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

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J. D. Nshimiyimana
F. Plumier
C. Ndagije
J. Gyselinck
C. Geuzain


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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Nshimiyimana, J. D., Plumier, F., Ndagije, C., Gyselinck, J., & Geuzain, C. (2020). High Order Relaxation Methods for Co-simulation of Finite Element and Circuit Solvers. Advanced Electromagnetics, 9(1), 49–58. https://doi.org/10.7716/aem.v9i1.1245
Research Articles


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