  In this paper, we develop a framework to construct energy-preserving methods
for multi-components Hamiltonian systems, combining the exponential integrator
and the partitioned averaged vector field method. This leads to numerical
schemes with both advantages of long-time stability and excellent behavior for
highly oscillatory or stiff problems. Compared to the existing
energy-preserving exponential integrators (EP-EI) in practical implementation,
our proposed methods are much efficient which can at least be computed by
subsystem instead of handling a nonlinear coupling system at a time. Moreover,
for most cases, such as the Klein-Gordon-Schr\"{o}dinger equations and the
Klein-Gordon-Zakharov equations considered in this paper, the computational
cost can be further reduced. Specifically, one part of the derived schemes is
totally explicit, and the other is linearly implicit. In addition, we present
rigorous proof of conserving the original energy of Hamiltonian systems, in
which an alternative technique is utilized so that no additional assumptions
are required, in contrast to the proof strategies used for the existing EP-EI.
Numerical experiments are provided to demonstrate the significant advantages in
accuracy, computational efficiency, and the ability to capture highly
oscillatory solutions.
