  We propose an adaptive planewave method for eigenvalue problems in electronic
structure calculations. The method combines a priori convergence rates and
accurate a posteriori error estimates into an effective way of updating the
energy cut-off for planewave discretizations, for both linear and nonlinear
eigenvalue problems. The method is error controllable for linear eigenvalue
problems in the sense that for a given required accuracy, an energy cut-off for
which the solution matches the target accuracy can be reached efficiently.
Further, the method is particularly promising for nonlinear eigenvalue problems
in electronic structure calculations as it shall reduce the cost of early
iterations in self-consistent algorithms. We present some numerical experiments
for both linear and nonlinear eigenvalue problems. In particular, we provide
electronic structure calculations for some insulator and metallic systems
simulated with Kohn--Sham density functional theory (DFT) and the projector
augmented wave (PAW) method, illustrating the efficiency and potential of the
algorithm.
