On the convergence rate of dynamic iteration for coupled problems with multiple subsystems

Bartel, Andreas; Brunk, Markus; Schöps, Sebastian

doi:10.1016/j.cam.2013.07.031

Cited by 17 publications

(14 citation statements)

References 7 publications

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“…Later, in [27], [28] the convergence analysis was extended to specific structured systems of differential algebraic equations. In [29], [30] a more detailed convergence order analysis was given in terms of the coupling variables of the subsystems. Co-simulation techniques can often be efficiently applied to heterogeneously coupled systems such as the ones arising from field-circuit coupling.…”

Section: Related Workmentioning

confidence: 99%

“…These techniques allow to solve the systems separately and exchange information between them to connect their behaviour. Some algorithms, such as the waveform relaxation method [143], perform this information exchange iteratively and thus convergence to the coupled (monolithical) solution must be proven for ODEs and even specific structured DAEs [28], [30].…”

Section: Optimised Waveform Relaxationmentioning

confidence: 99%

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Mathematical Analysis and Simulation of Field Models in Accelerator Circuits

Garcia¹

2021

Springer Theses

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Section: Related Workmentioning

confidence: 99%

Section: Optimised Waveform Relaxationmentioning

confidence: 99%

Mathematical Analysis and Simulation of Field Models in Accelerator Circuits

Garcia¹

2021

Springer Theses

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“…3. The transfer function of the first-order circuit model is given as G CIR (s) = I con (s) U con (s) = 1 sL eq + R eq (12) and the PI current controller transfer function reads…”

Section: Pi Controller Design For a First Order Modelmentioning

confidence: 99%

Application of the waveform relaxation technique to the co-simulation of power converter controller and electrical circuit models

Maciejewski

Garcia

Schöps

et al. 2017

2017 22nd International Conference on Methods and Models in Automation and Robotics (MMAR)

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In this paper we present the co-simulation of a PID class power converter controller and an electrical circuit by means of the waveform relaxation technique. The simulation of the controller model is characterized by a fixed-time stepping scheme reflecting its digital implementation, whereas a circuit simulation usually employs an adaptive time stepping scheme in order to account for a wide range of time constants within the circuit model. In order to maintain the characteristic of both models as well as to facilitate model replacement, we treat them separately by means of input/output relations and propose an application of a waveform relaxation algorithm. Furthermore, the maximum and minimum number of iterations of the proposed algorithm are mathematically analyzed. The concept of controller/circuit coupling is illustrated by an example of the co-simulation of a PI power converter controller and a model of the main dipole circuit of the Large Hadron Collider.

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“…where C > 0 is a problem dependent constant and K is an iteration matrix whose eigenvalues are λ K = O(H The problem dependent parameter p f is given by the type of coupling, see [3]: (a) for a coupled system of r DAEs with only differential coupling p f = r/(r − 1), (b) for a DAE with no algebraic-to-algebraic coupling p f = 1 and (c) for a general DAE p f = 0. For eigenvalues λ K < 1 the arguments in [1,2] guarantee convergence; while this is obvious in the first two cases (a) and (b) for small window size H n < 1, the third case (c) exhibits an additional coupling constraint independent of H n .…”

Section: Relation Of Splitting and Time Integration Errorsmentioning

confidence: 99%

“…To analyze the dynamic iteration scheme, we study a linear DAE test case from [3], which is an extension of the classical Prothero-Robinson test equation:…”

Section: Examplementioning

confidence: 99%

An Optimal p‐Refinement Strategy for Dynamic Iteration of Ordinary and Differential Algebraic Equations

Schöps

Bartel

Günther

2013

Proc Appl Math and Mech

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Multiphysical simulation tasks are often numerically solved by dynamic iteration schemes. Usually, this demands the efficient and stable coupling of existing simulation software for the contributing physical subdomains or subsystem. Since the coupling is weakened by such a simulation strategy, iteration is needed to enhance the quality of the numerical approximation. By the means of error recursions, one obtains estimates for the approximation order and the reduction of error per iteration (convergence rate). It is know that the first iterations can be coarsely sampled (in time), but the last iterations need to be refined (h-refinement) to obtain the accuracy gain of latter iterations ('sweeps'). In this work we discuss an optimal choice of the approximation order p used in the time integration with respect to the iteration 'sweep' count. It is deduced from the analytical error recursion and yields a p-refinement strategy. Numerical experiments show that our estimates are sharp and give a precise prediction of the correct convergence.

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On the convergence rate of dynamic iteration for coupled problems with multiple subsystems

Cited by 17 publications

References 7 publications

Mathematical Analysis and Simulation of Field Models in Accelerator Circuits

Mathematical Analysis and Simulation of Field Models in Accelerator Circuits

Application of the waveform relaxation technique to the co-simulation of power converter controller and electrical circuit models

An Optimal p‐Refinement Strategy for Dynamic Iteration of Ordinary and Differential Algebraic Equations

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