  We extend the recently introduced explicit divergence-free DG scheme for
incompressible hydrodynamics [arXiv:1808.04669]. to the incompressible
magnetohydrodynamics (MHD). A globally divergence-free finite element space is
used for both the velocity and the magnetic field. Highlights of the scheme
includes global and local conservation properties, high-order accuracy,
energy-stability, pressure-robustness. When forward Euler time stepping is
used, we need two symmetric positive definite (SPD) hybrid-mixed Poisson
solvers (one for velocity and one for magnetic field) to advance the solution
to the next time level. Since we treat both viscosity in the momentum equation
and resistivity in the magnetic induction equation explicitly, the method shall
be best suited for inviscid or high-Reynolds number, low resistivity flows so
that the CFL constraint is not too restrictive.
