  In this paper, we propose a globally hyperbolic regularization to the general
Grad's moment system in multi-dimensional spaces. Systems with moments up to an
arbitrary order are studied. The characteristic speeds of the regularized
moment system can be analytically given and only depend on the macroscopic
velocity and the temperature. The structure of the eigenvalues and eigenvectors
of the coefficient matrix is fully clarified. The regularization together with
the properties of the resulting moment systems is consistent with the simple
one-dimensional case discussed in [1]. Besides, all characteristic waves are
proven to be genuinely nonlinear or linearly degenerate, and the studies on the
properties of rarefaction waves, contact discontinuities and shock waves are
included.
