Block Preconditioners for the Incompressible Stokes Problem

Rehman, M. ur; Vuik, C.; Segal, Guus

doi:10.1007/978-3-642-12535-5_99

Cited by 4 publications

(5 citation statements)

References 11 publications

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“…which follows closely the steps in the SIMPLER preconditioner [51,52]. Unlike utilizing SIMPLE-type methods as iterative solvers, above operations (Eqs.…”

Section: Adjoint Solution Methodsmentioning

confidence: 99%

Topology optimization of turbulent flows

Dilgen

Fuhrman

et al. 2018

Computer Methods in Applied Mechanics and Engineering

164

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“…which follows closely the steps in the SIMPLER preconditioner [51,52]. Unlike utilizing SIMPLE-type methods as iterative solvers, above operations (Eqs.…”

Section: Adjoint Solution Methodsmentioning

confidence: 99%

Topology optimization of turbulent flows

Dilgen

Fuhrman

et al. 2018

Computer Methods in Applied Mechanics and Engineering

164

View full text Add to dashboard Cite

show abstract

“…The novelty of this paper with respect to [14] consists in operating a static condensation on the interface fluid variables, and in using SIMPLE [19,48,49,21,22,51,52] to precondition the resulting reduced fluid matrix. In fact, we notice that according to the (further) factorization (20) of P F , the critical term is P (3) F which corresponds to a linearized Navier-Stokes problem with additional constraints.…”

Section: Preconditioning Strategymentioning

confidence: 99%

“…Then, by a proper matrix factorization we identify three blocktriangular matrices: the first matrix refers solely to the structural problem, the second one solely to the geometry and the last solely to the fluid. Special attention is paid to the fluid matrix whose saddle-point structure features the additional presence of two coupling blocks: after carrying out static condensation of the interface fluid variables, we use a SIMPLE preconditioner [19,48,49,21,22,51,52] on the reduced fluid matrix. Finally, on the approximate factorization, FaCSI is obtained by replacing the diagonal blocks referring to each physical subproblem by suitable parallel preconditioners, e.g, those based on domain decomposition or multigrid strategies.…”

Section: Introductionmentioning

confidence: 99%

FaCSI: A block parallel preconditioner for fluid–structure interaction in hemodynamics

Deparis

Forti

Grandperrin

et al. 2016

Journal of Computational Physics

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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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“…In contrast with Feng et al [Feng and Warren 2012], we define a discrete Stokes-wise biharmonic operator using a finitedifference solution [Greenspan and Schultz 1972]. Finally, preconditioners for incompressible Stokes problems [Segal et al 2010;ur Rehman et al 2010] could also improve the accuracy of numerical results.…”

Section: Subspace Coordinates In Contrast Withmentioning

confidence: 99%

Stokes coordinates

Savoye

2017

Proceedings of the 33rd Spring Conference on Computer Graphics

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Figure 1: Stokes Cage Coordinates. We compute our fluid-inspired Stokes Coordinates using an input undeformed model and its shapeaware cage (left-hand side). To obtain coordinates via vorticity transport, we derive the Stokes stream function using a compact secondorder approximation with center-differencing. Given a collection of deformed cage poses, we output a sequence of deforming poses using our Stokes Coordinates (middle). To showcase the usefulness of our technique, we produce cartoon-style non-rigid deformation for a performance capture mesh. The resulting non-isometric deformation is quite fluid-like thanks to the local volume-preserving property since non-isometric deformation can be encoded using our proposed coordinates (right-hand side).

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Block Preconditioners for the Incompressible Stokes Problem

Cited by 4 publications

References 11 publications

Topology optimization of turbulent flows

Topology optimization of turbulent flows

FaCSI: A block parallel preconditioner for fluid–structure interaction in hemodynamics

Stokes coordinates

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