Fluid-structure interaction (FSI) solvers based on vector extrapolation methods are discussed. The FSI solver framework builds on a Dirichlet–Neumann partitioning between general purpose fluid and structural solver. For strong coupling of the two fields vector extrapolation methods are employed to obtain a matrix free nonlinear solver. The emphasis of this presentation is on the embedding of well known vector extrapolation methods in a popular FSI solver framework and, in particular, the relation of these vector extrapolation methods to established fixed-point FSI schemes.

1.
Kalro
,
V.
, and
Tezduyar
,
T. E.
, 2001, “
A Parallel 3D Computational Method for Fluid-Structure Interactions in Parachute Systems
,”
Comput. Methods Appl. Mech. Eng.
,
190
, pp.
321
332
. 0045-7825
2.
Stein
,
K.
,
Tezduyar
,
T.
, and
Benney
,
R.
, 2003, “
Computational Methods for Modeling Parachute Systems
,”
Comput. Sci. Eng.
1521-9615,
5
(
1
), pp.
39
46
.
3.
Farhat
,
C.
, 2004, “
CFD-Based Nonlinear Computational Aeroelasticity
,”
Encyclopedia of Computational Mechanics
, Vol.
3
,
E.
Stein
,
R. D.
Borst
, and
T.
Hughes
, eds.,
Wiley
,
New York
, Chap. 13.
4.
Wüchner
,
R.
,
Kupzok
,
A.
, and
Bletzinger
,
K. -U.
, 2007, “
A Framework for Stabilized Partitioned Analysis of Thin Membrane-Wind Interaction
,”
Int. J. Numer. Methods Fluids
,
54
(
6–8
), pp.
945
963
. 0271-2091
5.
Bazilevs
,
Y.
,
Calo
,
V. M.
,
Zhang
,
Y.
, and
Hughes
,
T. J. R.
, 2006, “
Isogeometric Fluid-Structure Interaction Analysis With Applications to Arterial Blood Flow
,”
Comput. Mech.
0178-7675,
38
(
4–5
), pp.
310
322
.
6.
Tezduyar
,
T. E.
, and
Sathe
,
S.
, 2007, “
Modeling of Fluid-Structure Interactions With the Space-Time Finite Elements: Solution Techniques
,”
Int. J. Numer. Methods Fluids
0271-2091,
54
, pp.
855
900
.
7.
Tezduyar
,
T. E.
,
Sathe
,
S.
,
Cragin
,
T.
,
Nanna
,
B.
,
Conklin
,
B. S.
,
Pausewang
,
J.
, and
Schwaab
,
M.
, 2007, “
Modelling of Fluid-Structure Interactions With the Space-Time Finite Elements: Arterial Fluid Mechanics
,”
Int. J. Numer. Methods Fluids
0271-2091,
54
(
6–8
), pp.
901
922
.
8.
Förster
,
C.
,
Wall
,
W. A.
, and
Ramm
,
E.
, 2007, “
Artificial Added Mass Instabilities in Sequential Staggered Coupling of Nonlinear Structures and Incompressible Viscous Flows
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
196
, pp.
1278
1293
.
9.
Wall
,
W. A.
,
Mok
,
D. P.
, and
Ramm
,
E.
, 1999, “
Partitioned Analysis Approach of the Transient Coupled Response of Viscous Fluids and Flexible Structures
,”
Solids, Structures and Coupled Problems in Engineering
,
Proceedings of ECCM ‘99
, Munich, Germany,
W.
Wunderlich
, ed.
10.
Mok
,
D. P.
, and
Wall
,
W. A.
, 2001, “
Partitioned Analysis Schemes for the Transient Interaction of Incompressible Flows and Nonlinear Flexible Structures
,”
Trends in Computational Structural Mechanics
,
W. A.
Wall
,
K. -U.
Bletzinger
, and
K.
Schweitzerhof
, eds.,
CIMNE
,
Barcelona
.
11.
Le Tallec
,
P.
, and
Mouro
,
J.
, 2001, “
Fluid Structure Interaction With Large Structural Displacements
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
(
24–25
), pp.
3039
3067
.
12.
Tezduyar
,
T. E.
,
Sathe
,
S.
,
Keedy
,
R.
, and
Stein
,
K.
, 2006, “
Space-Time Finite Element Techniques for Computation of Fluid-Structure Interactions
,”
Comput. Methods Appl. Mech. Eng.
,
195
, pp.
2002
2027
. 0045-7825
13.
Smith
,
D. A.
,
Ford
,
W. F.
, and
Sidi
,
A.
, 1987, “
Extrapolation Methods for Vector Sequences
,”
SIAM Rev.
0036-1445,
29
(
2
), pp.
199
233
.
14.
Smith
,
D. A.
,
Ford
,
W. F.
, and
Sidi
,
A.
, 1988, “
Erratum: Extrapolation Methods for Vector Sequences
,”
SIAM Rev.
0036-1445,
30
(
4
), pp.
623
624
.
15.
Brezinski
,
C.
, 2000, “
Convergence Acceleration During the 20th Century
,”
J. Comput. Appl. Math.
0377-0427,
122
, pp.
1
21
.
16.
Jbilou
,
K.
, and
Sadok
,
H.
, 2000, “
Vector Extrapolation Methods, Applications and Numerical Comparison
,”
J. Comput. Appl. Math.
,
122
, pp.
149
165
. 0045-7825
17.
