optimal Schwarz methods for the conforming spectral element discretization. SIAM J. Numer. Anal. 34:1997;2482.
5. M. Casarin, and, S. Sherwin, Low energy bases preconditioning for elliptic substructured solvers based on spectral/hp element discretisations, in preparation.
6. Chan T. F., Shao J. P. Parallel complexity of domain decomposition methods and optimal coarse grid size. Parallel Comput. 21:1995;1033.
7. Chen Q., Babuska I. Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle. Comp. Meths. Appl. Mech. Eng. 128:1995;405.
8. Chen Q., Babuska I. The optimal symmetrical points for polynomial interpolation of real functions in the tetrahedron. Comp. Meths. Appl. Mech. Eng. 137:1996;89.
9. Couzy W., Deville M. A fast Schur complement method for the spectral element discretization of the incompressible navier-stokes equations. J. Comp. Phys. 116:1995;135.
10. Dubiner M. Spectral methods on triangles and other domains. J. Sci. Comp. 6:1991;345.
11. Fischer P. F. An overlapping schwarz method for spectral element solution of the incompressible Navier-Stokes equations. J. Comp. Phys. 133:1997;84.
12. Fischer P. F., Rønquist E. Spectral element methods for large scale parallel Navier-Stokes calculations. Comp. Meths. Appl. Mech. Eng. 116:1994;69.
13. Guo B., Cao W. An additive Schwarz method for the h-b version of the finite element method in three dimensions. SIAM J. Numer. Anal. 35:1998;632.
14. Heinrichs W. Spectral collocation on triangular elements. J. Comp. Phys. 145:1998;743.
15. Henderson R. D. Unstructured Spectral Element Methods: Parallel Algorithms and Simulations. 1994.
16. Hesthaven J. From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex. SIAM J. Numer. Anal. 35:1998;655.
17. Karniadakis G. E., Sherwin S. J. Spectral/hp Element Methods for CFD. 1999.
18. Karypis G., Kumar V. Parallel multilevel k-way partitioning scheme for irregular graphs. SIAM Rev. 41:1999;278.
19. Katz I. N., Hu N. Multi-p methods: Iterative algorithms for the p-version of the finite element analysis. SIAM J. Sci. Comp. 16:1995;1308.
20. J. Mandel, Iterative solvers for p-version finite element method in three dimensions, Comp. Meths. Appl. Mech. Eng. 116, 175, 1994. [ICOSAHOM'92, Montpellier, France, June 1992, ].
21. J. Mandel, Iterative solvers for p-version finite element method in three dimensions, Comp. Meths. Appl. Mech. Eng. 116, 175, 1994. [ICOSAHOM'92, Montpellier, France, June 1992, ].
22. Mandel J. Iterative methods for p-version finite elements: Preconditioning thin solids. Comp. Meths. Appl. Mech. Eng. 133:1996;247.
23. Oden J., Patra A., Feng Y. Parallel domain decomposition solver for adaptive hp finite element methods. SIAM J. Numer. Anal. 34:1997;2090.
24. Pahl S. S. Schwarz Type Domain Decomposition Methods for Spectral Element Discretizations. December 1993.
25. Pavarino L. F. Additive Schwarz methods for the p-version finite element method. Numer. Math. 66:1994;493.
26. L. F. Pavarino, Domain decomposition algorithms for saddle point problems, in, Domain Decomposition Methods 10, editd by, Mandel, Farhat, and Cai, Contemporary Mathematics, Amer. Math. Soc. Providence, RI, 1998, p, 138.
27. L. F. Pavarino, Domain decomposition algorithms for saddle point problems, in, Domain Decomposition Methods 10, editd by, Mandel, Farhat, and Cai, Contemporary Mathematics, Amer. Math. Soc. Providence, RI, 1998, p, 138.
28. Pavarino L. F. Indefinite overlapping Schwarz methods for time-dependent Stokes problems. Comp. Meths. Appl. Mech. Eng. 2000.
29. Pavarino L. F., Widlund O. B. A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions. SIAM J. Numer. Anal. 33:1996;1303.
30. E. Rønquist, A domain decomposition method for elliptic boundary value problems: Application to unsteady incompressible fluid flow, in, Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, edited by, Chan, Keyes, Meurant, Scroggs, and Voigt, SIAM, Philadelphia, 1992.
31. E. Rønquist, Domain decomposition methods for the steady Stokes equations, in, Proc. of DD11, edited by, Lai, Bjorstad, Cross, and Widlund, DDM.org, 1999, to appear.
32. J. Sherwin, T. Warburton, and, G. Karniadakis, Spectral/hp methods for elliptic problems on hybrid grids, in, Domain Decomposition Methods 10, edited by, Mandel, Farhat, and Cai, Contemporary Mathematics, Amer. Math. Soc. Providence, RI, 1998, Vol, 218, p, 191.
33. J. Sherwin, T. Warburton, and, G. Karniadakis, Spectral/hp methods for elliptic problems on hybrid grids, in, Domain Decomposition Methods 10, edited by, Mandel, Farhat, and Cai, Contemporary Mathematics, Amer. Math. Soc. Providence, RI, 1998, Vol, 218, p, 191.
34. Sherwin S. J. Hierarchical hp finite elements in hybrid domains. Finite Elements Anal. Design. 27:1997;109.
35. Sherwin S. J., Karniadakis G. E. A New triangular and tetrahedral basis for high-order hp finite element methods. Int. J. Numer. Meth. Eng. 38:1995;3775.
36. Sherwin S. J., Karniadakis G. E. A triangular spectral element method; applications to the incompressible Navier-Stokes equations. Comp. Meths. Appl. Mech. Eng. 123:1995;189.
37. Smith B. F., Bjørstad P., Gropp W. D. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. 1996.
38. Szabo B., Babuška I. Finite Element Analysis. 1991.
39. Warburton T. Spectral/hp Methods on Polymorphic Multi-Domains: Algorithms and Applications. 1999.
40. Warburton T., Sherwin S., Karniadakis G. Spectral basis functions for 2D hybrid/hp elements. SIAM J. Sci. Comp. 1999.
41. Wingate B. A., Boyd J. P. Triangular spectral element methods for geophysical fluid dynamics applications. Houston J. Math. 1996;305.
42. B. A. Wingate, and, M. A. Taylor, Fekete collocation points for triangular spectral elements, manuscript submitted for publication.
43. B. A. Wingate, and, M. A. Taylor, The natural function space for triangular and tetrahedral spectral elements, manuscript submitted for publication.