A perturbation finite element method for modeling moving conductive and magnetic regions without remeshing

To develop a sub‐domain perturbation technique for efficiently modeling moving systems in magnetodynamics with a magnetic field h‐conform finite element (FE) formulation.

A reference problem is first solved in a global mesh excluding some moving regions and thus avoiding the inclusion of their meshes. Its solution gives the sources for a sequence of perturbation problems with the supplementary moving magnetic and conductive regions. Each of these sub‐problems requires an appropriate proper volume mesh of the associated moving region and its surrounding region, with no need of interconnection. The solutions are transferred from one problem to the other through projections of source fields between meshes.

The consideration of sub‐problems and associated sources, in a sequence of perturbation problems, leads to a significant speed‐up of the repetitive solutions in analyses of moving systems. A free movement in any direction can be considered with no need of remeshing.

When working with the perturbation fields, the volume sources can be limited to the moving regions, what allows for homogeneous perturbation boundary conditions and reduces the computational efforts for projecting and evaluating the sources. The curl‐conformity of the unknown magnetic field is preserved during the whole process thanks to the use of edge FEs for both the magnetic field and the intermediate source quantities. The sub‐problem approach also gives an easy way to directly express the time derivatives in moving frames.