  Numerical methods for the transmission eigenvalue problems are hot topics in
recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp.
71-88], we build a multigrid method to solve the problems. With our method, we
only need to solve a series of primal and dual eigenvalue problems on a coarse
mesh and the associated boundary value problems on the finer and finer meshes.
Theoretical analysis and numerical results show that our method is simple and
easy to implement and is efficient for computing real and complex transmission
eigenvalues.
