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

Coupled problems result in very stiff problems whose char- acteristic parameters differ with several orders in magni- tude. For such complex problems, solving them monolith- ically 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 applies the waveform relaxation methods for co-simulation of the finite element and circuit solvers, investigate the contribu- tion of higher order integration methods and also consid- ers the the theoretical modelling of a boost converter. 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 itera- tions 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.