Sidi
,
A.
, 1991, “
Efficient Implementation of Minimal Polynomial and Reduced Rank Extrapolation Methods
,”
J. Comput. Appl. Math.
,
36
(
3
), pp.
305
337
. 0045-7825
18.
Küttler
,
U.
, and
Wall
,
W. A.
, 2008, “
Fixed-Point Fluid-Structure Interaction Solvers With Dynamic Relaxation
,”
Comput. Mech.
,
43
(
1
), pp.
61
72
. 0178-7675
19.
Michler
,
C.
,
van Brummelen
,
E. H.
, and
de Borst
,
R.
, 2005, “
An Interface Newton–Krylov Solver for Fluid-Structure Interaction
,”
Int. J. Numer. Methods Fluids
0271-2091,
47
, pp.
1189
1195
.
20.
Gerstenberger
,
A.
, and
Wall
,
W. A.
, 2008, “
An Extended Finite Element Method/Lagrange Multiplier Based Approach for Fluid-Structure Interaction
,”
Comput. Methods Appl. Mech. Eng.
,
197
, pp.
1699
1714
. 0045-7825
21.
Wall
,
W. A.
,
Gamnitzer
,
P.
, and
Gerstenberger
,
A.
, 2008, “
Fluid-Structure Interaction Approaches on Fixed Grids Based on Two Different Domain Decomposition Ideas
,”
Int. J. Comput. Fluid Dyn.
,
22
(
6
), pp.
411
427
. 1061-8562
22.
Irons
,
B.
, and
Tuck
,
R. C.
, 1969, “
A Version of the Aitken Accelerator for Computer Implementation
,”
Int. J. Numer. Methods Eng.
0029-5981,
1
, pp.
275
277
.
23.
MacLeod
,
A. J.
, 1986, “
Acceleration of Vector Sequences by Multi-Dimensional δ2 Methods
,”
Commun. Appl. Numer. Methods
,
2
, pp.
385
392
. 1061-8562
24.
Gerbeau
,
J. -F.
, and
Vidrascu
,
M.
, 2003, “
A Quasi-Newton Algorithm Based on a Reduced Model for Fluid-Structure Interaction Problems in Blood Flows
,”
Math. Modell. Numer. Anal.
0764-583X,
37
(
4
), pp.
631
647
.
25.
Calvo
,
F. J.
,
Margetts
,
L.
,
Gabaldón
,
F.
, and
Romero
,
I.
, 2007, “
Parallel Three Dimensional Analysis of a Lid Driven Cavity Coupled to a Flexible Moving Base
,”
Proceedings of Coupled Problems
, Ibiza, Spain, pp.
623
626
.
26.
Hafez
,
M.
,
Parlette
,
E.
, and
Salas
,
M.
, 1986, “
Convergence Acceleration of Iterative Solutions of Euler Equations for Transonic Flow Computations
,”
Comput. Mech.
,
1
(
3
), pp.
165
176
. 1061-8562
27.
Brezinski
,
C.
, and
Zaglia
,
M. R.
, 1991,
Extrapolation Methods: Theory and Practice
(
Studies in Computational Mathematics 2
),
North-Holland
,
Amsterdam
.
28.
Saad
,
Y.
, and
Schultz
,
M. H.
, 1986, “
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
,”
SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
0196-5204,
7
(
3
), pp.
856
869
.
29.
Jbilou
,
K.
, and
Sadok
,
H.
, 1999, “
LU Implementation of the Modified Minimal Polynomial Extrapolation Method for Solving Linear and Nonlinear Systems
,”
IMA J. Numer. Anal.
,
19
(
4
), pp.
549
561
. 0272-4979
30.
Knoll
,
D. A.
, and
Keyes
,
D. E.
, 2004, “
Jacobian-Free Newton–Krylov Methods: A Survey of Approaches and Applications
,”
J. Comput. Phys.
0021-9991,
193
, pp.
357
397
.
31.
Gerbeau
,
J. -F.
,
Vidrascu
,
M.
, and
Frey
,
P.
, 2005, “
Fluid-Structure Interaction in Blood Flows on Geometries Coming From Medical Imaging
,”
Comput. Struct.
0045-7949,
83
, pp.
155
165
.
32.
Fernández
,
M.
, and
Moubachir
,
M.
, 2005, “
A Newton Method Using Exact Jacobians for Solving Fluid-Structure Coupling
,”
Comput. Struct.
0045-7949,
83
(
2–3
), pp.
127
142
.
33.
Michler
,
C.
,
van Brummelen
,
E. H.
, and
de Borst
,
R.
, 2006, “
Error-Amplification Analysis of Subiteration-Preconditioned GMRES for Fluid-Structure Interaction
,”
Comput. Methods Appl. Mech. Eng.
,
195
, pp.
2124
2148
. 0045-7825
34.
Vierendeels
,
J.
, 2006, “
Implicit Coupling of Partitioned Fluid-Structure Interaction Solvers Using Reduced-Order Models
,”
Fluid-Structure Interaction: Modelling, Simulation, Optimisation
(
LNCSE
), Vol.
53
,
Springer
,
New York
, pp.
1
18
.
35.
Wall
,
W. A.
, 1999, “
Fluid-Struktur-Interaktion mit Stabilisierten Finiten Elementen
,” Ph.D. thesis, Institut für Baustatik, Universität Stuttgart, Stuttgart.
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