Computing Forces by ECSW-Hyperreduction in Nonlinear Magnetodynamic FEM Problems

This contribution proposes a novel strategy to apply the hyperreduction principle for the mechanical force calculation of non-linear magnetodynamic problems in an FEM context. The already established energy-conserving sampling and weighting (ECSW) method is therefore adapted to exploit the structure of mechatronic systems, so the hyperreduction is only applied to the non-linear domain. It is consequently named partial hyperreduction, here the pECSW. Also, the force calculation is formulated such that ECSW is applied as sampling-based integration. The force computation requires a new element sampling and weighting process, here called cECSW, arising from the configurational updates of the geometry corresponding with the possible motions of the mobile part. The advantage is the possibility of avoiding treating the full-order model for the force calculation. Storing the reduced order model with two element sets for field and force calculation is sufficient. The strategy is demonstrated on the TEAM20 problem of the Compumag benchmark systems, which is extended to dynamic excitation. The new methods show the ability to produce accurate results for significantly smaller systems.