A Novel Mixed-Hybrid Formulation for Magnetostatics

Mixed-hybrid finite-element (MHFE) formulations for magnetostatic problems are appealing because - like the magnetic scalar potential (MSP) formulations - they yield to algebraic systems that can be effectively solved by black-box algebraic multigrid solvers. At the same time, the MHFE formulation is algebraically equivalent to the magnetic vector potential (MVP) formulation and therefore provides a conservative flux and superior accuracy. We introduce a novel mixed-hybrid (MH) formulation for magnetostatics which combines the best features of MSP and reduced MVP formulations. In particular, it avoids the explicit representation in the FE mesh of the shape of source current regions. Moreover, the new formulation - unlike the MHFE one - does not require the inversion of the local mass matrices, but still provides the same solution - on tetrahedral meshes and up to linear solver tolerance - of the corresponding MHFE formulation. Another advantage is that it can deal with very general polyhedral meshes, where div-conforming FE basis functions are not available.