  In magnetized plasmas of fusion devices the strong magnetic field leads to
highly anisotropic physics where solution scales along field lines are much
larger than perpendicular to it. Hence, regarding both accuracy and efficiency,
a numerical method should allow to address parallel and perpendicular
resolutions independently. In this work, we consider the eigenvalue problem of
a two-dimensional anisotropic wave equation with variable coefficients which is
a simplified model of linearized ideal magnetohydrodynamics. For this, we
propose to use a mesh that is aligned with the magnetic field and choose to
discretize the problem with a discontinuous Galerkin method which naturally
allows for non-conforming interfaces. First, we analyze the eigenvalue spectrum
of a constant coefficient anisotropic wave equation, and demonstrate that this
approach improves the accuracy by up to seven orders of magnitude, if compared
to a non-aligned method with the same number of degrees of freedom. In
particular, the results improve for eigenfunctions with high mode numbers. We
also apply the method to compute the eigenvalue spectrum of the associated
anisotropic wave equation with variable coefficients of flux surfaces of a
Stellarator configuration. We benchmark the results against a spectral code.
