Parallel overlapping Schwarz preconditioners are considered and applied to the structural block in monolithic fluid-structure interaction (FSI). The two-level overlapping Schwarz method uses a coarse level based on energy minimizing functions. Linear elastic as well as nonlinear, anisotropic hyperelastic structural models are considered in an FSI problem of a pressure wave in a tube. Using our recent parallel implementation of a two-level overlapping Schwarz preconditioner based on the Trilinos library, the total computation time of our FSI benchmark problem was reduced by more than a factor of two compared to the algebraic one-level overlapping Schwarz method used previously. Finally, also strong scalability for our FSI problem is shown for up to 512 processor cores.
- Coarse Level
- Arbitrary Lagrangian Eulerian
- Coarse Space
- Inexact Newton Method
- GMRES Iteration
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D. Balzani, P. Neff, J. Schröder, G.A. Holzapfel, A polyconvex framework for soft biological tissues. Adjustment to experimental data. Internat. J. Solids Struct. 43 (20), 6052–6070 (2006)
D. Brands, A. Klawonn, O. Rheinbach, J. Schröder, Modelling and convergence in arterial wall simulations using a parallel FETI solution strategy. Comput. Methods Biomech. Biomed. Eng. 11, 569–583 (2008)
D. Balzani, S. Deparis, S. Fausten, D. Forti, A. Heinlein, A. Klawonn, A. Quarteroni, O. Rheinbach, and J. Schröder, Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains. Int. J. Numer. Methods Biomed. Eng. (2015). http://dx.doi.org/10.1002/cnm.2756
S. Deparis, D. Forti, G. Grandperrin, A. Quarteroni, FaCSI: a block parallel preconditioner for fluid-structure interaction in hemodynamics. Technical report 13, 2015
C.R. Dohrmann, A. Klawonn, O.B. Widlund, Domain decomposition for less regular subdomains: overlapping Schwarz in two dimensions. SIAM J. Numer. Anal. 46 (4), 2153–2168 (2008)
L. Formaggia, A. Quarteroni, A. Veneziani, Cardiovascular Mathematics, vol. 1 (Springer, Milan/New York, 2009)
A. Heinlein, A. Klawonn, O. Rheinbach, Parallel overlapping Schwarz with an energy-minimizing coarse space, 2015, in To be Submitted to the Proceedings of the 23rd International Conference on Domain Decomposition Methods. Lecture Notes in Computational Science and Engineering, TUBAF Preprint 17/2015: http://tu-freiberg.de/fakult1/forschung/preprints
M.A. Heroux, R.A. Bartlett, V.E. Howle, R.J. Hoekstra, J.J. Hu, T.G. Kolda, R.B. Lehoucq, K.R. Long, R.P. Pawlowski, E.T. Phipps, A.G. Salinger, H.K. Thornquist, R.S. Tuminaro, J.M. Willenbring, A. Williams, K.S. Stanley, An overview of the Trilinos project. ACM Trans. Math. Softw. 31 (3), 397–423 (2005)
The authors gratefully acknowledge the Gauss Centre for Supercomputing (GCS) for providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS share of the supercomputer JUQUEEN at Jülich Supercomputing Centre (JSC). The authors also gratefully acknowledge the Cray XT6m at Universität Duisburg-Essen and the financial support by the German Science Foundation (DFG), project no. KL2094/3-1 and RH122/4-1.
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Heinlein, A., Klawonn, A., Rheinbach, O. (2016). Parallel Two-Level Overlapping Schwarz Methods in Fluid-Structure Interaction. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_50
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