Enhancing Quasi-Newton Acceleration for Fluid-Structure Interaction

Davis, Kyle; Schulte, Miriam; Uekérmann, Benjamin

doi:10.3390/mca27030040

Cited by 6 publications

(16 citation statements)

References 24 publications

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“…According to (6), f k+1 is the minimum of a one-dimensional function whose gradient is ⟨ g(x k ), s k ⟩/∥s k ∥. Due to the fact that this one-dimensional function also satisfies Condition 1, to estimate the numerator in (9), taking into account inequality (4), we obtain:…”

Section: Accelerating Properties Of Newton's Methods Under Conditions...mentioning

confidence: 99%

“…Numerous studies on the convergence rate of Newton methods and quasi-Newton methods in the extremum region have been conducted, and some of them are given in [1][2][3][4][5][6][7][8]. The results obtained in [9,10] refer to the convergence rate of quasi-Newton minimization methods under the assumption that the method operates in the extremum area of the function.…”

Section: Introductionmentioning

confidence: 99%

“…Based on Theorem 1, the convergence rate indicator for the gradient method ( 5), (6) with a choice of descent direction…”

mentioning

confidence: 99%

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Newtonian Property of Subgradient Method with Optimization of Metric Matrix Parameter Correction

Tovbis,

Krutikov,

Kazakovtsev

2024

Mathematics

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The work proves that under conditions of instability of the second derivatives of the function in the minimization region, the estimate of the convergence rate of Newton’s method is determined by the parameters of the irreducible part of the conditionality degree of the problem. These parameters represent the degree of difference between eigenvalues of the matrices of the second derivatives in the coordinate system, where this difference is minimal, and the resulting estimate of the convergence rate subsequently acts as a standard. The paper studies the convergence rate of the relaxation subgradient method (RSM) with optimization of the parameters of two-rank correction of metric matrices on smooth strongly convex functions with a Lipschitz gradient without assumptions about the existence of second derivatives of the function. The considered RSM is similar in structure to quasi-Newton minimization methods. Unlike the latter, its metric matrix is not an approximation of the inverse matrix of second derivatives but is adjusted in such a way that it enables one to find the descent direction that takes the method beyond a certain neighborhood of the current minimum as a result of one-dimensional minimization along it. This means that the metric matrix enables one to turn the current gradient into a direction that is gradient-consistent with the set of gradients of some neighborhood of the current minimum. Under broad assumptions on the parameters of transformations of metric matrices, an estimate of the convergence rate of the studied RSM and an estimate of its ability to exclude removable linear background are obtained. The obtained estimates turn out to be qualitatively similar to estimates for Newton’s method. In this case, the assumption of the existence of second derivatives of the function is not required. A computational experiment was carried out in which the quasi-Newton BFGS method and the subgradient method under study were compared on various types of smooth functions. The testing results indicate the effectiveness of the subgradient method in minimizing smooth functions with a high degree of conditionality of the problem and its ability to eliminate the linear background that worsens the convergence.

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Section: Accelerating Properties Of Newton's Methods Under Conditions...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Newtonian Property of Subgradient Method with Optimization of Metric Matrix Parameter Correction

Tovbis,

Krutikov,

Kazakovtsev

2024

Mathematics

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“…Initially, it relied only on input–output data pairs collected within the current time step. Follow‐up research revealed, however, that using past time step data is very advantageous, but also challenging: an explicit reutilization of data pairs may suffer from rank deficiency and the dependency on the number of reused time steps—although both effects can be alleviated by proper filtering techniques 14,15 . An implicit incorporation via an updated Jacobian avoids these issues, but typically brings along a costly explicit Jacobian 9,10 .…”

