  A workflow is developed based on the ideal MHD model to investigate the
linear physics of various Alfv\'en eigenmodes in general axisymmetric toroidal
geometry, by solving the coupled shear Alfv\'en wave (SAW) and ion sound wave
(ISW) equations in ballooning space. The model equations are solved by the
FALCON code in the singular layer, and the corresponding solutions are then
taken as the boundary conditions for calculating parallel mode structures in
the whole ballooning space. As an application of the code, the frequencies and
mode structures of toroidal Alfv\'en eigenmode (TAE) are calculated in the
reference equilibria of the Divertor Tokamak Test facility (DTT) with positive
and negative triangularities, respectively. By properly handling the boundary
conditions, we demonstrate finite TAE damping due to coupling with the local
acoustic continuum, and find that the damping rate is small for typical plasma
parameters.
