  For a class of fourth order gradient flow problems, integration of the scalar
auxiliary variable (SAV) time discretization with the penalty-free
discontinuous Galerkin (DG) spatial discretization leads to SAV-DG schemes.
These schemes are linear and shown unconditionally energy stable. But the
reduced linear systems are rather expensive to solve due to the dense
coefficient matrices. In this paper, we provide a procedure to pre-evaluate the
auxiliary variable in the piecewise polynomial space. As a result, the
computational complexity of $O(\mathcal{N}^2)$ reduces to $O(\mathcal{N})$ when
exploiting the conjugate gradient (CG) solver. This hybrid SAV-DG method is
more efficient and able to deliver satisfactory results of high accuracy. This
was also compared with solving the full augmented system of the SAV-DG schemes.
