Parallel iterative methods for Navier-Stokes equations and application to eigenvalue computation

Concurrency and Computation: Practice and Experience

Volumn 15, Issue 11-12, 2003, Pages 1151-1168

  Graham, Ivan G ^a   Spence, Alastair ^a   Vainikko, Eero ^b  

^a University of Bath   (United Kingdom)

^b UNIVERSITY OF TARTU   (Estonia)

Author keywords

Domain decomposition; Eigenvalues; Incompressible Navier Stokes equations; Parallel iterative methods

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; DEGREES OF FREEDOM (MECHANICS); EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; ITERATIVE METHODS; PARALLEL ALGORITHMS; STIFFNESS MATRIX;

DOMAIN DECOMPOSITION;

NAVIER STOKES EQUATIONS;

EID: 0141526322     PISSN: 15320626     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpe.785     Document Type: Conference Paper

References (31)

1. Gresho PM, Sani RL. Advection-diffusion and isothermal laminer flow. Incompressible Flow and the Finite Element Method. Wiley: New York, 1998.
2. Lehoucq RB, Sorensen DC, Yang C. ARPACK user's guide: Solution of large scale eigenvalue problems with implicitly restarted Arnoldi methods. http://www.caam.rice.edu/software/ARPACK [16 May 2003].
3. Smit P, Paardekooper M. The effects of inexact solvers in algorithms for symmetric eigenvalue problems. Linear Algebra Applications 1999; 287:337-357.
4. Golub GH, Ye Q. Inexact inverse iteration for generalised eigenvalue problems. BIT 2000; 40:671-684.
5. Simoncini V, Eldén L. Inexact Rayleigh Quotient-type methods for eigenvalue computations. BIT 2002; 42:159-182.
6. Sleijpen G, van der Vorst H. Jacobi-Davidson methods. Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, Bai Z, Demmel J, Dongarra J, Ruhe A, van der Vorst H (eds.). SIAM: Philadelphia, PA, 2000; 88-105.
7. Cliffe KA, Garrett TJ, Spence A. Eigenvalues of the discretized Navier-Stokes equations with application to the detection of Hopf bifurcations. Advances in Computational Mathematics 1993; 1:337-356.
8. ENTWIFE. http://www.entwife.com [16 May 2003].
9. Graham IG, Spence A, Vainikko E. Parallel iterative methods for Navier-Stokes equations and application to stability assessment. EupoPar2002 Parallel Processing (Lecture Notes in Computer Science, vol. 2400), Monien B, Feldmann R (eds.). Springer: Berlin, 2002; 705-714.
10. Saad Y. A flexible inner-outer preconditioned GMRES algorithm. SIAM Journal of Scientific Computing 1993; 14:461-469.
11. Elman HC, Silvester DJ. Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations. SIAM Journal of Scientific Computing 1996; 17:33-46.
12. Elman HC. Preconditioning for the steady-state Navier-Stokes equations with low viscosity. SIAM Journal of Scientific Computing 1999; 20:1299-1316.
13. Kay D, Loghin D. A Green's function preconditioner for the steady-state Navier-Stokes equations. Oxford Numerical Analysis Group Research Report NA-99/06, 1999.
14. Kay D, Loghin D, Wathen A. A preconditioner for the steady-state Navier-Stokes equations. SIAM Journal of Scientific Computing. 2002; 24(1):237-256.
15. Loghin D. Private communication.
16. DOUG: http://www.maths.bath.ac.uk/̃parsoft [16 May 2003].
17. Elman HC, Loghin D, Wathen AJ. Preconditioning techniques for Newton's method for the incompressible Navier-Stokes equations. Preprint, 2003.
18. Hagger MJ. Automatic domain decomposition on unstructured grids DOUG. Advances in Computational Mathematics 1998; 9:281-310.
19. Cliffe KA, Graham IG, Scheichl R, Stals L. Parallel computation of flow in heterogeneous media modelled by mixed finite-elements. Journal of Computational Physics 2000; 164:258-282.
20. Gropp W, Lusk E, Skjellum A. Using MPI - Portable Parallel Programming with the Message Passing Interface (2nd edn). MIT Press, 1999.
21. Karypis G, Kumar V. METIS: Unstructured graph partitioning and sparse matrix ordering system Department of Computer Science. University of Minnesota Report, Minneapolis, August 1995.
22. Davis TA, Duff IS. A combined unifrontal/multifrontal method for unsymmetric sparse matrices. ACM Transactions on Mathematical Software 1999; 25(1):1-19..
23. Schäfer M, Turek S. Benchmark computations of laminar flow around a cylinder. Flow Simulation with High-Performance Computers II (Notes on Numerical Fluid Mechanics), Hirschel EH (ed.). Vieweg, 1996; 547-566.
24. Vainikko E, Graham IG. A parallel solver for PDE systems and application to the incompressible Navier-Stokes equations. Applied Numerical Mathematics 2003; To appear.
25. Bouras A, Frassé V. A relaxation strategy for the Arnoldi method in eigenproblems. CERFACS Report TR/PA/00/16, 2000.
26. Parlett BN. The Symmetric Eigenvalue Problem. SIAM: Philadelphia, 1998.
27. Berns-Müller J, Graham IG, Spence A. Inexact inverse iteration for the symmetric matrices. http://www.maths.bath.ac.uk/igg/evalues submitting for publication 2003 [16 May 2003].
28. Berns-Müller J. Inexact inverse iteration and Galerkin-Krylov methods. PhD Thesis, University of Bath, June 2003.
29. Cliffe KA, Garrett TJ, Spence A. Eigenvalues of block matrices arising from problems in fluid mechanics. SIAM Journal of Matrix Analysis 1994; 15:1310-1318.
30. Mercier B, Osborne J, Rappaz J, Raviart PA. Eigenvalue approximation by mixed and hybrid methods. Mathematics of Computation 1981; 36:427-453.
31. Cliffe KA, Spence A, Tavener SJ. The numerical analysis of bifurcation problems with application to fluid mechanics. Acta Numerica 2000; 39-131.