Stabilized index-2 co-simulation approach for solver coupling with algebraic constraints

Schweizer, Bernhard; Lu, Daixing

doi:10.1007/s11044-014-9422-y

Cited by 28 publications

(21 citation statements)

References 27 publications

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“…For analyzing the numerical stability, Dahlquist's stability theory based on a linear test model has been applied and extended to co‐simulation approaches. In order to show the applicability of the presented co‐simulation approaches to nonlinear problems , we consider the planar double pendulum depicted in Fig. .…”

Section: Nonlinear Examplementioning

confidence: 99%

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Implicit co‐simulation methods: Stability and convergence analysis for solver coupling approaches with algebraic constraints

Schweizer¹,

Li²,

Lu³

2015

Z Angew Math Mech

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The analysis of the numerical stability of co‐simulation methods with algebraic constraints is subject of this manuscript. Three different implicit coupling schemes are investigated. The first method is based on the well‐known Baumgarte stabilization technique. Basis of the second coupling method is a weighted multiplier approach. Within the third method, a classical projection technique is applied. The three methods are discussed for different approximation orders. Concerning the decomposition of the overall system into subsystems, we consider all three possible approaches, i.e. force/force‐, force/displacement‐ and displacement/displacement‐decomposition. The stability analysis of co‐simulation methods with algebraic constraints is inherently related to the definition of a test model. Bearing in mind the stability definition for numerical time integration schemes, i.e. Dahlquist's stability theory based on the linear single‐mass oscillator, a linear two‐mass oscillator is used here for analyzing the stability of co‐simulation methods. The two‐mass co‐simulation test model may be regarded as two Dahlquist equations, coupled by an algebraic constraint equation. By discretizing the co‐simulation test model with a linear co‐simulation approach, a linear system of recurrence equations is obtained. The stability of the recurrence system, which reflects the stability of the underlying coupling method, can simply be determined by an eigenvalue analysis.

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Section: Nonlinear Examplementioning

confidence: 99%

“…by rigid joints). In this case, reaction forces/torques are used to describe the interaction between the subsystems . Secondly, the subsystems may be coupled by constitutive laws (i.e.…”

Section: Introductionmentioning

confidence: 99%

Implicit co‐simulation methods: Stability and convergence analysis for solver coupling approaches with algebraic constraints

Schweizer¹,

Li²,

Lu³

2015

Z Angew Math Mech

Self Cite

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“…[5]. A different coupling with algebraic constraints is presented, e.g., in [18], where a stabilized index-2 co-simulation is used and both subsystems are driven by constraint forces.…”

Section: Introductionmentioning

confidence: 99%

A new approach for force-displacement co-simulation using kinematic coupling constraints

Schneider

Burger

Arnold

et al. 2017

Z. Angew. Math. Mech.

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The separate numerical simulation of interacting subsystems, i.e. the co-simulation of subsystems, is widespread in advanced system simulation. Classically, mechanical subsystems are coupled by artificial stiffnesses, which often are unknown. In this paper, we present a coupling approach that uses no artificial stiffness, but a kinematic coupling constraint for the co-simulation of different subsystems. The algebraic constraint leads to corresponding constraint forces that only act in one direction of the coupling to avoid drift-off problems, while displacements are given in the opposite direction. Moreover, a strategy for an efficient computation of approximated constraint forces is provided. For the stability of the approach, we consider zero-stability as well as stability for finite time steps. Convergence is analyzed with a 2-mass spring-damper model, where the analytical solution is known. As application, we use our approach to simulate the more complex problem of a cable model, that is embedded in a multibody system.

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“…Refs. . In order to calculate the algebraic constraint equations on acceleration level, either the Lagrange multipliers – which can be interpreted as reaction forces – or the accelerations have to be transferred between the subsystems, see .…”

Section: Introductionmentioning

confidence: 99%

“…Refs. [5,16,20,24,31]. In order to calculate the algebraic constraint equations on acceleration level, either the Lagrange multipliers -which can be interpreted as reaction forces -or the accelerations have to be transferred between the subsystems, see [24].On the other hand the co-simulation methods differ in the sequence of time integration and data interchange, e.g.…”

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confidence: 99%

Continuous approximation techniques for co‐simulation methods: Analysis of numerical stability and local error

Busch

2016

Z Angew Math Mech

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Coupling multiphysical systems by means of a co-simulation, the data between the subsystems are interchanged at a discrete macro time grid, also denoted as communication time grid. Between the communication points the coupling variables are approximated so that the numerical solvers in the subsystems can calculate the differential equations. Classical approximation techniques based on extrapolation entail a discontinuity in the equations in each macro time step which can slow down the numerical time integration. In the paper at hand a C 0 -continuous technique for approximating the coupling variables is reconsidered and the numerical stability and the local error of the method are compared to the classical Lagrange approximation approach. Further, the method is enhanced to a C 1 -continuous (continuous and differentiable) approximation technique. Both methods are investigated in combination with different numerical coupling approaches (sequential Gauss-Seidel scheme, parallel Jacobi scheme, force/displacement coupling, displacement/displacement coupling) which are commonly applied for co-simulation in technical applications. It is shown that the C 1 -continuous approximation technique yields a similar numerical stability and a similar local error as the Lagrange approach which results in a comparable or even better overall performance (taking into account the advantage of continuity at the numerical calculation of the subsystem differential equations). Applying the C 0 -continuous approach, a similar numerical stability is obtained. However, the order of the local error is significantly lower than for the C 1 -continuous method and the Lagrange approach.

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Stabilized index-2 co-simulation approach for solver coupling with algebraic constraints

Cited by 28 publications

References 27 publications

Implicit co‐simulation methods: Stability and convergence analysis for solver coupling approaches with algebraic constraints

Implicit co‐simulation methods: Stability and convergence analysis for solver coupling approaches with algebraic constraints

A new approach for force-displacement co-simulation using kinematic coupling constraints

Continuous approximation techniques for co‐simulation methods: Analysis of numerical stability and local error

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