  We apply the compressive sensing lattice dynamics (CSLD) method to calculate
phonon dispersion for crystalline solids. While existing methods such as frozen
phonon, small displacement, and linear response are routinely applied for
phonon calculations, they are considerable more expensive or cumbersome to
apply to certain solids, including structures with large unit cells or low
symmetry, systems that require more expensive electronic structure treatment,
and polar semiconductors/insulators. In the latter case, we propose an approach
based on a corrected long-range force constant model with proper treatment of
the acoustic sum rule and the symmetric on-site force constant matrix. Our
approach is demonstrated to be accurate and efficient for these systems through
case studies of NaCl, CeO$_2$, Y$_3$Al$_5$O$_{12}$ and La$_2$Fe$_{14}$B.
