Energetic Galerkin Projection of Electromagnetic Fields Between Different Meshes

Mesh-to-mesh field transfer arises frequently in finite-element computations. Typical applications may concern remeshing, multigrid methods, domain decomposition, and multi-physics problems. For electromagnetic fields, one of the essential constraints in such transfers is to conserve energetic quantities such as magnetic energy and joule heating. Within the framework of Galerkin projection on overlapping domains, we introduce the definition of energetic norms for electromagnetic fields. The corresponding formulations we propose provide energy-conserving projection of electromagnetic fields between different meshes.