This paper focuses on a comparison of the cosimulation schemes for coupled problems with application to coupled electromagnetic field and power-electronic simulations. A co-simulation framework between a finite element solver and a circuit solver based on the waveform relaxation scheme results in an iterative process whose convergence depends on the kind of transmission coupling conditions (TCC) on the interface between the sub-problems. The convergence of TCC is illustrated on two test cases: a boost converter and a switched reluctance motor drive.Index terms -co-simulation, optimized waveform relaxation, electrical converters, finite element

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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