FaCSI: A block parallel preconditioner for fluid–structure interaction in hemodynamics. Modeling Fluid–Structure Interaction (FSI) in the vascular system is mandatory to reliably compute mechanical indicators in vessels undergoing large deformations. In order to cope with the computational complexity of the coupled 3D FSI problem after discretizations in space and time, a parallel solution is often mandatory. In this paper we propose a new block parallel preconditioner for the coupled linearized FSI system obtained after space and time discretization. We name it FaCSI to indicate that it exploits the Factorized form of the linearized FSI matrix, the use of static Condensation to formally eliminate the interface degrees of freedom of the fluid equations, and the use of a SIMPLE preconditioner for saddle-point problems. FaCSI is built upon a block Gauss–Seidel factorization of the FSI Jacobian matrix and it uses ad-hoc preconditioners for each physical component of the coupled problem, namely the fluid, the structure and the geometry. In the fluid subproblem, after operating static condensation of the interface fluid variables, we use a SIMPLE preconditioner on the reduced fluid matrix. Moreover, to efficiently deal with a large number of processes, FaCSI exploits efficient single field preconditioners, e.g., based on domain decomposition or the multigrid method. We measure the parallel performances of FaCSI on a benchmark cylindrical geometry and on a problem of physiological interest, namely the blood flow through a patient-specific femoropopliteal bypass. We analyze the dependence of the number of linear solver iterations on the cores count (scalability of the preconditioner) and on the mesh size (optimality).

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  1. Pozzi, Silvia; Redaelli, Alberto; Vergara, Christian; Votta, Emiliano; Zunino, Paolo: Mathematical modeling and numerical simulation of atherosclerotic plaque progression based on fluid-structure interaction (2021)
  2. Dede’, L.; Gerbi, A.; Quarteroni, A.: Segregated algorithms for the numerical simulation of cardiac electromechanics in the left human ventricle (2020)
  3. Failer, L.; Richter, T.: A parallel Newton multigrid framework for monolithic fluid-structure interactions (2020)
  4. Naseri, Alireza; Totounferoush, Amin; González, Ignacio; Mehl, Miriam; Pérez-Segarra, Carlos David: A scalable framework for the partitioned solution of fluid-structure interaction problems (2020)
  5. Garcia-Blanco, Emilio; Ortigosa, Rogelio; Gil, Antonio J.; Bonet, Javier: Towards an efficient computational strategy for electro-activation in cardiac mechanics (2019)
  6. Heinlein, Alexander; Hochmuth, Christian; Klawonn, Axel: Monolithic overlapping Schwarz domain decomposition methods with GDSW coarse spaces for incompressible fluid flow problems (2019)
  7. Pfister, Jean-Lou; Marquet, Olivier; Carini, Marco: Linear stability analysis of strongly coupled fluid-structure problems with the arbitrary-Lagrangian-Eulerian method (2019)
  8. Seo, Jongmin; Schiavazzi, Daniele E.; Marsden, Alison L.: Performance of preconditioned iterative linear solvers for cardiovascular simulations in rigid and deformable vessels (2019)
  9. Aulisa, Eugenio; Bnà, Simone; Bornia, Giorgio: A monolithic ALE Newton-Krylov solver with multigrid-Richardson-Schwarz preconditioning for incompressible fluid-structure interaction (2018)
  10. Forti, Davide; Bukac, Martina; Quaini, Annalisa; Canic, Suncica; Deparis, Simone: A monolithic approach to fluid-composite structure interaction (2017)
  11. Heinlein, Alexander; Klawonn, Axel; Rheinbach, Oliver: Parallel overlapping Schwarz with an energy-minimizing coarse space (2017)
  12. Quarteroni, A.; Manzoni, A.; Vergara, C.: The cardiovascular system: mathematical modelling, numerical algorithms and clinical applications (2017)
  13. Deparis, Simone; Forti, Davide; Gervasio, Paola; Quarteroni, Alfio: INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces (2016)
  14. Deparis, Simone; Forti, Davide; Grandperrin, Gwenol; Quarteroni, Alfio: Facsi: a block parallel preconditioner for fluid-structure interaction in hemodynamics (2016)
  15. Deparis, Simone; Forti, Davide; Quarteroni, Alfio: A fluid-structure interaction algorithm using radial basis function interpolation between non-conforming interfaces (2016)
  16. Heinlein, Alexander; Klawonn, Axel; Rheinbach, Oliver: Parallel two-level overlapping Schwarz methods in fluid-structure interaction (2016)
  17. Heinlein, Alexander; Klawonn, Axel; Rheinbach, Oliver: A parallel implementation of a two-level overlapping Schwarz method with energy-minimizing coarse space based on trilinos (2016)
  18. Quarteroni, A.; Veneziani, A.; Vergara, C.: Geometric multiscale modeling of the cardiovascular system, between theory and practice (2016)