A multi-vector interface quasi-Newton method with linear complexity for partitioned fluid–structure interaction

Spenke, Thomas; Hosters, Norbert; Behr, Marek

doi:10.1016/j.cma.2019.112810

Cited by 30 publications

(37 citation statements)

References 30 publications

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“…27 Since then, it has been widely used and become a standard technique to handle moving domains in fluid-structure interaction (FSI) simulations. [28][29][30] More recent FSI simulations relying on this approach are presented in the work of Spenke et al, 31 La Spina et al, 32 and Liu et al 33 Furthermore, EMUM has been used in the context of free-surface flows 34 and to update finite element meshes according to prescribed boundary displacements. 35 The four-dimensional extension of EMUM (4DEMUM) presented in Section 3 allows us to obtain boundary-conforming pentatope meshes of complex geometries.…”

Section: F I G U R Ementioning

confidence: 99%

Four‐dimensional elastically deformed simplex space‐time meshes for domains with time‐variant topology

Danwitz

Antony

Key

et al. 2021

Numerical Methods in Fluids

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Considering the flow through biological or engineered valves as an example, there is a variety of applications in which the topology of a fluid domain changes over time. This topology change is characteristic for the physical behavior, but poses a particular challenge in computer simulations. A way to overcome this challenge is to consider the application‐specific space‐time geometry as a contiguous computational domain. In this work, we obtain a boundary‐conforming discretization of the space‐time domain with four‐dimensional simplex elements (pentatopes). To facilitate the construction of pentatope meshes for complex geometries, the widely used elastic mesh update method is extended to four‐dimensional meshes. In the resulting workflow, the topology change is elegantly included in the pentatope mesh and does not require any additional treatment during the simulation. The potential of simplex space‐time meshes for domains with time‐variant topology is demonstrated in a valve simulation, and a flow simulation inspired by a clamped artery.

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Section: F I G U R Ementioning

confidence: 99%

Four‐dimensional elastically deformed simplex space‐time meshes for domains with time‐variant topology

Danwitz

Antony

Key

et al. 2021

Numerical Methods in Fluids

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“…Especially, simulations with a high number of degrees of freedom u on the fluid-structure interface favor a matrix-free method. Alternative, matrixfree implementations of the multi-vector approach have been proposed, but these reintroduce a reuse parameter [17,18]. The methods using the multi-vector approach are IQN-MVJ and MVQN.…”

Section: Multi-vector Approach To Reusementioning

confidence: 99%

Comparison of Different Quasi-Newton Techniques for Coupling of Black Box Solvers

Delaissé¹,

Demeester²,

Fauconnier³

et al. 2021

14th WCCM-ECCOMAS Congress

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Fluid-structure interaction (FSI) problems are frequently solved using partitioned simulation techniques with black-box solvers, reusing reliable and optimized codes. These problems can principally be reduced to solving a root-finding problem. In case of strong coupling, pure Gauss-Seidel iterations between the structure and flow solvers are unstable for lower modes. In these cases, quasi-Newton techniques are used, which construct an approximation of the Jacobian or its inverse by reusing information from previous iterations and time steps. Four different quasi-Newton techniques are compared: the interface quasi-Newton algorithm with an approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS), the interface block quasi-Newton algorithm with approximate Jacobians from least-squares models (IBQN-LS), the interface quasi-Newton technique with multiple vector Jacobian (IQN-MVJ) and the multi-vector update quasi-Newton technique (MVQN). These coupling algorithms are differentiated based on whether the approximation of the Jacobian is performed for the entire black-box system (IQN-ILS and IQN-MVJ) or for both individual solvers (IBQN-LS and MVQN). Moreover, a distinction is made between methods which perform the approximation with either least-squares models (IQN-ILS and IBQN-LS) or multivector techniques (IQN-MVJ and MVQN). Their performance is compared by solving a 1D flexible tube case, using the in-house coupling software CoCoNuT. Both the memory usage and number of iterations between structure and flow solvers in each time step are examined. The techniques using a multi-vector approach require explicit matrix construction, so that memory requirements scale quadratically, whereas the least-squares techniques have a matrix-free implementation, resulting in linear scaling. In terms of convergence they are comparable.

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“…The Jacobian approximation is successively improved by collecting information from the intermediate results of each coupling iteration. This way, IQN methods almost completely overcome the added-mass difficulty [1,2,3].…”

Section: Dirichlet-neumann Schemementioning

confidence: 99%

“…To handle the added-mass instability, which is expected to be strong because of the high density ratio ρ f /ρ s = 1.0, the structural deformation is updated via the IQN-IMVLS method [3]. The convergence criteria were chosen as ε Coupling = 10 −5 for the coupling and ε P roblem = 10 −10 for both fluid and structure.…”

Section: Example: Tank With Elastic Bottommentioning

confidence: 99%

“…Partitioned algorithms enjoy great popularity in the fluid-structure interaction (FSI) community: Treated as black boxes, the fluid and structural solvers are coupled only via the exchange of interface data. Over the last decade, the inherent drawbacks regarding stability were mitigated significantly, e.g., by interface quasi-Newton methods [1,2,3].…”

Section: Introductionmentioning

confidence: 99%

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Performance Impact of the Newton Iterations per Solver Call in Partitioned Fluid-Structure Interaction

Spenke¹,

Hosters²,

Behr³

2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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The cost of a partitioned fluid-structure interaction scheme is typically assessed by the number of coupling iterations required per time step, while ignoring the Newton loops within the nonlinear sub-solvers. In this work, we discuss why these singlefield iterations deserve more attention when evaluating the coupling's efficiency and how to find the optimal number of Newton steps per coupling iteration.

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A multi-vector interface quasi-Newton method with linear complexity for partitioned fluid–structure interaction

Cited by 30 publications

References 30 publications

Four‐dimensional elastically deformed simplex space‐time meshes for domains with time‐variant topology

Four‐dimensional elastically deformed simplex space‐time meshes for domains with time‐variant topology

Comparison of Different Quasi-Newton Techniques for Coupling of Black Box Solvers

Performance Impact of the Newton Iterations per Solver Call in Partitioned Fluid-Structure Interaction

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