  Computational magnetohydrodynamics (MHD) for space physics has become an
essential area in understanding the multiscale dynamics of geophysical and
astrophysical plasma processes, partially motivated by the lack of space data.
Full MHD simulations are typically very demanding and may require substantial
computational efforts. In particular, computational space-weather forecasting
is an essential long-term goal in this area, motivated for instance by the
needs of modern satellite communication technology. We present a new feature of
a recently developed compressible two- and three-dimensional MHD solver, which
has been successfully implemented into the parallel AMROC (Adaptive Mesh
Refinement in Object-oriented C++) framework with improvements concerning the
mesh adaptation criteria based on wavelet techniques. The developments are
related to computational efficiency while controlling the precision using
dynamically adapted meshes in space-time in a fully parallel context.
