Co-simulation of of finite element and circuit solvers using optimized waveform relaxation

Nshimiyimana, Jean de Dieu; Plumier, Frédéric; Dular, Patrick; Geuzaine, Christophe; Gyselinck, Johan

doi:10.1109/energycon.2016.7513958

Cited by 6 publications

(12 citation statements)

References 6 publications

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“…As was investigated before [1,2,3], the voltageimpedance transmission coupling conditions (VZ-TCCs) converge very fast than the current-voltage conditions (VI-TCCs). The current-voltage transmission coupling conditions can be improved by introducing more sophisticated optimized transmission coupling conditions (OTCCs).…”

Section: Introductionmentioning

confidence: 85%

High Order Relaxation Methods for Co-simulation of Finite Element and Circuit Solvers

Nshimiyimana

Plumier

Ndagije

et al. 2020

AEM

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Coupled problems result in very stiff problems whose char- acteristic parameters differ with several orders in magni- tude. For such complex problems, solving them monolithi- cally becomes prohibitive. Since nowadays there are op- timized solvers for particular problems, solving uncoupled problems becomes easy since each can be solved indepen- dently with its dedicated optimized tools. Therefore the co-simulation of the sub-problems solvers is encouraged. The design of the transmission coupling conditions between solvers plays a fundamental role. The current paper ap- plies the waveform relaxation methods for co-simulation of the finite element and circuit solvers by also investigating the contribution of higher order integration methods. The method is illustrated on a coupled finite element inductor and a boost converter and focuses on the comparison of the transmission coupling conditions based on the waveform iteration numbers between the two sub-solvers. We demon- strate that for lightly coupled systems the dynamic iterations between the sub-solvers depends much on the inter- nal integrators in individual sub-solvers whereas for tightly coupled systems it depends also to the kind of transmission coupling conditions.

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Section: Introductionmentioning

confidence: 85%

High Order Relaxation Methods for Co-simulation of Finite Element and Circuit Solvers

Nshimiyimana

Plumier

Ndagije

et al. 2020

AEM

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“…For a detailed overview on optimised Schwarz methods and their history see [36], [37]. Later, the same techniques were also applied to systems arising from electric networks [38], [39] or even to field-circuit coupled systems [40].…”

Section: Related Workmentioning

confidence: 99%

“…In [138], these type of methods are used to optimise the convergence of a WR scheme for the one dimensional advection reaction diffusion equation. Other works, such as [38], [39], [145], [146], optimise the information exchange between circuit subsystems or even in field-circuit coupled problems (see [40]). In [144] t 1,1…”

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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“…Moreover, if the RC circuits in the field-circuit coupled problem is divided into multiple sub-circuits, then the results obtained in our manuscript can be directly implemented in them. Further, OWR methods are also applied for the coupled electromagnetic field and power-electronic simulations [7].…”

mentioning

confidence: 99%

Analysis of Overlap in Waveform Relaxation Methods for RC Circuits

Gander

Kumbhar

Ruehli

2018

Lecture Notes in Computational Science and Engineering

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Waveform relaxation (WR) methods are based on partitioning large circuits into sub-circuits which then are solved separately for multiple time steps in so called time windows, and an iteration is used to converge to the global circuit solution in each time window. Classical WR converges quite slowly, especially when long time windows are used. To overcome this issue, optimized WR (OWR) was introduced which is based on optimized transmission conditions that transfer information between the sub-circuits more efficiently than classical WR. We study here for the first time the influence of overlapping sub-circuits in both WR and OWR applied to RC circuits. We give a circuit interpretation of the new transmission conditions in OWR, and derive closed form asymptotic expressions for the circuit elements representing the optimization parameter in OWR. Our analysis shows that the parameter is quite different in the overlapping case, compared to the non-overlapping one. We then show numerically that our optimized choice performs well, also for cases not covered by our analysis. This paper provides a general methodology to derive optimized parameters and can be extended to other circuits or system of differential equations or space-time PDEs.

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Co-simulation of of finite element and circuit solvers using optimized waveform relaxation

Cited by 6 publications

References 6 publications

High Order Relaxation Methods for Co-simulation of Finite Element and Circuit Solvers

High Order Relaxation Methods for Co-simulation of Finite Element and Circuit Solvers

Mathematical Analysis and Simulation of Field Models in Accelerator Circuits

Analysis of Overlap in Waveform Relaxation Methods for RC Circuits

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