  In this manuscript we present a novel and efficient numerical method for the
compressible viscous and resistive MHD equations for all Mach number regimes.
The time-integration strategy is a semi-implicit splitting, combined with a
hybrid finite-volume and finite-element (FE) discretization in space. The
non-linear convection is solved by a robust explicit FV scheme, while the
magneto-acoustic terms are treated implicitly in time. The resulting CFL
stability condition depends only on the fluid velocity, and not on the
Alfv\'enic and acoustic modes. The magneto-acoustic terms are discretized by
compatible FE based on a continuous and a discrete de Rham complexes designed
using Finite Element Exterior Calculus (FEEC). Thanks to the use of FEEC,
energy stability, magnetic-helicity conservation and the divergence-free
conditions can be preserved also at the discrete level. A very efficient
splitting approach is used to separate the acoustic and the Alfv\'enic modes in
such a fashion that the original symmetries of the PDE governing equations are
preserved. In this way, the algorithm relies on the solution of linear,
symmetric and positive-definite algebraic systems, that are very efficiently
handled by the simple matrix-free conjugate-gradient method. The resulting
algorithm showed to be robust and accurate in low and high Mach regimes even at
large Courant numbers. Non-trivial tests are solved in one-, two- and three-
space dimensions to confirm the robustness, accuracy, and the low-dissipative
and conserving properties of the final algorithm. While the formulation of the
method is very general, numerical results for a second-order accurate FV-FE
scheme will be presented.