Section: Introductionmentioning

confidence: 99%

“…Follow-up research revealed, however, that using past time step data is very advantageous, but also challenging: an explicit reutilization of data pairs may suffer from rank deficiency and the dependency on the number of reused time steps-although both effects can be alleviated by proper filtering techniques. 14,15 An implicit incorporation via an updated Jacobian avoids these issues, but typically brings along a costly explicit Jacobian. 9,10 However, recent formulations circumventing this drawback were presented by Scheufele and Mehl 16 as well as Spenke et al.…”

Section: Introductionmentioning

confidence: 99%

A Robin‐Neumann scheme with quasi‐Newton acceleration for partitioned fluid‐structure interaction

Spenke

Make

Hosters

2022

Numerical Meth Engineering

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The Dirichlet-Neumann scheme is the most common partitioned algorithm for fluid-structure interaction (FSI) and offers high flexibility concerning the solvers employed for the two subproblems. Nevertheless, it is not without shortcomings: to begin with, the inherent added-mass effect often destabilizes the numerical solution severely. Moreover, the Dirichlet-Neumann scheme cannot be applied to FSI problems in which an incompressible fluid is fully enclosed by Dirichlet boundaries, as it is incapable of satisfying the volume constraint.In the last decade, interface quasi-Newton methods have proven to control the added-mass effect and substantially speed up convergence by adding a Newton-like update step to the Dirichlet-Neumann coupling. They are, however, without effect on the incompressibility dilemma. As an alternative, the Robin-Neumann scheme generalizes the fluid's boundary condition to a Robin condition by including the Cauchy stresses. While this modification in fact successfully tackles both drawbacks of the Dirichlet-Neumann approach, the price to be paid is a strong dependency on the Robin weighting parameter, with very limited a priori knowledge about good choices. This work proposes a strategy to merge these two ideas and benefit from their combined strengths. The resulting quasi-Newton-accelerated Robin-Neumann scheme is compared to both Robinand Dirichlet-Neumann variants. The numerical tests demonstrate that it does not only provide faster convergence, but also massively reduces the influence of the Robin parameter, mitigating the main drawback of the Robin-Neumann algorithm. K E Y W O R D Sinterface quasi-newton methods, partitioned fluid-structure interaction, Robin-Neumann scheme

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Numerical study on slamming characteristics of an elastic wedge based on a two-way coupled finite volume and modal superposition method

Han,

Li,

Guo

et al. 2024

Physics of Fluids

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In marine engineering, fluid–structure interaction (FSI) problems caused by wave impact are prevalent and often accompanied by violent free-surface changes. To accurately capture the free-surface and optimize the solution strategy for FSI problems, this study proposes a solver (overInterISODyMFoam) that combines isoAdvector and overset for refined free-surface capturing and a partitioned approach that couples finite volume and modal superposition (FVMS) based on the preCICE platform for solving FSI wave impact problems. The performance of solver and the FVMS method are verified by comparing them to the experimental results of a 20° wedge entering the water. The results indicated that the free-surface capturing method proposed can achieve a sharper interface than the Multidimensional Universal Limiter with Explicit Solution method and exhibits less numerical dissipation at the spray front. As a three-dimensional two-way coupled method, the calculations of FVMS method are in good agreement with the experimental results. The average error for the pressure and stress peaks is approximately 5.60% and 4.52%, respectively. The FVMS method shows better applicability than the two-dimensional (2D) one-way coupled method. Due to the ignored elasticity effect, the slamming pressure peak and stress peak calculated by the 2D one-way coupled method are approximately 4%–11% and 6%–23% higher than the experimental results, respectively.

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Enhancing Quasi-Newton Acceleration for Fluid-Structure Interaction

Cited by 6 publications

References 24 publications

Newtonian Property of Subgradient Method with Optimization of Metric Matrix Parameter Correction

Newtonian Property of Subgradient Method with Optimization of Metric Matrix Parameter Correction

A Robin‐Neumann scheme with quasi‐Newton acceleration for partitioned fluid‐structure interaction

Numerical study on slamming characteristics of an elastic wedge based on a two-way coupled finite volume and modal superposition method

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