Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows

Manguoğlu, Murat; Sameh, Ahmed; Saied, Faisal; Tezduyar, Tayfun E.; Sathe, Sunil

doi:10.1115/1.3059576

Cited by 45 publications

(18 citation statements)

References 46 publications

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“…A recent demonstration of this potential can be found in [53,57,58,64]. Segregated equation solver techniques recently developed by the T AFSM for FSI computations were described in Section 6 of [52].…”

Section: Segregated Equation Solversmentioning

confidence: 98%

Space–time fluid–structure interaction modeling of patient‐specific cerebral aneurysms

Tezduyar

Takizawa

Brummer

et al. 2011

Numer Methods Biomed Eng

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SUMMARYWe provide an extensive overview of the core and special techniques developed earlier by the Team for Advanced Flow Simulation and Modeling (T AFSM) for space-time fluid-structure interaction (FSI) modeling of patient-specific cerebral aneurysms. The core FSI techniques are the Deforming-SpatialDomain/Stabilized Space-Time (DSD/SST) formulation and the stabilized space-time FSI (SSTFSI) technique. The special techniques include techniques for calculating an estimated zero-pressure (EZP) arterial geometry, a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, techniques for using variable arterial wall thickness, mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, a recipe for pre-FSI computations that improve the convergence of the FSI computations, the Sequentially-Coupled Arterial FSI (SCAFSI) technique and its multiscale versions, techniques for the projection of fluid-structure interface stresses, calculation of the wall shear stress (WSS) and calculation of the oscillatory shear index (OSI) and arterial-surface extraction and boundary condition techniques. We show how these techniques work with results from earlier computations. We also describe the arterial FSI techniques developed and implemented recently by the T AFSM and present a sample from a wide set of patient-specific cerebral-aneurysm models we computed recently.

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Section: Segregated Equation Solversmentioning

confidence: 98%

Space–time fluid–structure interaction modeling of patient‐specific cerebral aneurysms

Tezduyar

Takizawa

Brummer

et al. 2011

Numer Methods Biomed Eng

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“…But there are also other techniques to solve nonsymmetric systems of linear equations as the generalized minimal residual method (GMRES in Saad and Schultz, 1986), multigrid approaches (see Wesseling and Sonneveld, 1980;Trottenberg et al, 2001), the induced dimension reduction (IDR) method (Sonneveld and van Gijzen, 2008;van Gijzen and Sonneveld, 2011) or a combination of IDR and BiCGstab called IDRstab (Sleijpen and van Gijzen, 2010). In line with replacing the solver is the use of a more appropriate preconditioner for matrix inversion for incompressible fluid dynamics (see Manguoglu et al, 2009). Another option is to combine the applied solver with some correction algorithm that improves the convergence rate.…”

Section: Discussionmentioning

confidence: 99%

Improved convergence and stability properties in a three-dimensional higher-order ice sheet model

et al. 2011

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Abstract. We present a finite difference implementation of a three-dimensional higher-order ice sheet model. In comparison to a conventional centred difference discretisation it enhances both numerical stability and convergence. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, a centred difference discretisation that operates exclusively on the regular grid serves as a reference. The reprise of the ISMIP-HOM experiments indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This setup allows a direct comparison of the two numerical implementations also with respect to their convergence behaviour. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the accuracy for the resultant velocity field can be chosen higher in the novel finite difference implementation. Changing the discretisation also prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation.The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher accuracy and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented.

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“…Figure 5 depicts our nested scheme [55,59,60]. In Section 5 we present a new parallel sparse solver for handling the (1, 1) block of Equation (4).…”

Section: Solution Of the Linear Systemsmentioning

confidence: 99%

Nested and parallel sparse algorithms for arterial fluid mechanics computations with boundary layer mesh refinement

Manguoğlu

Takizawa

Sameh

et al. 2010

Numerical Methods in Fluids

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SUMMARYArterial fluid-structure interaction (FSI) computations involve a number of numerical challenges. Because blood flow is incompressible, iterative solution of the fluid mechanics part of the linear equation system at every nonlinear iteration of each time step is one of those challenges, especially for computations over slender domains and in the presence of boundary layer mesh refinement. In this paper we address that challenge. As test cases, we use equation systems from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm, with thin layers of elements near the arterial wall. We show how the preconditioning techniques, we propose for solving these large sparse nonsymmetric systems, perform at different time steps of the computation over a cardiac cycle. We also present a new hybrid parallel sparse linear system solver 'DD-Spike' and demonstrate its scalability.

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Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows

Cited by 45 publications

References 46 publications

Space–time fluid–structure interaction modeling of patient‐specific cerebral aneurysms

Space–time fluid–structure interaction modeling of patient‐specific cerebral aneurysms

Improved convergence and stability properties in a three-dimensional higher-order ice sheet model

Nested and parallel sparse algorithms for arterial fluid mechanics computations with boundary layer mesh refinement

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