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 analyse 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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Abstract. We present new results on the Relaxed Dimensional Factorization (RDF) preconditioner for solving saddle point problems, first introduced in [5]. This method contains a parameter α > 0, to be chosen by the user. Previous works provided an estimate of α in the 2D case using Local Fourier Analysis. Novel algebraic estimation techniques for finding a suitable value of the RDF parameter in both the 2D and the 3D case with arbitrary geometries are proposed. These techniques are tested on a variety of discrete saddle point problems arising from the approximation of the Navier-Stokes equations using a Marker-and-Cell scheme and a finite element one. We also show results for a large-scale problem relevant for hemodynamics simulation that we solve in parallel using up to 8196 cores.

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