Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 49-50, 2008, Pages 4216-4232

  Badia, Santiago ^a,b   Quaini, Annalisa ^c   Quarteroni, Alfio ^c,d  

^a INTERNATIONAL CENTER FOR NUMERICAL METHODS IN ENGINEERING CIMNE   (Spain)

^b SANDIA NATIONAL LABORATORIES   (United States)

^c EPFL   (Switzerland)

^d POLITECNICO DI MILANO   (Italy)

Author keywords

Added mass effect; Fluid structure interaction; Hemodynamics; Partitioned procedures; Preconditioners; Semi implicit coupling

Indexed keywords

CODES (STANDARDS); CODES (SYMBOLS); COMPUTER SIMULATION; FLUID DYNAMICS; FLUID MECHANICS; FLUID STRUCTURE INTERACTION; FLUIDS; MATRIX ALGEBRA; STRUCTURAL DYNAMICS; THREE DIMENSIONAL;

ADDED-MASS EFFECT; COMPUTATIONAL COSTS; COUPLED SYSTEMS; DIAGONAL SCALING; DIRICHLET; FLUID VELOCITIES; FLUID-STRUCTURE SYSTEMS; HEMODYNAMICS; IMPLICIT ALGORITHMS; KRYLOV METHODS; LU FACTORIZATION; MASS EFFECTS; MODULAR APPROACH; NEUMANN; NON-LINEARITIES; NUMERICAL SIMULATIONS; PARTITIONED PROCEDURES; PRECONDITIONER; PRECONDITIONERS; SEMI-IMPLICIT; SEMI-IMPLICIT COUPLING; SPACE-TIME DISCRETIZATION; SPLITTING TECHNIQUES; STRUCTURE SYSTEMS;

ITERATIVE METHODS;

EID: 53049084167     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.04.018     Document Type: Article

References (36)

