On the nonnormality of subiteration for a fluid-structure-interaction problem

SIAM Journal on Scientific Computing

Volumn 27, Issue 2, 2006, Pages 599-621

  Van Brummelen, E H ^a   De Borst, R ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Convergence and stability; Fluid structure interaction; Monolithic methods; Nonnormality; Subiteration

Indexed keywords

COMPUTATION THEORY; CONVERGENCE OF NUMERICAL METHODS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PROBLEM SOLVING;

CONVERGENCE AND STABILITY; FLUID-STRUCTURE INTERACTION; MONOLITHIC METHODS; NONNORMALITY; SUBITERATION;

ITERATIVE METHODS;

EID: 33644956691     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827503431430     Document Type: Article

References (28)

1. J. ALONSO AND A. JAMESON, Fully-implicit time-marching aeroelastic solutions, AIAA, 56 (1994), pp. 1-13.
2. M. BATHE AND R. KAMM, A fluid-structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery, Journal of Biomechanical Engineering, 121 (1999), pp. 361-369.
3. K. BØHMER, P. HEMKER, AND H. STETTER, The defect correction approach, Comput. Suppl., 5 (1984), pp. 1-32.
4. L. BRODERICK AND J. LEONARD, Nonlinear response of membranes to ocean waves using boundary and finite elements, Ocean Engrg., 22 (1995), pp. 731-745.
5. E. VAN BRUMMELEN, S. HULSHOFF, AND R. DE BORST, Energy conservation under incompatibility for fluid-structure interaction problems, Comput. Methods Appl. Mech. Engrg., 192 (2003), pp. 2727-2748.
6. E. VAN BRUMMELEN, C. MICHLER, AND R. DE BORST, Interface-GMRES(R) Acceleration of Subiteration for Fluid-Structure-Interaction Problems, Tech. report DACS05-001, Delft University of Technology, Delft, The Netherlands, 2005. Available at http://www.em.lr.tudelft.nl/downloads/DACS-05-001.pdf.
7. C. FARHAT, P. GEUZAINE, AND G. BROWN, Application of a three-field nonlinear fluidstructure formulation to the prediction of the aeroelastic parameters of an f-16 fighter, Comput. & Fluids, 32 (2003), pp. 3-29.
8. C. FARHAT, P. GEUZAINE, AND C. GRANDMONT, The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids, J. Comput. Phys., 174 (2001), pp. 669-694.
9. C. FELIPPA, K. PARK, AND C. FARHAT, Partitioned analysis of coupled mechanical systems, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 3247-3270.
10. I. GOHBERG AND M. KREǏN, Introduction to the Theory of Linear Nonselfadjoint Operators, Translations of Mathematical Monographs 18, AMS, Providence, RI, 1969.
11. G. GOLUB AND P. LOAN, Matrix Computations, Johns Hopkins, 1996.
12. A. GREENBAUM, Iterative Methods for Solving Linear Systems, Frontiers Appl. Math. 17, SIAM, Philadelphia, 1997.
13. M. HEIL, Stokes flow in an elastic tube - a large-displacement fluid-structure interaction problem, Internat. J. Numer. Methods Fluids, 28 (1998), pp. 243-265.
14. T. KATO, Perturbation Theory for Linear Operators, Grundlehren der Mathematischen Wissenschaft 132, Springer, Berlin, corrected print of the 2nd ed., 1984.
15. J. KEVORKIAN AND J. COLE, Perturbation Methods in Applied Mathematics, Appl. Math. Sci. 34, Springer-Verlag, Berlin, 1981.
16. P. LETALLEC AND J. MOURO, Fluid structure interaction with large structural displacements, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 3039-3067.
17. R. B. MELVILLE AND S. A. MORTON, Fully-implicit aeroelasticity on overset grid systems, 36th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 1998.
18. J. ODEN AND J. REDDY, An Introduction to the Mathematical Theory of Finite Elements, Pure and Applied Mathematics, John Wiley & Sons, New York, 1974.
19. S. PlPERNO, Simulation Numérique de Phénomènes d'Interaction Fluide-Structure, Ph.D. thesis, école Nationale des Ponts et Chaussées, France, 1995 (partly in French).
20. S. PIPERNO, Explicit/implicit fluid/structure staggered procedures with a structural predictor and fluid subcycling for 2D inviscid aeroelastic simulations, Internat. J. Numer. Methods Fluids, 25 (1997), pp. 1207-1226.
21. S. PIPERNO AND C. FARHAT, Partitioned procedures for the transient solution of coupled aeroelastic problems. II: Energy transfer analysis and three-dimensional applications, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 3147-3170.
22. S. PIPERNO, C. FARHAT, AND B. LARROUTUROU, Partitioned procedures for the transient solution of coupled aeroelastic problems. I: Model problem, theory and two-dimensional application, Comput. Methods Appl. Mech. Engrg., 124 (1995), pp. 79-112.
23. S. C. REDDY, P. J. SCHMID, AND D. S. HENNINGSON, Pseudospectra of the Orr-Sommerfeld operator, SIAM J. Appl. Math., 53 (1993), pp. 15-47.
24. I. ROBERTSON, S. SHERWIN, AND P. BEARMAN, Prediction of flutter instability due to cross winds of the second forth road bridge, in Computational Fluid Dynamics '01: Proceedings of the ECCOMAS CFD Conference 2001, Swansea, Wales, U.K., 2001, on CD-rom.
25. L. TREFETHEN, Pseudospectra of linear operators, SIAM Rev., 39 (1997), pp. 383-406.
26. L. TREFETHEN, A. TREFETHEN, S. REDDY, AND T. DRISCOLL, Hydrodynamic stability without eigenvalues, Science, 261 (1993), pp. 578-584.
27. T. WRIGHT, Matlab Pseudospectra GUI, Oxford University Computing Laboratory. Available at http://www.comlab.ox.ac.uk/pseudospectra/eigtool/.
28. E. ZEIDLER, Applied Functional Analysis: Applications to Mathematical Physics, Appl. Math. Sci. 108, Springer, Berlin, 1995.