A hybrid interface preconditioner for monolithic fluid–structure interaction solvers

Mayr, Matthias; Noll, Maximilian; Gee, Michael W.

doi:10.1186/s40323-020-00150-9

Cited by 10 publications

(10 citation statements)

References 50 publications

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“…Putting the residual expressions r S , r G and r F from the solid, the ALE, and the fluid field as well as the kinematic constraint r kin together yields the monolithic nonlinear residual vector r FSI T = r S r G r F r kin T that needs to vanish in every time step. The nonlinearity is treated by a Newton-Krylov method with FSI-specific preconditioning as proposed by Gee et al [2] or Mayr et al [49]. After the assembly and the subsequent static condensation of the Lagrange multiplier and slave side interface degrees of freedom, the monolithic system of linear equations schematically reads…”

Section: The Monolithic Solution Methods For Fsimentioning

confidence: 99%

Adaptive time stepping for fluid-structure interaction solvers

Mayr

Wall

Gee

2018

Finite Elements in Analysis and Design

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A novel adaptive time stepping scheme for fluid-structure interaction (FSI) problems is proposed that allows for controlling the accuracy of the time-discrete solution. Furthermore, it eases practical computations by providing an efficient and very robust time step size selection. This has proven to be very useful, especially when addressing new physical problems, where no educated guess for an appropriate time step size is available. The fluid and the structure field, but also the fluid-structure interface are taken into account for the purpose of a posteriori error estimation, rendering it easy to implement and only adding negligible additional cost. The adaptive time stepping scheme is incorporated into a monolithic solution framework, but can straightforwardly be applied to partitioned solvers as well. The basic idea can be extended to the coupling of an arbitrary number of physical models. Accuracy and efficiency of the proposed method are studied in a variety of numerical examples ranging from academic benchmark tests to complex biomedical applications like the pulsatile blood flow through an abdominal aortic aneurysm. The demonstrated accuracy of the time-discrete solution in combination with reduced computational cost make this algorithm very appealing in all kinds of FSI applications.

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Section: The Monolithic Solution Methods For Fsimentioning

confidence: 99%

Adaptive time stepping for fluid-structure interaction solvers

Mayr

Wall

Gee

2018

Finite Elements in Analysis and Design

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“…One way of tackling this challenge consists in developing or applying sophisticated linear solvers and/or pre-conditioners capable of dealing with given large and poorly conditioned systems. This approach was followed by various researchers in the field of monolithic FSI [2][3][4][5][6][7]. In this case computational efficiency of the model is determined predominantly by the selected linear solver.…”

Section: Introductionmentioning

confidence: 99%

A Unified Arbitrary Lagrangian–Eulerian Model for Fluid–Structure Interaction Problems Involving Flows in Flexible Channels

2022

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In this work a finite element-based model for analyzing incompressible flows in flexible channels is presented. The model treats the fluid–solid interaction problem in a monolithic way, where the governing equations for both sub-domains are solved on a single moving grid taking advantage of an arbitrary Lagrangian/Eulerian framework (ALE). The unified implementation of the governing equations for both sub-domains is developed, where these are distinguished only in terms of the mesh-moving strategy and the constitutive equation coefficients. The unified formulation is derived considering a Newtonian incompressible fluid and a hypoelastic solid. Hypoelastic constitutive law is based on the strain rate and thus naturally facilitates employing velocity as a kinematic variable in the solid. Unifying the form of the governing equations and defining a semi-Lagrangian interface mesh-motion algorithm, one obtains the coupled problem formulated in terms of a unique kinematic variable. Resulting monolithic system is characterized by reduced variable heterogeneity resembling that of a single-media problem. The model used in conjunction with algebraic multigrid linear solver exhibits attractive convergence rates. The model is tested using a 2D and a 3D example.

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“…We propose a novel aggregation strategy for the discrete Lagrange multiplier unknowns along the contact interface, which we consider simpler to implement, computationally less expensive, and more intuitive for contact problems compared with the ideas from Reference 55. Inspired by our prior work on fluid–structure interaction, 64,65 where we have investigated the beneficial effect of satisfying interface constraints within the preconditioner, we will then use segregated transfer operators suitable for block matrices to transfer and incorporate the contact constraints in all coarse levels. We analyze various Schur complement block smoothers and assess their suitability for satisfying the contact constraints.…”

Section: Introductionmentioning

confidence: 99%

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

Wiesner¹,

Mayr

Popp

et al. 2021

Numerical Meth Engineering

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In this article, a fully aggregation-based algebraic multigrid strategy is developed for nonlinear contact problems of saddle point type using a mortar finite element approach. While the idea of extending multigrid methods to saddle point systems can already be found, for example, in the context of Stokes and Oseen equations in literature, the main contributions of this work are (i) the development and open-source implementation of an interface aggregation strategy specifically suited for generating Lagrange multiplier aggregates that are required for coupling structural equilibrium equations with contact constraints and (ii) a review of saddle point smoothers in the context of constrained interface problems. The new interface aggregation strategy perfectly fits into an aggregation-based multigrid framework and can easily be combined with segregated transfer operators, which allow to preserve the saddle point structure on the coarse levels. Further analysis provides insight into saddle point smoothers applied to contact problems, while numerical experiments illustrate the robustness of the new method.We have implemented the proposed algorithm within the MueLu package of the open-source Trilinos project. Numerical examples demonstrate the robustness of the proposed method in complex dynamic contact problems as well as its scalability up to 23.9 million unknowns on 480 MPI ranks.

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A hybrid interface preconditioner for monolithic fluid–structure interaction solvers

Cited by 10 publications

References 50 publications

Adaptive time stepping for fluid-structure interaction solvers

Adaptive time stepping for fluid-structure interaction solvers

A Unified Arbitrary Lagrangian–Eulerian Model for Fluid–Structure Interaction Problems Involving Flows in Flexible Channels

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

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