1. Atanga J., and Silvester D. Iterative methods for stabilized mixed velocity-pressure finite elements. Int. J. Numer. Methods Fluids 14 (1992) 71-81
2. Badia S., and Codina R. Analysis of a stabilized finite element approximation of the transient convection-diffusion equation using an ALE framework. SIAM J. Numer. Anal. 44 5 (2006) 2159-2197
3. Badia S., and Codina R. On some fluid-structure iterative algorithms using pressure segregation methods. Application to aeroelasticity. Int. J. Numer. Methods Engrg. 72 (2007) 46-71
4. S. Badia, F. Nobile, C. Vergara, Fluid-structure partitioned procedures based on Robin transmission conditions, J. Comput. Phys. (2008), doi:10.1016/j.jcp.2008.04.006.
5. Badia S., Quaini A., and Quarteroni A. Splitting methods based on algebraic factorization for fluid-structure interaction. SIAM J. Sci. Comput. 30 4 (2008) 1778-1805
6. Ben Belgacem F. The mortar finite element method with lagrange multipliers. Numer. Math. 84 (1999) 173-197
7. Brezzi F., and Fortin M. Mixed and Hybrid Finite Element Methods (1991), Springer-Veralg
8. Brezzi F., Fortin M., and Marini L.D. Error analysis of constant pressure aprroximations of Darcy's law. Comput. Methods Appl. Mech. Engrg. 195 (2006) 1547-1559
9. Brezzi F., Hughes T.J.R., and Süli E. Variational approximation of flux in conforming finite element methods for elliptic partial differential equations: a model problem. Rend. Mat. Acc. Lincei s 9 12 (2001) 167-183
10. Burman E., and Fernández M.A. Stabilized explicit coupling for fluid-structure interaction using Nitsche's method. C.R. Acad. Sci. Paris Sér. I Math. 345 (2007) 467-472
11. Causin P., Gerbeau J.F., and Nobile F. Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Comput. Methods Appl. Mech. Engrg. 194 42-44 (2005) 4506-4527
12. Codina R. Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Comput. Methods Appl. Mech. Engrg. 191 (2002) 4295-4321
13. Deparis S., Discacciati M., Fourestey G., and Quarteroni A. Fluid-structure algorithms based on Steklov-Poincaré operators. Comput. Methods Appl. Mech. Engrg. 195 41-43 (2006) 5797-5812
14. Elman H., Silvester D., and Wathen A. Finite Elements and Fast Iterative Solvers (2005), Oxford Science Publications
15. Farhat C., Geuzaine P., and Brown G. Application of a three-field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter. Comput. Fluids 32 (2003) 3-29
16. Fernández M.A., Gerbeau J.F., and Grandmont C. A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid. Int. J. Numer. Methods Engrg. 69 4 (2007) 794-821
17. Fernández M.A., and Moubachir M. A Newton method using exact Jacobians for solving fluid-structure coupling. Comput. Struct. 83 2-3 (2005) 127-142
18. Figueroa C., Vignon-Clementel I., Jansen K., Hughes T., and Taylor C. A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput. Methods Appl. Mech. Engrg. 195 (2006) 5685-5706
19. Fisher B., Ramage A., Silvester D.J., and Wathen A.J. On parameter choice and iterative convergence for stabilised discretisations of advection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 179 (1999) 179-195
20. Gerbeau J.F., and Vidrascu M. A quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows. Math. Modell. Numer. Anal. 37 4 (2003) 631-648
21. Heil M. An efficient solver for the fully coupled solution of large-displacement fluid-structure interaction problems. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1-23
22. Hughes T.J.R. Multiscale phenomena: Green's function, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized formulations. Comput. Methods Appl. Mech. Engrg. 127 (1995) 387-401
23. Karner G., Perktold K., Hofer M., and Liepsch D. Flow characteristics in an anatomically realistic compliant carotid artery bifurcation model. Methods Biomech. Biomed. Engrg. 2 39-41 (1999) 171-185
24. Matthies H.G., and Steindorf J. Partitioned strong coupled algorithms for fluid-structure interaction. Comput. Struct. 81 (2003) 805-812
25. Michler C., van Brummelen E.H., and de Borst R. An interface Newton-Krylov solver for fluid-structure interaction. Int. J. Numer. Methods Fluids 47 10-11 (2005) 1189-1195
26. D.P. Mok, W.A. Wall, Partitioned analysis schemes for transient interaction of incompressible flows and nonlinear flexible structures, in: W.A. Wall, K.U. Bletzinger, K. Schweizerhof (Eds.), Trends in Computational Structural Mechanics, CIMNE, Barcelona, Spain, 2001.
27. Moran H.J.-P., and Ohayon R. Fluid-Structure Interaction: Applied Numerical Methods (1995), John Wiley & Sons
28. F. Nobile. Numerical Approximation of Fluid-Structure Interaction problems with application to Haemodynamics. Ph.D. Thesis, École Polytechnique Fédérale de Lausanne, 2001.
29. Nobile F., and Vergara C. An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions. SIAM J. Sci. Comput. 30 2 (2008) 731-763
30. Piperno S., and Farhat C. Partitioned procedures for the transient solution of coupled aeroelastic problems - Part II: energy transfer analysis and three-dimensional applications. Comput. Methods Appl. Mech. Engrg. 190 (2001) 3147-3170
31. Quarteroni A., and Valli A. Domain Decomposition Methods for Partial Differential Equations (1999), Oxford Science Publications
32. Y. Saad. SPARSKIT: A basic tool for sparse matrix computation. Technical Report CSRD TR 1029, CSRD, University of Illinois, 1990.
33. Saad Y. Iterative Methods for Sparse Linear Systems (1996), PWS Publishing, Boston, MA
34. Silvester P.J., and Kechkar N. Stabilised bilinear-constant velocity-pressure finite elements for the conjugate gradient solution of the Stokes problem. Comput. Methods Appl. Mech. Engrg. 79 (1990) 71-86
35. Le Tallec P., and Mouro J. Fluid structure interaction with large structural displacements. Comput. Methods Appl. Mech. Engrg. 190 (2001) 3039-3067
36. Washio T., Hisada T., Watanabe H., and Tezduyar T.E. A robust preconditioner for fluid-structure interaction problems. Comput. Methods Appl. Mech. Engrg. 194 39-41 (2005) 4027-4047